Orthogonal Frequency Division Multiplexing for Wireless Networks

Transcription

1 Autonomous Transportation Agents for On-Scene Networked Incident Management Orthogonal Frequency Division Multiplexing for Wireless Networks Standard IEEE a UNIVERSITY OF CALIFORNIA SANTA BARBARA By ANÍBAL LUIS INTINI Graduate Student Electrical and Computer Engineering Department December, 2000

2 Contents 1. Introduction 1 2. The Standard IEEE a 5 3. Carrier Sense Multiple Access/Collision Avoidance Propagation Characteristics of mobile radio channels Attenuation Multipath Effects Rayleigh fading Frequency Selective Fading Delay Spread Doppler Shift OFDM General Structure Implementation Guard time and cyclic extension Windowing Forward Error Correction Coding Block Codes Interleaving Synchronization Synchronization Using Special Training Symbols Detection Coherent Detection Two-Dimensional Channel Estimators Simulation 36 Conclusion 38 Acknowledgements 39 References 39

3 Figures Figure 1. Concept of OFDM signal: orthogonal multicarrier technique...2 Figure 2. Spectra of (a) an OFDM subchannel and (b) and OFDM signal....3 Figure 3. 5-Ghz frequency spectrum allocation...7 Figure 4. IEEE a frame format for 5 GHz....8 Figure 5. IEEE a channel scheme...10 Figure 6. Typical Rayleigh fading while the Mobile Unit is moving (900 MHz)[11]...13 Figure 7. Multipath Delay Spread...15 Figure 8 OFDM modulator...17 Figure 9. Block diagram of an OFDM transceiver...19 Figure 10. OFDM frame with cyclic extension and windowing for (a) single...21 Figure 11. Convolutional encoder (k = 7)...22 Figure 12. BER of the (16,11,4) RM code and rate 2/3 memory 2 and Figure 13. Convolutional interleaver...26 Figure 14. Synchronization using the cyclic prefix...26 Figure 15. Received phasor, showing effect of noise on the received phase angle...28 Figure 16. OFDM training structure...30 Figure 17. Block diagram of an OFDM receiver with coherent detection...32 Figure 18. Pilot Sequence Generator...34 Figure 19. Pilot Frequency Allocation...34 Figure 20. Simulink OFDM Model...36 Figure 21. OFDM Signal Spectrum...37 Figure 22. Received constellation for a given amout of noise...38 Tables Table 1. Typical attenuation in a radio channel...12 Table 2. Cumulative distribution for Rayleigh distribution [11]...13 Table 3. Typical Delay Spread [11]...15 Table 4. Physical layer parameters Table 5. Physical layer parameters....20

4 ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING FOR WIRELESS NETWORKS Abstract. Orthogonal frequency division multiplexing (OFDM) is a special case of multicarrier transmission, where a single datastream is transmitted over a number of lower rate subcarriers. In July 1998, the IEEE standardization group decided to select OFDM as the basis for their new 5-GHz standard, targeting a range of data stream from 6 up to 54 Mbps. This new standard is the first one to use OFDM in packet-based communications, while the use of OFDM until now was limited to continuous transmission systems. In this project, transmitter and receiver were simulated according to the parameters established by the standard, to evaluate the performance and different possibilities in the implementation. Also, some considerations about forward error correction coding, synchronization and channel estimation are given oriented to improve the system performance. 1. Introduction OFDM is of great interest by researchers and research laboratories all over the world. It has already been accepted for the new wireless local area network standards IEEE a, High Performance LAN type 2 (HIPERLAN/2) and Mobile Multimedia Access Communication (MMAC) Systems. Also, it is expected to be used for wireless broadband multimedia communications. Data rate is really what broadband is about. The new standard specify bit rates of up to 54 Mbps. Such high rate imposes large bandwidth, thus pushing carriers for values higher than UHF band. For instance, IEEE802.11a has frequencies allocated in the 5- and 17- GHz bands. This project is oriented to the application of OFDM to the standard IEEE a, following the parameters established for that case. OFDM can be seen as either a modulation technique or a multiplexing technique. One of the main reasons to use OFDM is to increase the robustness against frequency selective fading or narrowband interference. In a single carrier system, a single fade or interferer can cause the entire link to fail, but in a multicarrier system, only a small percentage of the subcarriers will be affected. Error correction coding can then be used to correct for the few erroneous subcarriers. The concept of using parallel data transmission and frequency division multiplexing was published in the mid-1960s [1, 2]. Some early December, 2000 Page 1-40

5 development is traced back to the 1950s [3]. A U.S. patent was filed and issued in January 1970 [4]. In a classical parallel data system, the total signal frequency band is divided into N nonoverlapping frequency subchannels. Each subchannel is modulated with a separate symbol and then the N subchannels are frequency-multiplexed. It seems good to avoid spectral overlap of channels to eliminate interchannel interference. However, this leads to inefficient use of the available spectrum. To cope with the inefficiency, the ideas proposed from the mid-1960s were to use parallel data and FDM with overlapping subchannels, in which, each carrying a signaling rate b is spaced b apart in frequency to avoid the use of high-speed equalization and to combat impulsive noise and multipath distortion, as well as to fully use the available bandwidth. Figure 1. Concept of OFDM signal: orthogonal multicarrier technique versus conventional multicarrier technique Figure 1 illustrates the difference between the conventional nonoverlapping multicarrier technique and the overlapping multicarrier modulation technique. As shown in Figure 1, by using the overlapping multicarrier modulation technique, we save almost 50% of bandwidth. To realize the overlapping multicarrier technique, however we need to December, 2000 Page 2-40

6 reduce crosstalk between subcarriers, which means that we want orthogonality between the different modulated carriers. The word orthogonal indicates that there is a precise mathematical relationship between the frequencies of the carriers in the system. In a normal frequency-division multiplex system, many carriers are spaced apart in such a way that the signals can be received using conventional filters and demodulators. In such receivers, guard bands are introduced between the different carriers and in the frequency domain, which results in a lowering of spectrum efficiency. It is possible, however, to arrange the carriers in an OFDM signal so that the sidebands of the individual carriers overlap and the signals are still received without adjacent carrier interference. To do this, the carriers must be mathematically orthogonal. The receiver acts as a bank of demodulators, translating each carrier down to DC, with the resulting signal integrated over a symbol period to recover the raw data. If the other carriers all beat down the frequencies that, in the time domain, have a whole number of cycles in the symbol period T, then the integration process results in zero contribution from all these other carriers. Thus, the carriers are linearly independent (i.e., orthogonal) if the carrier spacing is a multiple of 1/T. (a) (b) Figure 2. Spectra of (a) an OFDM subchannel and (b) and OFDM signal. Much of the research focuses on the high efficient multicarrier transmission scheme based on "orthogonal frequency" carriers. In 1971, Weinstein and Ebert applied the discrete Fourier transform (DFT) to parallel data transmission systems as part of the modulation and demodulation process. Figure 2(a) shows the spectrum of the individual data of the subchannel. The OFDM signal, multiplexed in the individual spectra with a December, 2000 Page 3-40

7 frequency spacing b equal to the transmission speed of each subcarrier, is shown in Figure 1(b). Figure 2 shows that at the center frequency of each subcarrier, there is no crosstalk from other channels. Therefore, if we use DFT at the receiver and calculate correlation values with the center of frequency of each subcarrier, we recover the transmitted data with no crosstalk. In addition, using the DFT-based multicarrier technique, frequency-division multiplex is achieved not by bandpass filtering but by baseband processing. Moreover, to eliminate the banks of subcarrier oscillators and coherent demodulators required by frequency-division multiplex, completely digital implementations could be built around special-purpose hardware performing the fast Fourier transform (FFT), which is an efficient implementation of the DFT. Recent advances in very-large-scale integration (VLSI) technology make high-speed, large-size FFT chips commercially affordable. Using this method, both transmitter and receiver are implemented using efficient FFT techniques that reduce the number of operations from N 2 in DFT down to N log N. In the 1980s, OFDM was studied for high-speed modems, digital mobile communications, and high-density recording. One of the systems realized the OFDM techniques for multiplexed QAM using DFT, and by using pilot tone, stabilizing carrier and clock frequency control and implementing trellis coding are also implemented. Moreover, various-speed modems were developed for telephone networks. In the 1990s, OFDM was exploited for wideband data communications over mobile radio FM channels, high-bit-rate digital subscriber lines (HDSL; 1.6 Mbps), asymmetric digital subscriber lines (ADSL; up to 6 Mbps), very-high-speed digital subscriber lines (VDSL; 100 Mbps), digital audio broadcasting (DAB), and high-definition television (HDTV) terrestrial broadcasting. The OFDM transmission scheme has the following key advantages: Makes efficient use of the spectrum by allowing overlap By dividing the channel into narrowband flat fading subchannels, OFDM is more resistant to frequency selective fading than single carrier systems are. Eliminates ISI and IFI through use of a cyclic prefix. Using adequate channel coding and interleaving one can recover symbols lost due to the frequency selectivity of the channel. Channel equalization becomes simpler than by using adaptive equalization techniques with single carrier systems. It is possible to use maximum likelihood decoding with reasonable complexity, as discussed in OFDM is computationally efficient by using FFT techniques to implement the modulation and demodulation functions. December, 2000 Page 4-40

8 In conjunction with differential modulation there is no need to implement a channel estimator. Is less sensitive to sample timing offsets than single carrier systems are. Provides good protection against cochannel interference and impulsive parasitic noise. In terms of drawbacks OFDM has the following characteristics: The OFDM signal has a noise like amplitude with a very large dynamic range, therefore it requires RF power amplifiers with a high peak to average power ratio. It is more sensitive to carrier frequency offset and drift than single carrier systems are due to leakage of the DFT. 2. The Standard IEEE a The IEEE specification is a wireless LAN (WLAN) standard that defines a set of requirements for the physical layer (PHY) and a medium access control (MAC) layer. For high data rates, the standard provides two PHYs - IEEE b for 2.4-GHz operation and IEEE a for 5-GHz operation. The IEEE a standard is designed to serve applications that require data rates higher than 11 Mbps in the 5-GHz frequency band. The wireless medium on which the WLANs operate is different from wired media in many ways. One of those differences is the presence of interference in unlicensed frequency bands, which can impact communications between WLAN NICs. Interference on the wireless medium can result in packet loss, which causes the network to suffer in terms of throughput performance. Current 2.4-GHz b radios handle interference well because they support a feature in the MAC layer known as fragmentation. In fragmentation, data frames are broken into smaller frames in an attempt to increase the probability of delivering packets without errors induced by the interferer. When a frame is fragmented, the sequence control field in the MAC header indicates placement of the individual fragments and whether the current fragment is the last in the sequence. When frames are fragmented into request-to-send (RTS), clear-to-send (CTS), and acknowledge (ACK), control frames are used to manage the data transmission. Therefore, using fragmentation, designers can avoid interference problems in their WLAN designs. But interference is not the only problem for today's WLAN designers. Security issues are also a major concern. To solve potential security problems, the IEEE has December, 2000 Page 5-40

9 incorporated a MAC-level privacy mechanism within the specification, which protects the content of data frames going over a wireless medium from eavesdroppers. The mechanism, dubbed wired equivalent privacy (WEP), is an encryption engine that takes the contents of the entire data frame and passes them through an encryption algorithm. The encrypted data frames are transmitted with the WEP bit set in the frame control field of the MAC header. The received encrypted data frames are decrypted using the same encryption algorithm employed by the sending unit. The encryption algorithm used by is RC4. RC4 is a symmetric stream cipher developed by RSA Data Security, Inc. that supports variable key lengths up to 256 bits. The standard specifies a 40-bit key, but many compliant products shipping today support key lengths of up to 128 bits. In order for a mobile station to communicate with other mobile wireless NICs in a given service area, it must first locate those wireless NICs or access points. To enable communication between the mobile station and the NIC, active and passive scanning techniques are supported in the MAC. Passive scanning involves listening for traffic only on an network. Passive scanning allows a mobile wireless NIC to find an IEEE network while minimizing DC power consumption. In this mode, the wireless NIC listens for special frames called beacons and probe responses, while extracting information about the particular frequency channel. Although passive scanning expends minimal power, the cost is the time spent listening for a frame on a channel that is idle or may never occur. Active scanning, on the other hand, requires the scanning wireless NIC to transmit and receive responses from wireless NICs and access points. Active scanning allows the mobile wireless NIC to interact with another wireless NIC or access point. The standard does not specify a method for scanning. However, many WLAN OEMs support both methods and variants to differentiate their products in the market. When developing WLAN systems, choosing the right modulation and frequency band should be a priority in RF design, especially when designing IEEE a radios. For the past decade, WLAN systems have been designed to operate in the unlicensed 2.4- GHz frequency band. The 2.4-GHz band provides 83 MHz of total contiguous bandwidth, spanning from 2.4 to GHz. Moving to the 5-GHz band offers over three times the operating bandwidth over the available spectrum in the 2.4-GHz band. The 5-GHz band is also less susceptible to interference, unlike the 2.4-GHz unlicensed band, which shares spectrum with other wireless appliances such as Bluetooth devices. December, 2000 Page 6-40

10 There are, however, a few things to consider when switching to 5 GHz. The first is that the frequency allocation isn't contiguous across the band, and the transmit power levels are restricted depending on which block of frequency is occupied. Secondly, in order to achieve the same effective range as covered in the 2.4-GHz band, the transmit power of a 5-GHz system must be slightly increased. As a designer of 5-GHz radios, these issues must be carefully considered in product development. In the US, 300 MHz of bandwidth is allocated in the 5-GHz band to WLANs under the rules of the Unlicensed-National Information Infrastructure (U-NII). The bandwidth is fragmented into two blocks that are noncontiguous across the 5-GHz band. In Europe, only Hiperlan WLANs are allowed to operate in the 5-GHz frequency band. A total of 455 MHz of spectrum is allocated for Hiperlan radios. The frequency spectrum allocations for each of the geographic regions are shown in Figure 3. Figure 3. 5-Ghz frequency spectrum allocation It's important to point out that although the PHY specifications for IEEE a are similar to the Hiperlan2, radios compliant with the a specification are not allowed to operate in the 5-GHz band according to ETSI rules. Efforts are under way by IEEE 802 and ESTI together with the ITU-R to harmonize a global allocation of 5-GHz spectrum for WLANs. Global harmonization could occur by late When the IEEE began evaluating proposals for a, the working group adopted a joint proposal from NTT and Lucent that recommended orthogonal frequency December, 2000 Page 7-40

11 division multiplexing (OFDM) as the baseline technology for 5-GHz WLAN systems. OFDM was chosen because of its superior performance in combating fading multipath. This battle is extremely important, particularly in applications that transmit streaming video. During the development of the a specification, ESTI was charging ahead with a 5-GHz WLAN project called Hiperlan2. They too adopted OFDM. For the most part, the PHY for a is similar to Hiperlan2. The differences between the two standards are minimal and reside in the method by which convolution encoding is used to generate the OFDM symbols and data rates. But it has been said that by making the convolution encoder a programmable feature in the baseband processor, the same silicon can be used to support both standards. This is an extremely attractive feature for those who want to develop products for both standards. Unfortunately, the MAC layers are very different. In the U-NII band, eight carriers are spaced across 200 MHz in the lower spectrum ( GHz) and four carriers are spaced across 100 MHz in the upper spectrum ( GHz). The channels are spaced 20 MHz apart, which allows for high bit rates per channel. The channel scheme used for 5 GHz is illustrated in figure 4. Figure 4. IEEE a frame format for 5 GHz. As figure 2 illustrates, there are 52 subcarriers per channel in the 5-GHz band. Of these channels, only 48 carry actual data. The remaining four subcarriers are used as pilot tones, which assist in phase tracking for coherent demodulation. The duration of the guard interval is equal to 800 ns, which provides excellent performance on channels with delay spread of up to 250 ns. To efficiently use the spectrum provided in the 5-GHz range, designers of IEEE a systems use OFDM techniques. OFDM is a unique form of multicarrier modulation. The basic concept is to transmit high data rate information into December, 2000 Page 8-40

12 several interleaved, parallel bit streams and let each of these bit streams modulate a separate sub carrier. In this way, the channel spectrum is passed into a number of independent, non-selective frequency sub-channels for transmission between wireless NICs and access points. The OFDM modulation technique is generated through the use of complex signal processing approaches such as fast Fourier transforms (FFTs) and inverse FFTs in the transmitter and receiver sections of the radio. One of the benefits of OFDM is its strength in fighting the adverse effects of multipath propagation with respect to intersymbol interference in a channel. OFDM is also spectrally efficient because the channels are overlapped and contiguous. OFDM is well tested and has been adopted by a number of standards bodies for several applications, including a wired global standard for asymmetric digital subscriber line (ADSL) and for digital audio broadcasting (DAB) in the European market. To complement OFDM, the IEEE a specification also offers support for a variety of other modulation and coding alternatives. For example, the standard allows engineers to combine BPSK, QPSK, and 16-QAM modulations with convolution encoding (R = 1/2 and constraint length seven) to generate data rates of 6, 12, and 24 Mbps. All other combinations of encoding rates, including R = 2/3 and R = 3/4 combined with 64- QAM, are used to generate rates up to 54 Mbps, which are optional in the standard. During development of the a standard, the IEEE working group carefully optimized the PHY for traffic transmitting multimedia content such as streaming video. The packet date frame defined in the a specification consists of the PHY header, PHY layer convergence protocol (PLCP) and the payload (PSDU). This is similar to the structure used in the IEEE b specification. The first field of the PLCP header is called the preamble. The preamble consists of 12 symbols, which are used to synchronize the receiver. The second field is the signal field. The signal field is used to indicate the rate at which the OFDM symbols of the PSDU payload are transmitted. The PLCP header is always BPSK modulated and convolution encoded at R = 1/2. The PSDU packet payload is modulated and transmitted at the rate indicated in the signal field. This rate is variable from 6 up to 54 Mbps. The structure of the packet data frame is illustrated in figure 5. December, 2000 Page 9-40

13 Figure 5. IEEE a channel scheme 3. Carrier Sense Multiple Access/Collision Avoidance Since different physical transmission layers are supported by IEEE , the wireless MAC protocol should be transparency to physical layers, which include Direct Sequence Spread Spectrum (DSSS), Frequency Hopping Spread Spectrum (FHSS) diffused infrared and recently OFDM. Since spectrum is a scare resource above all different physical layers, the throughput and packet delay performance is one of the most critical considerations in the design of a wireless MAC protocol. The basic protocol level in the MAC protocol is the Distributed Coordination Function (DCF), which supports asynchronous communication between multiple users [5]. The DCF allows sharing medium between similar and dissimilar systems through the use of the CSMA/CA and a random back off delay algorithm. The CSMA/CA is similar to the Carrier Sense Multiple Access with Collision Detection (CSMA/CD) used in a Ethernet. As the Ethernet, the CSMA/CA uses carrier-sense mechanism to determine whether other terminals are using the medium. If a channel is sensed idle, the packet transmission is started immediately in both cases. However, if the channel is sensed busy, the CSMA/CA and the CSMA/CD operate differently to resolve the contention. In the case of the CSMA/CD, when a terminal senses a busy channel, it waits until the channel goes idle and then it transmits a packet with probability one. When two or more terminals are waiting to transmit, a collision is absolutely occurred because each terminal will transmit immediately at the end of channel busy period. While a terminal, operates in the CSMA/CA protocol, senses the busy channel, it waits until the channel goes idle and waits for delay period, which is called backoff delay. In the CSMA/CA, the collision probability between multiple terminals under above situation is reduced since a random backoff arrangement is used to resolve medium contention conflicts. The Collision Detection (CD) function detects collisions in the CSMA/CD, but the CD function is not viable in wireless LANs because the dynamic range of signals in the medium is very large. Thus, packet transmission errors are increased in wireless December, 2000 Page 10-40

14 communication environments. The IEEE MAC protocol supports coexisting asynchronous and time-bounded services using different priority levels with different Inter Frame Space (IFS) delay controls. Three kinds of IFS are used to support three backoff priorities such as a Short IFS (SIFS), a Point coordination function IFS (PIFS) and Distributed Coordination function IFS (DIFS); SIFS is the shortest IFS and is used for all immediate response actions which include ac-knowledgement (ACK) packet transmissions, Clear To Send (CTS) packet transmissions and contention-free response packet transmissions. PIFS is a middle length IFS and is used for terminal polling in time-bounded services. DIFS is the longest IFS and is used as a minimum delay for asynchronous transmission in the contention period. A random backoff algorithm of the IEEE MAC is similar to that of Ethernet.The slot time is the sum of transmitter turn-on time, medium propagation delay and medium busy detect response time. In wireless communication environments, packet transmission suffers from hidden terminal, so IEEE MAC protocol provides three alternative ways of packet transmission flow control [5]. First, actual data packet is only used for packet transmission which is called Basic CSMA/CA. Second, immediate positive acknowledgements are employed to confirm the successful reception of each packet. We call this scheme Stop-and-Wait (SW) CSMA/CA. The last is 4-Way Handshake (4-WH) CSMA/CA which use Request To Send (RTS) and Clear To Send (CTS) packets prior to the transmission of the actual data packet. The packet transmission flow of three kinds of CSMA/CA is summarized as follow 1. Basic CSMA/CA: Data Data - 2. SW CSMA/CA: Data - ACK - Data - ACK WH CSMA/CA: RTS - CTS - Data - ACK - 4. Propagation Characteristics of mobile radio channels In an ideal radio channel, the received signal would consist of only a single direct path signal, which would be a perfect reconstruction of the transmitted signal. However in a real channel, the signal is modified during transmission in the channel. The received signal consists of a combination of attenuated, reflected, refracted, and diffracted replicas of the transmitted signal. On top of all this, the channel adds noise to the signal and can cause a shift in the carrier frequency if the transmitter, or receiver is moving (Doppler effect). Understanding of these effects on the signal is important because the performance of a radio system is dependent on the radio channel characteristics. December, 2000 Page 11-40

15 4.1. Attenuation Attenuation is the drop in the signal power when transmitting from one point to another. It can be caused by the transmission path length, obstructions in the signal path, and multipath effects. Any objects, which obstruct the line of sight signal from the transmitter to the receiver, can cause attenuation. Shadowing of the signal can occur whenever there is an obstruction between the transmitter and receiver. It is generally caused by buildings and hills, and is the most important environmental attenuation factor. Shadowing is most severe in heavily built up areas, due to the shadowing from buildings. However, hills can cause a large problem due to the large shadow they produce. Radio signals diffract off the boundaries of obstructions, thus preventing total shadowing of the signals behind hills and buildings. However, the amount of diffraction is dependent on the radio frequency used, with low frequencies diffracting more then high frequency signals. Thus high frequency signals, especially, Ultra High Frequencies (UHF), and microwave signals require line of sight for adequate signal strength. To over come the problem of shadowing, transmitters are usually elevated as high as possible to minimise the number of obstructions. Typical amounts of variation in attenuation due to shadowing are shown in table 1. Description Typical Attenuation due to Shadowing Heavily built-up urban center 20dB variation from street to street Sub-urban area (fewer large buildings) 10dB greater signal power then built-up urban center Open rural area 20dB greater signal power then sub-urban areas Terrain irregularities and tree foliage 3-12dB signal power variation Table 1. Typical attenuation in a radio channel Shadowed areas tend to be large, resulting in the rate of change of the signal power being slow. For this reason, it is termed slow-fading, or log-normal shadowing Multipath Effects Rayleigh fading In a radio link, the RF signal from the transmitter may be reflected from objects such as hills, buildings, or vehicles. This gives rise to multiple transmission paths at the receiver. The relative phase of multiple reflected signals can cause constructive or destructive interference at the receiver. This is experienced over very short distances (typically at half wavelength distances), thus is given the term fast fading. These variations can vary from December, 2000 Page 12-40

16 10-30dB over a short distance. Figure 6 shows the level of attenuation that can occur due to the fading. Figure 6. Typical Rayleigh fading while the Mobile Unit is moving (900 MHz)[11] The Rayleigh distribution is commonly used to describe the statistical time varying nature of the received signal power. It describes the probability of the signal level being received due to fading. Table 2 shows the probability of the signal level for the Rayleigh distribution. Signal Level % Probability of Signal (db about median) Level being less than the value given Table 2. Cumulative distribution for Rayleigh distribution [11] Frequency Selective Fading In any radio transmission, the channel spectral response is not flat. It has dips or fades in the response due to reflections causing cancellation of certain frequencies at the receiver. Reflections off near-by objects (e.g. ground, buildings, trees, etc) can lead to multipath signals of similar signal power as the direct signal. This can result in deep nulls in the received signal power due to destructive interference. December, 2000 Page 13-40

17 For narrow bandwidth transmissions if the null in the frequency response occurs at the transmission frequency then the entire signal can be lost. This can be partly overcome in two ways. By transmitting a wide bandwidth signal or spread spectrum as CDMA, any dips in the spectrum only result in a small loss of signal power, rather than a complete loss. Another method is to split the transmission up into many small bandwidth carriers, as is done in a COFDM/OFDM transmission. The original signal is spread over a wide bandwidth thus, any nulls in the spectrum are unlikely to occur at all of the carrier frequencies. This will result in only some of the carriers being lost, rather then the entire signal. The information in the lost carriers can be recovered provided enough forward error corrections is sent Delay Spread The received radio signal from a transmitter consists of typically a direct signal, plus reflections of object such as buildings, mountings, and other structures. The reflected signals arrive at a later time than the direct signal because of the extra path length, giving rise to a slightly different arrival time of the transmitted pulse, thus spreading the received energy. Delay spread is the time spread between the arrival of the first and last multipath signal seen by the receiver. In a digital system, the delay spread can lead to inter-symbol interference. This is due to the delayed multipath signal overlapping with the following symbols. This can cause significant errors in high bit rate systems, especially when using time division multiplexing (TDMA). Figure 7 shows the effect of inter-symbol interference due to delay spread on the received signal. As the transmitted bit rate is increased the amount of intersymbol interference also increases. The effect starts to become very significant when the delay spread is greater then ~50% of the bit time. December, 2000 Page 14-40

18 Figure 7. Multipath Delay Spread Table 3 shows the typical delay spread that can occur in various environments. The maximum delay spread in an outdoor environment is approximately 20µsec, thus significant intersymbol interference can occur at bit rates as low as 25kbps. Environment or cause Delay Spread Maximum Path Length Difference Indoor (room) 40nsec - 12m - 60 m 200nsec Outdoor 1usec - 20usec 300m - 6km Table 3. Typical Delay Spread [11] Inter-symbol interference can be minimized in several ways. One method is to reduce the symbol rate by reducing the data rate for each channel (i.e. split the bandwidth into more channels using frequency division multiplexing). Another is to use a coding scheme, which is tolerant to intersymbol interference such as CDMA Doppler Shift When a wave source and a receiver are moving relative to one another the frequency of the received signal will not be the same as the source. When they are moving toward each other the frequency of the received signal is higher then the source, and when they are approaching each other the frequency decreases. This is called the Doppler effect. An December, 2000 Page 15-40

19 example of this is the change of pitch in a car s horn as it approaches then passes by. This effect becomes important when developing mobile radio systems. The amount the frequency changes due to the Doppler effect depends on the relative motion between the source and receiver and on the speed of propagation of the wave. The Doppler shift in frequency can be written: [10] f ± f0 where f is the change in frequency of the source seen at the receiver, f o is the frequency of the source, v is the speed difference between the source and transmitter, and c is the speed of light. For example: Let f o = 5.9 GHz, and v = 80km/hr = 22.22m/s (50 miles/hr aprox) then the Doppler shift will be: m / s f0 = 5.9x10 Hertz = 437Hz 8 3x10 m / s This shift of 437Hz in the carrier will generally not effect the transmission. However, Doppler shift can cause significant problems if the transmission technique is sensitive to carrier frequency offsets or the relative speed is higher, which is the case for OFDM. If we consider now a link between to cars moving in opposite directions, each one with a speed of 80 km/hr, the Doppler shift will be double. v c 5. OFDM 5.1. General Structure The basic principle of OFDM is to split a high-rate datastream into a number of lower rate streams that are transmitted simultaneously over a number of subcarriers. The relative amount of dispersion in time caused by multipath delay spread is decreased because the symbol duration increases for lower rate parallel subcarriers. The other problem to solve is the intersymbol interference, which is eliminated almost completely by introducing a guard time in every OFDM symbol. This means that in the guard time, the OFDM symbol is cyclically extended to avoid intercarrier interference. An OFDM signal is a sum of subcarriers that are individually modulated by using phase shift keying (PSK) or quadrature amplitude modulation (QAM). The symbol can be written as: December, 2000 Page 16-40

20 NS 1 2 s( t) = Re di+ N j S 2 exp( 2 NS i= 2 s( t) = 0, t < ts and t > ts + T where : N S is the number of subcarriers T is the symbol duration f c is the carrier frequency / π ( f c i )( t ts )), t T S t t S + T The equivalent complex baseband notation is given by: NS 1 2 s( t) = NS i= 2 d exp( j2 i+ NS / 2 π i ( t ts )) T t t s( t) = 0, t < ts and t > ts + T In this case, the real and imaginary parts correspond to the in-phase and quadrature parts of the OFDM signal. They have to be multiplied by a cosine and sine of the desired frequency to produce the final OFDM signal. Figure 8 shows the block diagram for the OFDM modulator. exp(-jπn S (t-t s )/T), t S S + T (1) QAM data Serial to Parallel... exp(-jπ(n S -2)(t-t s )/T) OFDM signal Figure 8 OFDM modulator The complex baseband OFDM signal defined the equation (1) is the inverse Fourier transform of N s QAM input symbols. The time discrete case is the inverse discrete Fourier transform. In practice, this transform can be implemented very efficiently by the inverse fast Fourier transform (IFFT). The IFFT drastically reduces the amount of calculations by exploiting the regularity of the operations in the IDFT. December, 2000 Page 17-40

21 5.2. Implementation In practice, the OFDM signal for the standard IEEE a is generated as follows: In the transmitter, binary input data is encoded by a rate ½ convolutional encoder. The rate can be increased to 2/3 and ¾. After interleaving, the binary values are converted to QAM values. Four pilot values are added each 48 data values, resulting in a total of 52 QAM values per OFDM symbol. The symbol is modulated onto 52 subcarriers by applying the Inverse Fast Fourier Transform (IFFT). The output is converted to serial and a cyclic extension is added to make the system robust to multipath propagation. Windowing is applied after to get a narrower output spectrum. Using an IQ modulator, the signal is converted to analog, which is upconverted to the 5 GHz band, amplified, and transmitted through the antenna. Basically, the receiver performs the reverse operations of the transmitter, with additional training tasks. In the first step, the receiver has to estimate frequency offset and symbol timing, using special training symbols in the preamble. After removing the cyclic extension, the signal can be applied to a Fast Fourier Transform to recover the 52 QAM values of all subcarriers. The training symbols and the pilot subcarriers are used to correct for the channel response as well as remaining phase drift. The QAM values are then demapped into binary values, and finally a Viterbi decoder decodes the information bits. Figure 9 shows the block diagram of an OFDM modem, including the transmitter and the receiver. The IFFT modulates a block of input QAM values onto a number of subcarriers. In the receiver, the subcarriers are demodulated by the FFT, which is the reverse operation of the IFFT. These two operations are almost identical. In fact, the IFFT can be made using an FFT by conjugating input and output of the FFT and dividing the output by the FFT size. This makes it possible to use the same hardware for both the transmitter and the receiver. Of course, this saving in complexity is only possible when the modem does not have to transmit and receive simultaneously, which is the case for the standard. December, 2000 Page 18-40

22 HPA IQ modulator Add cyclic extension and windowing Binary input data FEC Encoder Interleaving QAM Mapping Pilot Insertion Serial to Parallel IFFT (TX) Parallel to Serial FFT(RX) Binary output data FEC Decoder Deinterleaving QAM demapping Channel Correction Parallel to Serial Serial to Parallel AGC Amp IQ Detector Timing and frequency synchronization Frequency corrected signal Remove cyclic extension LNA AFC Clock Recovery Symbol timing Figure 9. Block diagram of an OFDM transceiver In case of the standard IEEE a, the parameters for the physical layer (e.g. for OFDM) are as follows: Data rate (Mbits/s) Modulation Coding rate (R) Coded bits per subcarrier (NBPSC) Coded bits per OFDM symbol (NCBPS) Data bits per OFDM symbol (NDBPS) 6 BPSK 1/ BPSK 3/ QPSK 1/ QPSK 3/ QAM 1/ QAM 3/ QAM 2/ QAM 3/ Table 4. Physical layer parameters. December, 2000 Page 19-40

23 Parameter Value N SD : Number of data subcarriers 48 N SP : Number of pilot subcarriers 4 N S : Number of subcarriers, total 52 (N SD + N SP ) F : Subcarrier frequency spacing MHz (=20 MHz/64) T FFT : IFFT/FFT period 3.2 µs (1/ F ) T PREAMBLE : PLCP preamble duration 16 µs (T SHORT + T LONG ) T SIGNAL : Duration of the SIGNAL BPSK-OFDM symbol 4.0 µs (T GI + T FFT ) T GI : GI duration 0.8 µs (T FFT /4) T GI2 : Training symbol GI duration 1.6 µs (T FFT /2) T SYM : Symbol interval 4 µs (T GI + T FFT ) T SHORT : Short training sequence duration 8 µs (10 T FFT /4) T LONG : Long training sequence duration 8 µs (T GI2 + 2 T FFT ) Table 5. Physical layer parameters Guard time and cyclic extension One of the most important problems in for wireless communications is the multipath delay spread. OFDM deals with it very efficiently. The parallel transmission implies that the input datastream is divided in N S subcarriers and the symbol duration is made N S times smaller, which also reduces the relative multipath delay spread, relative to the symbol time, by the same factor. The intersymbolic interference is almost completely eliminated by introducing a guard time for a each OFDM symbol. The guard time is chosen larger than the expected delay spread such that multipath components from one symbol cannot interfere with the next symbol. This guard time could be no signal at all but the problem of intercarrier interference (ICI) would arise. Then, the OFDM symbol is cyclically extended in the guard time. Using this method, the delay replicas of the OFDM symbol always have an integer number of cycles within the FFT interval, as long as the delay is smaller than the guard time. Multipath signals with delays smaller than the guard time cannot cause ICI. If multipath delay exceeds the guard time by a small fraction of the FFT interval (for example 3%), the subcarriers are not orthogonal anymore, but the interference is still small enough to get a reasonable constellation. Considering that the multipath delay exceeds the guard time by 10% of the FFT interval, the constellation is seriously affected and an unacceptable error rate is obtained Windowing Essentially, an OFDM signal consists of a number of unfiltered QAM subcarriers. This means that the out-of-band spectrum decreases rather slowly, following a sinc December, 2000 Page 20-40

24 function. For larger number of subcarriers, the spectrum goes down rapidly in the beginning, which is caused by the fact that the sidelobes are closer together. To make the spectrum decrease faster, windowing is applied to the OFDM signal. The standard doesn t specify the kind of window to be used but an example is included using the following function [5]: 2 sin π t TTR wt ( t) = 1 2 sin π t T TTR T for( 2 T for( 2 TR TR T for( T 2 T < t < 2 T t < T 2 TR TR ) TR ) T t < T + 2 considering that T TR is the transition time between two consecutive periods of FFT, as it can be seen in Figure. TR ) (2) Figure 10. OFDM frame with cyclic extension and windowing for (a) single reception or (b) two receptions of the FFT period Figure 10 also illustrates the possibility of extending the windowing function over more than one period, T FFT, and additionally shows smoothed transitions by application of a windowing function, as exemplified in Equation (2). In particular, window functions that extend over multiple periods of the FFT are utilized in the definition of the preamble. December, 2000 Page 21-40

25 Several other conventional windows were simulated including raised cosine, Hann, Hamming, Blackman and Kaiser. The best performance was obtained for the Blackman window, considering the resulting stopband attenuation and the transition bandwidth Forward Error Correction Coding According to the standard, data must be encoded with a convolutional encoder of coding rate R = 1/2, 2/3, or 3/4, corresponding to the desired data rate. The convolutional encoder uses the industry-standard generator polynomials, g 0 = and g 1 = of rate R = 1/2, as shown in Figure 11. Output data A Input data T b T b T b T b T b T b T b Output data B Figure 11. Convolutional encoder (k = 7) The bit denoted as A shall be output from the encoder before the bit denoted as B. Higher rates are derived from it by employing puncturing. Puncturing is a procedure for omitting some of the encoded bits in the transmitter reducing the number of transmitted bits and increasing the coding rate, and inserting a dummy zero metric into the convolutional decoder on the receive side in place of the omitted bits. Decoding by the Viterbi algorithm is recommended. Even thought the convolutional code is established by the standard, block codes may be more desirable in certain applications, such as packet voice or data communications, in which the length of the packet may be made equal to a multiple of the code length. In these applications, block codes are more attractive than convolutional codes, since the memory of the convolutional codes must be brought to a known state to terminate the trellis, which lowers the effective code rate Block Codes December, 2000 Page 22-40

26 A block code encodes a block of k input symbols into n coded symbols, with n being larger than k. The purpose of adding the redundant n-k symbols is to increase the minimum Hamming distance, which is the minimum number of different symbols between any pair of code words. For a minimum Hamming distance of d min, the code can correct t errors where t is given by: d 1 t floor min (3) 2 The minimum Hamming distance is upperbound by the number of redundant symbols n-k as: d min n k +1 (4) For binary codes, only repetition codes and single-parity check codes reach this upperbound. A class of nonbinary codes that doesn t reach the above bound are the Reed- Solomon codes. Because of their good distance properties and the availability of efficient coding and decoding algorithms, Reed-Solomon codes are the most popularly used block codes. Reed-Solomon codes are defined for block symbols with m bits per symbol, where the code length n is related to m by: n = 2 m 1 The number of input symbols k is related to m and the required minimum Hamming distance d min as: k = 2 m d min There appears to be little flexibility in the available code lengths. However, a Reed- Solomon code can easily be shortened to any arbitrary length by leaving a number of input bits zero and deleting the same amount of output bits. It is also possible to extend the code length to a power of 2 by adding an extra parity symbol. Using equations (3) and (4), a Reed-Solomon code can correct up to floor ((n-k)/2) erroneous symbols. Each symbol contains m bits, so a maximum amount of m floor((nk)/2) erroneous bits may be corrected. If the Reed-Solomon code is designed to correct up to two symbol errors containing 8 bits per symbol, it cannot correct an arbitrary combination of three bit errors, as these errors can occur in three different symbols. This characteristic makes Reed-Solomon codes particularly useful for correcting bursty channels. The OFDM link in presence of fading multipath is a very good application for this code. Another block codes is the Reed-Muller code [6]. Using the Viterbi algorithm with soft decision it results a very attractive implementation. Using the results from [7], the performance of this code can be evaluated and compared with that of convolutional codes. Also, compared with other block codes, Reed December, 2000 Page 23-40

27 Muller codes are preferable where soft decision decoding is required since they have a simple structure, resulting in computationally manageable decoding. Figure compares the performance of the (16,11,4) RM code with rate 2/3, memory 2 and 3 punctured convolutional codes [8]. This figure shows that the performance curve of the (16,11,4) RM code falls midway between that of the two convolutional codes Interleaving Figure 12. BER of the (16,11,4) RM code and rate 2/3 memory 2 and 3 Because of the frequency fading of typical radio channels, the OFDM subcarriers generally have different amplitudes. Deep fades in the spectrum may cause groups of subcarriers to be less reliable than others, thereby causing bit errors to occur in bursts rather than being randomly scattered. Interleaving is applied to randomize the occurrence of bit errors prior to decoding. At the transmitter, the coded bits are permuted in a certain way, which makes sure that adjacent bits are separated by several bits after interleaving. According to the standard, all data bits must be interleaved by a block interleaver with a block size corresponding to the number of bits in a single OFDM symbol, N CBPS. The interleaver is defined by a two-step permutation. The first permutation ensures that adjacent coded bits are mapped onto nonadjacent subcarriers. The second ensures that adjacent coded bits are mapped alternately onto less and more significant bits of the constellation and, thereby, long runs of low reliability (LSB) bits are avoided. December, 2000 Page 24-40

28 Considering k the index of the coded bit before the first permutation, i the index after the first and before the second permutation and j the index after the second permutation, just prior to modulation mapping, the first permutation is defined by the rule: i = (N CBPS /16) (k mod 16) + floor(k/16) k = 0,1,,N CBPS 1 The function floor (.) denotes the largest integer not exceeding the parameter. The second permutation is defined by the rule: j = s floor(i/s) + (i + N CBPS floor(16 i/n CBPS )) mod s i=0,1, N CBPS 1 The value of s is determined by the number of coded bits per subcarrier, N BPSC, according to: s = max(n BPSC /2,1) The deinterleaver, which performs the inverse relation, is also defined by two permutations. Here, j denotes the index of the original received bit before the first permutation, I the index after the first and before the second permutation, and k the index after the second permutation, just prior to delivering the coded bits to the convolutional (Viterbi) decoder. The first permutation is defined by the rule: i = s floor(j/s) + (j + floor(16 j/n CBPS )) mod s j = 0,1, N CBPS 1 where s = max(n BPSC /2,1) The second permutation is defined by the rule: k = 16 i (N CBPS 1)floor(16 i/n CBPS ) i = 0,1, N CBPS 1 Instead of a block interleaver, it is possible to use a convolutional interleaver. Figure 13 shows a convolutional interleaver. The interleaver cyclically writes each input symbol or bit into one of the K shift registers that introduce a delay of 0 to k-1 symbol durations. December, 2000 Page 25-40

29 T Input data T T Output data T T T T Figure 13. Convolutional interleaver T 6. Synchronization Before an OFDM receiver can demodulate the subcarriers, it has to perform at least two synchronization tasks. The first one is to find out where the symbol boundaries are and what the optimal timing instants are to minimize the effects of intercarrier interference (ICI) and intersymbol interference (ISI). The second task is to estimate and correct the carrier frequcncy offset of the received signal to avoid the ICI. Also, for coherent receivers, the carrier phase has to be synchronized. Further, a coherent QAM receiver needs to detect the amplitudes and phases of all subcarriers to define the decision boundaries for the QAM cosntellation of each subcarrier. Usually, the OFDM received signal has a frequency offset, which immediately results in ICI. This means that the subcarries are not perfectly orthogonal, producing phase noise. Using the cyclic prefix an considering that the first T G seconds of each symbol is identical to the last part, this property can be exploited for both timing and frequency synchronization, using a system showed in figure 14. T Delay Conjugation Phase of maximum Frequency offset OFDM signal dt T G Maximum correlation Timming Figure 14. Synchronization using the cyclic prefix December, 2000 Page 26-40

30 This device correlates a T G long part of the signal with a part that is T seconds delayed. The output can be written as [12]: T G = x( t) r( t τ ) r( t τ T ) dτ 0 The correlation function produce several peaks, corresponding to the different symbols and the peak amplitudes show a significant variation. The reason for this is that although the average power for a T-seconds interval of each OFDM symbol is constant, the power in the guard time can substantially vary from this average power level. Another effect is the level of the undesired correlation sidelobes between the main correlation peaks. These sidelobes reflect the correlation between two pieces of the OFDM signal that belong partly or totally to two different OFDM symbols. Because different OFDM symbols contain independent data values, the correlation output is a random variable, which may reach a value that is larger than the desired correlation peak. The standard deviation of the random correlation magnitude is related to the number of independent samples over which the correlation is performed. The larger the number of independent samples, the smaller the standard deviation is. In the extreme case where the correlation is performed over only one sample, the output magnitude is proportional to the signal power, and there is no distinct correlation peak in this case. In the other extreme case where the correlation is performed over a very large number of samples, the ratio of sidelobes-topeak amplitude will go to zero. Because the number of independent samples is proportional to the number of subcarriers, the cyclic extension correlation technique is only effective when a large number of subcarriers are used, preferably more than 100. An exception to this is the case where instead of random data symbols, specially designed training symbols are used. In this case, the integration can be done over the entire symbol duration instead of the guard time only. The level of undesired correlation sidelobes can be minimized by a proper selection of the training symbols. The phase of the correlation output is equal to the phase drift between samples that are T seconds apart. Hence, the frequency offset can simply be found as the correlation phase divided by 2πT. This method works up to a maximum absolute frequency offset of half the subcarrier spacing. To increase this maximum range, shorter symbols can be used, or special training symbols with different PN sequences on odd and even subcarrier frequencies to identify a frequency offset of an integer number of subcarrier spacings [13]. The noise performance of the frequency offset estimator is now determined for an input signal r(t) that consists of an OFDM signal s(t) with power P and additive Gaussian noise n(t) with a one-sided noise power spectral density of N 0 within the bandwidth of the OFDM signal: r(t) = s(t) + n(t) December, 2000 Page 27-40

31 The frequency offset estimator multiplies the signal by a delayed and conjugated version of the input to produce an intermediate signal y(t) given by [13] y(t) = r(t)r * (t - T) = s(t) 2 exp(jφ) + n(t)s * (t - T)+ n * (t - T)s(t) + n(t)n * (t - T) (5) The first term in the right-hand side of the equation 5 is the desired output component with a phase equal to the phase drift over a T-second interval and a power equal to the squared signal power. The next two terms are products of the signal and the Gaussian noise. Because the signal and noise are uncorrelated, and because noise samples separated by T seconds are uncorrelated, the power of the two terms is equal to twice the product of signal power and noise power. Finally, the power of the last term is equal to the squared noise power. If the input SNR is much larger than one, the power of the squared noise component becomes negligible compared with the power of the other two noise terms. The frequency offset is estimated by averaging y(t) over an interval equal to the guard time T G and then estimating the phase of y(t). Because the desired output component of ( ) is a constant vector, averaging reduces the noise that is added to this vector. Assuming that the squared noise component may be neglected, the output SNR is approximated as [13]. 2 P PT SNR0 = 2PN / T 2N 0 G G 0 Figure show the effect of noise on the received phase angle. If we let the amplitude of the transmitted signal be 1, and the length of the noise vector be A with angle f, then the received phase error is θ err. Figure 15. Received phasor, showing effect of noise on the received phase angle December, 2000 Page 28-40

32 Using trigonometry, Since, Therefore, The signal to ratio determines the relative amplitude of the received signal and the noise level. Since the signal is scaled to an amplitude of 1, the amplitude of the noise is: The SNR is base on the amplitudes of the signals thus must be scaled correctly when converting it to db. Substituting this in, 6.1. Synchronization Using Special Training Symbols The synchronization technique based on the cyclic extension is particularly suited to tracking or to blind synchronization in a circuit-switched connection, where no special training signals are available. For packet transmission, however, there is a drawback because an accurate synchronization needs an averaging over a large (>10) number of OFDM symbols to attain a distinct correlation peak and a reasonable SNR. For high-rate packet transmission, the synchronization time needs to be as short as possible, preferably a few OFDM symbols only. To achieve this, special OFDM t symbols can be used for which the data content is known to the receiver. In this, the entire received training signal can be used to achieve synchronization, whereas the cyclic extension method only uses a fraction of each symbol. December, 2000 Page 29-40

33 According to [5], the physical layer convergence procedure (PLCP) preamble field is used for synchronization. It consists of 10 short symbols and 2 long symbols, shown in figure 16. Figure 16. OFDM training structure Figure 16 shows the OFDM training structure (PLCP preamble), where t 1 to t 10 denote short training symbols and T 1 and T 2 denote long training symbols. The PLCP preamble is followed by the SIGNAL field and DATA. The total training length is 16 µs. The dashed boundaries in the figure denote repetitions due to the periodicity of the inverse Fourier transform. A short OFDM training symbol consists of 12 subcarriers, which are modulated by the elements of the sequence S, given by S 26, 26 = 13 / 6 {0, 0, 1+j, 0, 0, 0, 1 j, 0, 0, 0, 1+j, 0, 0, 0, 1 j, 0, 0, 0, 1 j, 0, 0, 0, 1+j, 0, 0, 0, 0,0, 0, 0, 1 j, 0, 0, 0, 1 j, 0, 0, 0, 1+j, 0, 0, 0, 1+j, 0, 0, 0, 1+j, 0, 0, 0, 1+j, 0,0} The multiplication by a factor of is in 13 / 6 order to normalize the average power of the resulting OFDM symbol, which utilizes 12 out of 52 subcarriers. The fact that only spectral lines of S 26:26 with indices that are a multiple of 4 have nonzero amplitude results in a periodicity of T FFT /4 = 0.8 µs. The interval T SHORT is equal to ten 0.8 µs periods (i.e., 8 µs). A long OFDM training symbol consists of 53 subcarriers plus a zero value at dc, which are modulated by the elements of the sequence L, given by L 26, 26 = {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0,1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1} This information is used, also, to estimate the channel and to improve the system performance. December, 2000 Page 30-40

34 The receiver has to perform two operations: tracking and acquisition. During the tracking mode, only small frequency fluctuations have to be corrected. But during the acquisition mode the frequency offset can take large values. This is the most challenging task to be managed by the synchronizer structure. During the tracking mode, it can be assume that the remaining frequency offset is substantially smaller than F /2, with F representing the subcarrier frequency spacing (for the standard, F =0.3125MHz [5]). Considering just one subchannel, then this frequency synchronization problem is similar to that in case of single carrier problem. Therefore, frequency estimation algorithms derived from maximum likelihood theory [14] can be used in this case. The underlying principle of these frequency algorithms is that the frequency estimation problem can be reduced to a phase estimation problem by considering the phase shift between two subsequent subchannel samples. The influence of the modulation is removed in this case by the multiplication with the conjugate complex value of the transmitted symbols. The known symbols are taken from the training sequence and the pilot signals. In several papers, like [14], it is recommended to transmit the synchronization sequences in different channels instead of doing it over a single subchannel. They should be spread uniformly over the whole frequency domain. That is how the standard implement it. Equations (6) and (7) in [15] describe generalized estimators for this cases. In order to avoid a large decoder performance degradation due to the crosstalk, it may be necessary to correct the frequency offset prior to the demodulation even during the tracking mode. It is theoretically possible to correct a small offset on the subchannel level. In practice, this will depend on the maximum magnitude of the frequency offset which the tracking unit has to cope with. The acquisition process should be performed fast. The special acquisition training preamble should be avoided to increase the transmission efficiency. Using the same training synchronization symbols from the pilot signals, the operation involved in acquiring an initial frequency offset estimate coincides with the search operation for the training symbols transmitted on the channel. The acquisition rule is based on the fact that the magnitude of the correlation function reaches a maximum, if the estimation coincides with the received frequency. The acquisition time is directly proportional to the frequency range to be scanned, depending of the expected Doppler value in the channel. 7. Detection In an OFDM link, the data bits are modulated on the subcarriers by some form of phase shift keying (PSK) or quadrature amplitude modulation (QAM). To estimate the bits December, 2000 Page 31-40

35 at the receiver, knowledge is required about the reference phase and amplitude of the constellation on each subcarrier. In general, the constellation of each subcarrier shows a random phase shift and amplitude change, caused by carrier frequency offset, timing offset, and frequency selective fading. To cope with these unknown phase and amplitude variations, two different approaches exist. The first one is coherent detection, which uses estimates of the reference amplitudes and phases to determine the best possible decision boundaries for the constellation of each subcarrier. The main issue with coherent detection is how to find the reference values without introducing too much training overhead. The second approach is differential detection, which does not use absolute reference values, but only looks at the phase and/or amplitude differences between two QAM values. Differential detection can be done both in the time domain and in the frequency domain. In the first case, each subcarrier is compared with the subcarrier of the previous OFDM symbol. In the case of differential detection in the frequency domain, each subcarrier is compared with the adjacent subcarrier within the same OFDM symbol. Differential detection implies differential encoding, which is not the case for the standard IEEE a, so this last case will not be treated Coherent Detection Figure 17 shows a block diagram of a coherent OFDM receiver. After downconversion and analog-to-digital conversion, the fast Fourier transform (FFT) is used to demodulate the N subcarriers of the OFDM signal. For each symbol, the FFT output contains N QAM values. However, these values contain random phase shifts and amplitude variations caused by the channel response, local oscillator drift, and timing offset. It is the task of the channel estimation block to learn the reference phases and amplitudes for all subcarriers, such that the QAM symbols can be converted to binary soft decisions. RF Receiver ADC FFT Coherent Detection Deinterleaving Decoding Binary Output Data Channel Estimation Figure 17. Block diagram of an OFDM receiver with coherent detection. December, 2000 Page 32-40

36 7.2. Two-Dimensional Channel Estimators In general, radio channels are fading both in time and in frequency. Hence, a channel estimator has to estimate time-varying amplitudes and phases of all subcarriers. One way to do this is to use a two-dimensional channel estimator that estimates the reference values based on a few known pilot values. In this case, the signal has 4 subcarriers containing known pilot values to allow the estimation. To be able to interpolate the channel estimates both in time and frequency from the available pilots, the pilot spacing has to fulfill the Nyquist sampling theorem, which states that the sampling interval must be smaller than the inverse of the double-sided bandwidth of the sampled signal. For the case of OFDM, this means that there exist both a minimum subcarrier spacing and a minimum symbol spacing between pilots. By choosing the pilot spacing much smaller than these minimum requirements, a good channel estimation can be made with a relatively easy algorithm. The more pilots are used, however, the smaller the effective SNR, becomes that is available for data symbols. Hence, the pilot density is a tradeoff between channel estimation performance and SNR loss. To determine the minimum pilot spacing in time and frequency, we need to find the bandwidth of the channel variation in time and frequency, These bandwidths are equal to the Doppler spread B d in the time domain and the maximum delay spread τ max in the frequency domain [16]. Hence, the requirements for the pilot spacings in time and frequency s t and s f are s t < 1/B d s f < 1/τ max These simple equations can be used to estimate the theoretical limits of the standard. In terms of Doppler effect, and considering that the pilot signals are transmitted continuously, the pilot spacing in time is not a limitation. The spacing in frequency imposes a limit to the delay spread. The pilots signal are the subcarriers number 21, -7, 7 and 21. This means that the spacing between pilots is 4.375MHz ( MHz). In these conditions, the maximum delay spread τ max to be allowed is 228 nsec. In the literature, there are several algorithms to estimate the OFDM channel the one explained in [12]. This algorithm can be used with the parameters indicated by the standard. According to it, the pilots must be BPSK modulated by a pseudo binary sequence to prevent the generation of spectral lines.the contribution of the pilot subcarriers for the n th OFDM symbol is produced by Fourier transform of sequence P, given by: December, 2000 Page 33-40

37 P 26, 26 = {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0} The polarity of the pilot subcarriers is controlled by the sequence, p n, which is a cyclic extension of the 127 elements sequence and is given by: p = {1,1,1,1, -1, -1, -1,1, -1, -1, -1, -1, 1,1, -1,1, -1, -1,1,1, -1,1,1, -1, 1,1,1,1, 1,1, -1,1,1,1, -1,1, 1, -1, -1,1, 1,1, -1,1, -1, -1, -1,1, -1,1,-1,-1, 1,-1,-1,1, 1,1,1,1, -1,-1,1,1,-1,-1,1,-1, 1,-1,1,1, -1,-1,-1,1, 1,-1,-1,-1, -1,1,-1,-1, 1,-1,1,1, 1,1,-1,1, -1,1,-1,1,-1,-1,-1,-1, -1,1,-1,1, 1,-1,1,-1, 1,1,1,-1, -1,1,-1,-1, -1,1,1,1, -1,-1,-1,-1, -1,-1,-1} The sequence, p n can be generated by the scrambler defined by figure 18 when the all ones initial state is used, and by replacing all 1 s with 1 and all 0 s with 1. Each sequence element is used for one OFDM symbol. X 7 X 6 X 5 X 4 X 3 X 2 X 1 Output Sequence Figure 18. Pilot Sequence Generator The subcarrier frequency allocation is shown in figure 19. Figure 19. Pilot Frequency Allocation The channel estimation techniques were designed to estimate a channel that varied both in time and frequency. These techniques are especially suitable for continuous transmission systems such as Digital Audio Broadcasting or Digital Video Broadcasting. Even thought the standard has previsions about it, according to [12] they are not very suited for packet-type communications for two reasons. First, in many packet transmission December, 2000 Page 34-40

38 systems, such as wireless LAN, the packet length is short enough to assume a constant channel during the length of the packet. This means there is no need to estimate time fading, which greatly simplifies the channel estimation problem. Second, using pilots scattered over several OFDM data symbols introduces a delay of several symbols before the first channel estimates can be calculated. Such a delay is undesirable in packet transmission like in an IEEE wireless LAN, which requires an acknowledgment to be sent after each packet transmission. Any delay in the reception of a packet will also delay the acknowledgment and hence decrease the effective throughput of the system. An additional disadvantage is the fact that the receiver needs to buffer several OFDM symbols, thereby requiring extra hardware. However, for applications with fading and strong Doppler effect, like the signal between a car in movement and an access point in a highway, the pilot signals can be useful to improve the BER. The mobile channel introduces multipath distortion of the signaling waveforms. Both the amplitude and phase are corrupted and the channel characteristics changes because of movements of the mobile. In order to perform coherent detection, reliable channel estimates are required. The problem is to decide where and how often to insert pilot symbols. The spacing between the pilot symbols shall be chosen small enough to enable reliable channel estimates but large enough not to increase the overhead too much. In a multicarrier system there exist a unique opportunity to determine various parts of the channel impulse response, as opposed to a single-carrier system. It is no use to make efforts to determine already known parts. The impact of pilot signals was analyzed by Cavers in [17] who made an exhaustive theoretical analysis for single-carrier systems. He pointed out that it was appropriate that 14% of the sent symbols were pilot symbols to be able to handle large Doppler values (f d T S = 0.05). This means that the standard pilot scheme could be redundant. Also, Tufvesson and Maseng [18] analyzed several pilot patterns specifically for OFDM systems, arriving to the conclusion that the ability to estimate the channel reliably when it changes due to e.g. vehicle movements is highly dependent on the pilot pattern used. By rearranging the pilot pattern it is, in some cases, possible to handle 10 times higher Doppler frequency and to reduce the number of needed pilot symbols the same amount, still retaining the same bit error rate. Alternatively the new pilot pattern could be used to reduce the bit error rate up to a factor 5, even more in a low noise environment. For a given propagation environment, e.g. a base station site, it is possible to precalculate a suitable pilot pattern. This is an alternative to improve the standard performance in terms of throughput. December, 2000 Page 35-40

39 8. Simulation The OFDM system was modeled using Matlab to allow various parameters of the system to be varied and tested, including those established by the standard. The aim of doing the simulations was to measure the performance of OFDM under different channel conditions, and to allow for different OFDM configurations to be tested. OFDM Modulation and Demodulation Run "Parameters.m" in the Workspace before simulation C 1 Re(u) Random int Random Data Generator Convolutional Encoder Convolutional Encoder Pulse Transmitter Block MATLAB A-QASK interleave Function PIlot Insertion Interleave Mapping Serial to parallel IQ Modulator Subsystem Window Function Parallel to serial blackman Out1 In1 Add cyclic Extension MATLAB Function MATLAB Function zeropad IFFT IFFT Complex to Real Im(u) Complex to Imag Time Scope Time Scope1 B-FFT Complex Rayl Fading Complex Rician Noise AWGN Buffered FFT Frame Scope Complex Rayleigh fading Channel Additive Rician Noise AWGN channel MATLAB Function FFT MATLAB Function Out1 In1 Commutator2 Remove zeros simout1 C1 FFT 1 Remove cyclic Extension1 Serial to parallel1 IQ Demodulator Subsystem A-QASK Constellation To Workspace Block interleave Viterbi Decoder A-map QASK demod baseband Pulse Interleave1 Receiver Viterbi Decoder In1 Out1 In1 In2 Out1 Errors 0 Delay Subsystem Run "constellation" after the simulation in the workspace to watch the received constellation The following routines must be included in the path: zeropad.m zerounpad.m cyclic.m remcyc.m Error counter Subsystem Figure 20. Simulink OFDM Model December, 2000 Page 36-40

40 Using MatLab 5.3 and Simulink the OFDM transceiver was simulated. The model can be seen in figure 20 The simulation includes all the stages for transceiver and receiver, according to the standard. Because of the Matlab sampling time, the transmission was implemented in baseband to avoid long periods of simulation. Considering Gaussian and Rician noise and Rayleigh fading effect, a good approximation to the real performance can be observed, over all in the degradation of the BER. Also the channel effect can be observed in the output constellation before the Viterbi decoder using some routines in MatLab. In figure 21, the OFDM signal spectrum can be seen corresponding to a random binary input sequence. According to the standard, the 0 (DC) input must be set to zero in the IFFT implementation. This can be clearly observed at frequency zero on the graph B d e, d itu M agn Frequency (MHz) Figure 21. OFDM Signal Spectrum December, 2000 Page 37-40

41 Using the 64QAM modulation scheme, the signal is observed after the QAM demodulator with the distortion due to the noise. The effect of the channel over the constellation can be seen in the figure 22. Figure 22. Received constellation for a given amout of noise Conclusion The IEEE Standard Committee has developed the standard for wireless networks with a 5GHz PHY layer and OFDM modulation. But, the industry has not offered any interface yet. Many companies are still researching and developing, over all for the receiver, which is the key part of the system. The standard does not give rules about it and its implementation is up to the designer. According to the simulations, OFDM appears to be a good modulation technique for high performance wireless telecommunications. Some factors were not tested here like peak power clipping, start time error and the effect of frequency stability errors. The codification used for the system could be improved, just using block codes instead of convolutional codes, but this fact would be out of the standard. Also, the pilot signal distribution could be modified to reduce the redundancy. December, 2000 Page 38-40