OFDM and Downlink Physical Layer Design

Transcription

1 Seminar Ausgewählte Kapitel der Nachrichtentechnik, WS 2009/2010 LTE: Der Mobilfunk der Zukunft OFDM and Downlink Physical Layer Design Shahram Zarei 11. November 2009 Abstract In the last years the tendency to have higher data rates in cellular mobile phone networks, has been growing very rapidly. LTE (Long Term Evolution) is the current standard, which provides very high data rates having Orthogonal Frequency Multiplexing (OFDM) as a key feature. In this work rst is the question why OFDM is neccessary for LTE downlink is answered and then topics like OFDM receiver and transmitter structures and OFDM parameter dimensioning are introduced. In the second part the physical layer in the downlink is analyzed. Signal structure in the time domain, resource management, signal generation chain and Multiple-Input Multiple-Output (MIMO) technique are topics of the second part. 1 Introduction Digital cellular communications beginning with GSM called as 2nd generation were serving only speech communication at the very early versions. Adding GPRS and EDGE as data packet services gaining higher spectral eciency were the rst steps to make cellular networks capable of transporting data packets. If we look at the development of the later generations like UMTS (3G) or extensions like EGDE, EGPRS, EGPRS2 (extension of EDGE with 16QAM instead of 8PSK and Turbo encoder), HSDPA and HSUPA, we will observe that the main trend is to achieve higher data rates. LTE (Long Term Evolution) is the current element in the development chain of digital cellular communication systems with following key design targets: Signicantly higher peak data rates than older standards (e.g. 100 Mbps in 20 MHz bandwidth Downlink and 50 Mbps in 20 MHz bandwidth Uplink)

2 2 Shahram Zarei Scalable bandwidth for more spectrum exibility: 1.25, 1.6, 2.5, 5, 10, 15, 20 MHz MIMO (Multiple-Input Multiple-Output) Low latency (round trip delay < 10 ms) Packet oriented data transmission (all IP network) High UE (User Equipment) mobility conditions: Up to 350 or even 500 km/h 2 OFDM 2.1 Why OFDM? One of the central goals of LTE is the signicantly higher peak data rate compared to the older standards like GSM/EDGE or UMTS. For example in the downlink, employing MIMO (Multiple-Input Multiple-Output), data rates of up to 100 Mbps are reachable. In a single carrier system, where the information is modulated on a single carrier, the data symbols will have very short duration compared to the delay caused by the multipath propagation, which causes ISI (intersymbol interference). This eect can be seen in Fig. 1. Figure 1: Single carrier transmission with short symbols (according to [3]) A very intuitive solution to avoid ISI would be using longer symbols. But if we want to transfer the same data rate, we have to use another resource dimension, for example frequency. This leads to the concept of multicarrier communication, which can be seen in Fig. 2. The concept of multicarrier communication is based on the fact, that data transmission occurs in two resource dimensions: time and frequency. Data is transported in form of symbols in the time domain and each symbol in the time domain consists of several subcarriers in the frequency domain, each carrying part of the information to be transported.

3 OFDM and Downlink Physical Layer Design 3 Figure 2: Multicarrier transmission with long symbols (according to [3]) As we can see in the Fig. 2, using longer symbols ISI can be reduced enormously. In multicarrier systems the main data stream is splitted into data streams with lower bit-rates and thus longer symbols. Each sub-data stream is modulated on a subcarrier. Due to the fact that data symbols are longer, ISI would be much smaller. One very interesting eect in multicarrier systems is that the whole frequency band is divided into much smaller subbands and therefore the channel in each subband can be considered as a at fading channel because of a very small bandwidth which means the channel behaves as a constant complex factor. In this case the channel can be equalized in the receiver by simply multiplying the samples by the inverse of the DFT coecients of the channel impulse response corresponding to each subband. This eect can be seen in Fig OFDM signal structure OFDM stands for Orthogonal Frequency Division Multiplexing and is a special form of multicarrier modulation, where the subcarriers are orthogonal to each other. The OFDM signal in the time domain has the form: S OFDM (t) = 1 N 2 T n=0 a k [n]e j2πnt + 1 T N 1 n=n N 1 a k [n]e j2πnt, in the kth interval : kt < t < (k+1)t Note, that T is the duration of the modulation symbol and inverse of subcarrier spacing. We can formulate orthogonality as following: (1) (k+1)t kt e j2π(fn fν)t dt = 0, for n ν (2)

4 4 Shahram Zarei Figure 3: Equalization in multicarrier systems (according to [3]) An interesting point concerning modulation in OFDM systems is, that each subcarrier can have an individual modulation scheme and an individual data rate, depending on the signal quality (e.g. signal-to-noise ratio (SNR) ) in the considered sub-band. That means there are some algorithms, which can dedicate part of the whole data rate on each carrier, depending on its SNR: The bigger the SNR, the bigger the data rate dedicated. Due to the orthogonality of the subcarriers to each other, there isn't any problem regarding the existing overlapping part between the subbands and therefore there isn't any need for some guard-bands between subcarriers. This makes the OFDM concept more ecient concerning the bandwidth eciency. 2.3 OFDM signal in the frequency domain In the following discussion it is assumed, that the symbols are i.i.d. (independent and identically distributed). We assume, that the modulation pulse is a rectangular pulse, then we have: g rect (t) = 1/T, for 0 t T 0, otherwise (3) The power spectral density of a rectangular pulse is: G rect (f) 2 = T sin2 (πft ) (πft ) 2 (4) The rectangular pulse in the time domain and its power spectral density can be seen in Fig. 4 and Fig. 5.

5 OFDM and Downlink Physical Layer Design 5 Figure 4: Rectangular pulse in the time domain (according to [3]) Figure 5: Power spectral density of the rectangular pulse (according to [3]) Due to the fact that symbols are i.i.d., the power spectral density of the OFDM signal will be the sum of shifted versions of the power spectral density of the rectangular pulse: G OFDM (f) = N 2 n=0 N 1 G rect (f n T ) 2 + G rect (f n n=n N 1 T ) 2 (5) In Fig. 6 the PSD (power spectral density) of an OFDM signal can be seen. Figure 6: Power spectral density of an OFDM signal (according to [3]) 2.4 OFDM transmitter based on IDFT The early versions of multicarrier modulators in the 60ies were using oscillator banks. Inverse discrete Fourier transform (IDFT) is today the standard method for generating OFDM signals. If the number of subcarriers is a power of two, then a fast Fourier transform (FFT) can be used, which is a computationally ecient (fast) variant of the DFT.

6 6 Shahram Zarei In the Fig. 7 the general structure of an OFDM transmitter based on the IDFT can be seen. At the very rst step data symbols coming from earlier modules, e.g. channel encoder, are parallelized using a seria-to-parallel converter. This is done because of the fact that IDFT works blockwise. After serial-to-parallel converter, comes the mapping module, which maps the incoming symbols on complex-valued samples. The mapping schemes in LTE downlink are QPSK, 16QAM and 64QAM. Then the samples are fed into the IDFT module to get the time domain samples. An interesting point here is, that usually some carriers are left unused, which is done by simply putting zeros into the IDFT at the corresponding subcarrier position. Using less carriers has the advantage that the ltering of the OFDM shoulders is much easier. After the IDFT there is a parallel-to-serial converter followed by the DAC (Digital-to-Analog Converter), which converts the signal from digital to analog form. In order to lter out the shoulders of the OFDM signal which produce out-of-band emissions, there is a spectral shaping lter after the DAC. Finally an upconverter module consisting of a mixer and a local oscillator mixes the generated signal from baseband into the RF domain. Figure 7: OFDM transmitter based on IDFT (according to [3]) 2.5 OFDM receiver based on DFT In the OFDM receiver, after mixing down in the baseband or low IF, the analog signal is rst matched ltered and then converted to digital samples with an ADC (Analog-to-Digital Converter). A very important module here is the synchronization block, which synchronizes the local oscillator frequency and clock frequency of the ADC using information gained from the received samples. Channel estimation and frame synchronization are further tasks of this module. As we see later, frequency synchronization is a must in OFDM systems, because of their very high sensitivity against frequency shifts. The samples are then parallelized and processed blockwise by the DFT module. Assuming a frequency-selective channel the equalization in the receiver is simply done by multiplying the samples with the inverse of the corresponding channel coecients. This is one of the most important attractions of OFDM. After equalization there

7 OFDM and Downlink Physical Layer Design 7 is a decision module, which is a hard desicion slicer here. In scenarios with channel coding, a soft decision is often used, which works with LLRs (Log Likelihood Ratios). A demapping module recovers the bits from symbol delivered by the decision module. The bits are nally converted from parallel to serial form. Fig. 8 shows the structure of an OFDM receiver based on the DFT. Figure 8: OFDM receiver based on DFT (according to [3]) 2.6 Concept of Guard Interval As we already know, if the data symbols are long enough compared to the longest delay in the channel, then the ISI would be small but it has not completely vanished. In order to eliminate the ISI properly, one can use some kind of guard space between adjacant symbols. There are several methods to do so, for example putting zeros in the guard space. However the most popular way is to use a Cyclic Prex (CP), which means the last samples of the OFDM symbol are copied and pasted into the front of it. The number of copied samples or the length of the Guard Interval are important design parameters, which depend on the channel characteristics and the largest delay existing in the channel. Fig. 9 shows the functionality of the Guard Interval. The Cyclic Prex has following properties: Converts linear convolution to circular convolution Orthogonality is maintained

8 8 Shahram Zarei Figure 9: Guard interval in multicarrier systems (according to [3]) 2.7 Matrix representation of multicarrier systems based on DFT and CP The model discussed here consists of IDFT in the transmitter, the channel which is described by a channel coecient matrix, additive noise, which for simplicity is not considered here, and a DFT block at the receiver. a [n] are the complex-valued samples from the mapper, which are processed blockwise by the IDFT module. The mathematical description of the whole process is as follows: The vector with data symbols is given by: After the IDFT we get the samples in the time domain: The DFT matrix is dened as: a = [a[1],..., a[n]] T. (6) x = [x[1],..., x[n]] T = 1 N W H a. (7) W = ω ω N ω N 1 ω (N 1)(N 1), (8) with ω = e j 2π N. (9)

9 OFDM and Downlink Physical Layer Design 9 Appending the Cyclic Prex with the length of N 0 to the samples results in: x cp = [x[n N 0 + 1],..., x[n], x[1],..., x[n]] T, (10) and the relation between the signal at the input and the output of the channel is: y cp = Hx cp, (11) where H is the channel matrix and q h the order of the channel impulse response: H = h[0] h[1] h[0] h[2] h[1] h[0] h[q h ] h[q h 1] h[q h 2] h[0] 0 0 h[q h ] h[q h 1] h[1] h[0]. (12) After the removal of the Cyclic Prex we get: with H c as the cyclic channel matrix: y = H c x, (13) H c = h[0] 0 h[q h ] h[2] h[1] h[1] h[0] 0 h[3] h[2] h[2] h[1] h[0] h[4] h[3]..... h[q h ] h[q h 1] h[q h 2] h[0] 0 0 h[q h ] h[q h 1] h[1] h[0]. (14) After the DFT we get: a = 1 N Wy = 1 N WH c x = 1 N WH c 1 N W H a = 1 N WH cw H a. (15) A very interesting property of the cyclic channel matrix is: which leads to: WH c W H = WW H Λ, (16) or simply: a = 1 N WWH Λa = 1 NIΛa = Λa, (17) N

10 10 Shahram Zarei a = Λ a, (18) Λ = diag(λ 1, λ 2,..., λ N ), (19) λ i = q h µ=0 2πµ(i 1) j h[µ] e N, with i {1, 2,..., N}. (20) The λ i are the DFT coecients of the channel or the eigenvalues of the channel coecient matrix. At this point we have derived a very important feature of ODFM with Cyclic Prex, namely that the communication chain reduces to a diagonal matrix with the DFT of the channel coecients as diagonal elements, which means, if we want to equalize the channel, we have to multiply by the inverse of this diagonal matrix, which is also a diagonal matrix with inverted diagonal elements. In other words, we can simply multiply each output of the DFT module by its inverted channel coecient. 2.8 OFDM system parameter dimensioning An OFDM system has some key parameters, which have to be designed correctly depending on the considering scenario. The design parameters of OFDM are: f: Subcarrier spacing Demand in order to keep Doppler caused ICI low: f f dmax, f dmax : Max. Doppler shift T CP : Length of the Cyclic Prex To prevent ISI: T CP T d, T d : Length of the channel impulse response Demand for high spectral eciency: T CP T, T: OFDM symbol duration N: Number of subcarriers N < B f, B: OFDM signal bandwidth The physical layer parameters of the LTE downlink are summarized in Fig. 10. The technology used in LTE downlink is OFDMA, which stands for Orthogonal Frequency Division Multiple Access. In OFDMA, in contrast to OFDM, dierent subcarriers can be assigned to dierent users.

11 OFDM and Downlink Physical Layer Design OFDM drawbacks OFDM has two main disadvantages: Figure 10: LTE downlink physical layer parameters PAPR (or crest factor): Stands for Peak-to-Average Power Ratio and can be formulated as follows: PAPR = max{ x[n] 2 } (21) E{ x[n] 2 } Power ampliers for signals with high PAPR should be highly linear over a broad range. This makes the transmitters expensive. There are several solutions to overcome this problem. The rst and the simplest one is to use power ampliers with large back o e.g. using a 1 kw amplier for 100 W output power. This, however, is quite inecient. The second solution is to use algorithms, which reduce the PAPR without disturbing the main information content of the signal. Of course there is a certain signal processing complexity with PAPR reduction algorithms. Sensitivity to frequency osets: The second disadvantage of OFDM systems is their high sensitivity to frequency osets. This eect can be seen in Fig. 11 and 12. As we can see in Fig. 12, if there is a frequency oset between transmitter and receiver, the subcarriers are not orthogonal to each other anymore and this causes ICI (Inter Carrier Interference). To avoid this the local oscillator in the receiver should be well synchronized to the transmitter frequency.

12 12 Shahram Zarei Figure 11: Zero ICI Figure 12: Nonzero ICI if some frequency oset is present

13 OFDM and Downlink Physical Layer Design 13 3 Physical layer in downlink 3.1 LTE signal in time domain: Generic frame structure The LTE signal in time domain is based on frames, which are 10 ms long and consist of 10 subframes each of 1 ms duration. The subframes are divided further into two slots each 0.5 ms long. In each slot 7 or 6 OFDM symbols are contained depending on whether normal or short Cyclic Prex is used, cf. [1]. The time domain frame structure of the LTE downlink can be seen in the Fig. 13. Figure 13: LTE downlink signal structure in time domain 3.2 Resource management in LTE downlink physical layer LTE uses a three dimensional space to manage the resources time, frequency and space (antennas). In Fig. 14 only time and frequency dimensions are shown. The smallest unit is the so-called Resource Element (RE), which consists of a time interval of duration of one OFDM symbol and one subcarrier. Seven OFDM symbols (in case of normal CP length) or 6 symbols (in case of long CP length) build a time slot. The area consisting of 12 subcarriers (180 khz) and one time slot is called Resource Block and contains 12x7=84 Resource Elements in case of normal Cyclic Prex. Figure 14: Resource management in LTE downlink

14 14 Shahram Zarei 3.3 Downlink reference symbols In each Resource Block four so-called reference symbols are transmitted. The position of the reference symbols can be seen in the Fig. 15, cf. [7]. The main task of the reference symbols can be summarized as given below: Cell search and initial aquisition Channel estimation Coherent detection Channel quality estimation Figure 15: Reference symbols in LTE downlink 3.4 LTE downlink signal generation chain In Fig. 16 the components of the downlink physical layer signal generation chain can be seen. First a 24 bit CRC (Cyclic Redundancy Check) eld is introduced to detect errors in the receiver. After the CRC module comes a turbo encoder as forward error correction (FEC) channel coder. The LTE downlink turbo encoder has R = 1/3 as basic code rate and is (can be) with puncturing. There is an HARQ module following the turbo encoder. HARQ stands for Hybrid Automatic Repeat Request and is a mechanism based on stop and wait ARQ which transmits the packets again in case of errors detected by the CRC. In order to achieve more coding gain, a scrambling module based on a 31 bit Gold sequence is used after the HARQ module. The nal module is the modulator, which can use QPSK, 16QAM or 64QAM in LTE downlink, cf. [1].

15 OFDM and Downlink Physical Layer Design 15 In LTE there is the possibility to use MIMO. In this case an antenna mapping module decides on which antenna the packets are to be sent. In LTE downlink up to 4 antennas can be used. Finally the resource management module selects the appropriate resources, which are in LTE time slots and subcarriers to transmit the packet. Figure 16: Signal generation chain in LTE downlink physical layer 3.5 MIMO in LTE One of the important technologies used in LTE downlink is MIMO. MIMO stands for Multiple- Input Multiple-Output. In MIMO systems, independent parts of a data block are sent over uncorrelated antennas (with a minimum distance greater than e.g. 10λ to ensure uncorrelatedness). The number of transmit and receive antennas can vary from 1 to 4. For example a 4x4 system MIMO has four TX and four RX antennas. MIMO exploits the independency of the scattered signal components in a radio channel und makes some data rate gain possible. The greater the independencies between dierent paths in a channel with scattering, the higher the achieved data rate gains. Example: Downlink peak data rates (64QAM): MIMO (2x2): Mbps MIMO (4x4): Mbps

16 16 Shahram Zarei 3.6 Summary Figure 17: MIMO in LTE LTE is a high performance technology for mobile broadband services. OFDMA is the key core of the LTE downlink physical layer and makes signicantly higher data rates possible. With higher order modulation schemes (up to 64QAM), greater spectrum eciency is achievable. With the MIMO feature, the scattering behavior of the channel is used to increase data rate even more. References [1] E. Dahlman, S. Parkvall, J. Sköld, P. Beming: 3G Evolution: HSDPA und LTE for mobile broadband, 2007, Academic Press. [2] S. Sesia, I. Touk, M. Baker: LTE - The UMTS Long Term Evolution: From Theory to Practice, 2009, John Wiley Sons. [3] W. Koch: Lecture script "Fundamentals of Mobile Communications", 2008, University of Erlangen-Nuremberg. [4] R. Fischer, J. Huber: Skriptum zur Vorlesung "Digitale Übertragung", 2009, University of Erlangen-Nuremberg. [5] U. Barth: 3GPP Long Term Evolution / System architecture evolution overview, 2006, Alcatel. [6] J. Zyren, W. McCoy: Overview of the 3GPP Long Term Evolution physical layer [7] E. Seidel, V. Pauli: Nomor 3GPP Newsletter, Overview LTE PHY, Nomor Research