Design Error Performance of Space-Frequency Block Coded OFDM Systems with Different Equalizers and For Different Modulation Schemes
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1 International Journal of Electronics and Computer Science Engineering 84 Available Online at ISSN Design Error Performance of Space-Frequency Block Coded OFDM Systems with Different Equalizers and For Different Modulation Schemes 1 Rijhun Tripathi, 2 Ruchi Giri, 3 Amit Kumar 1 Assistant Professor, 2 3 Lecturer Department of Electronics & Communication 1 2 Vishveshwarya Group Of Institutes, G.B. Nagar, Uttar Pradesh,India rijhun25@gmail.com,ruchigiri14@gmail.com 3 Colleges of Engineering and Rural Technology, Meerut, Uttar Pradesh rasdee@gmail.com Abstract Multiple transmit and receive antennas can be used to form multiple-input multiple-output (MIMO) channels to increase the capacity (by a factor of the minimum number of transmit and receive antennas) and data rate. In this paper, the combination of MIMO technology and orthogonal frequency division multiplexing (OFDM) systems is considered for wideband transmission to mitigate inter symbol interference and to enhance system capacity. It owns the advantages of both MIMO and OFDM. MIMO-OFDM system exploits the space and frequency diversity simultaneously to improve the performance of system. The coding is done across OFDM subcarriers rather than OFDM symbols. In this paper, the performance of Space-Frequency (SF) block coding for MIMO-OFDM along with different equalizers is investigated. Bit Error Rate (BER) analysis is presented using different equalizers and then optimum equalization method is suggested. Keywords: MIMO-OFDM, Space-frequency Block coding, ZF Equalizer, Decision Feedback Equalizer, ML Equalizer. I. INTRODUCTION It is well known that multiple-input multiple-output (MIMO) systems increase the capacity and the diversity of wireless communication systems. Most of the current researches focus on designing MIMO codes to extract the multiplexing gain (increase spectral efficiency) [1] or the diversity gain (increase the link reliability) using orthogonal or quasi-orthogonal designs [2] [3] in wireless flat fading channels. However in both cases, the bit-errorrate (BER) performance and the spectral efficiency depend also on the outer codes associated to the MIMO schemes. For frequency selective channels, MIMO schemes can be combined with orthogonal frequency division multiplexing (OFDM) as space-time block coded (STBC)-OFDM or space-frequency block coded (SFBC)-OFDM [4] [5]. OFDM [6] is based on the principle of frequency division multiplexing (FDM), but is utilized as a digital modulation scheme via DFT. In OFDM, the entire channel is divided into N parallel narrow sub-channels depending upon IFFT size. Thus symbol duration becomes N times longer than in a single carrier system with the same symbol rate. The symbol duration is made even longer by adding a cyclic prefix to each symbol. As long as the cyclic prefix
2 Design Error Performance of Space-Frequency Block Coded OFDM Systems with Different Equalizers and For Different Modulation Schemes is longer than the channel delay spread, OFDM offers inter symbol interference (ISI) free transmission. Another key advantage of using OFDM is that it reduces the equalization complexity to great extent by enabling equalization in frequency domain. In this paper, we combine multiple transmit and receive antennas for OFDM to form MIMO- OFDM. The air-link architecture of MIMO-OFDM [7] has also been suggested for the future 4G wireless systems. MIMO-OFDM has potential to meet high data rate requirements and high performance over various challenging channels that may be time-selective and frequency selective. Further, MIMO channels can boost the capacity and the diversity of the system. The rest of the paper is organized as follows. In section 2, we introduce ST/SF Coded MIMO-OFDM transceiver model and briefly review the SF code design criteria for 2 1 and 2 2 systems. In section 3, various equalizer algorithms are presented along with their implementation issues in frequency domain. The simulation results are presented in section 4, and some conclusions are drawn in section 5. II. ST/SF CODED MIMO-OFDM SYSTEM MODEL ST coding combines coding with transmit diversity to achieve high diversity performance. ST coding can be implemented in two forms i.e. ST Trellis and block coding. In first scheme, information stream is encoded via M convolution encoders to obtain M streams of symbols but its decoding complexity increases exponentially as a function of diversity and transmission rate [8]. To address this problem Alamouti proposed Orthogonal ST block codes (OSTBC) for 2 1 and 2 2 systems. In this scheme at a particular time instant two symbols are simultaneously transmitted from the two antennas. The symbol transmitted from antenna one and two is S 0 and S 1.During the next time period symbol S 1 is transmitted from antenna 1 and S 0 from antenna 2. Where is the complex conjugate operation. This scheme is illustrated in Table 1. Table 1 SPACE-TIME SCHEME FOR 2 X 1SYSTEM Time TX 1 TX 2 T S 0 S 1 t + T -S 1 S 0 Diversity order can be increased for more reliable communication by employing two receiver antennas on receiver side as in Table 2. Table 2 RECEIVED SIGNALS AT TWO RECIEVERS Time RX 1 RX 2 t Y 11 Y 21 t + T Y 12 Y 22 For some applications, where reliability is of more concern we can increase the diversity order [3] to 2N. N is the number of receiving antennas but the number of transmitting antenna will remain 2. Unfortunately, OSTBC also lacks in providing any coding gain and to achieve a rate larger than 3/4 [10] for more than two transmit antennas. In SF scheme, coding is done across antennas and OFDM sub-channels. SF coding [11. 12] can be realized by applying the Alamouti code over two adjacent sub-channels in one OFDM block as in Table 3. Table 3 SPACE-FREQUENCY SCHEME FOR 2 TX SYSTEMS Antenna OFDM Sub-channel TX 1 S 0 -S 1 TX 2 S 1 S 0
3 IJECSE,Volume1,Number 1 Rijhun Tripathi et al. 86 Table 3 shows that two symbols S 0 and S 1 are sent from sub-channels K and L of the same OFDM block through transmitting antenna 1. Similarly symbols S 1 and S 0 are sent from sub-channels K and L of the same OFDM block but through transmitting antenna 2. However, this simple SF coding approach can only achieve space diversity gain, whereas the maximum diversity gain in MIMO-OFDM system will equal to NMD [6]. Where D is number of coherence bandwidths. Research is going on in improving above parameter. The general transceiver structure of MIMO-OFDM is presented in Figure 1. MIMO channel in the presented model consists of 2 transmit and receive antennas. First the incoming data stream is mapped into data symbols via some modulation technique like BPSK, 16-QAM (in this paper).a serial to parallel converter (SPC) coverts the incoming symbols into number of parallel sub-streams. Number of parallel streams depends upon the number of transmitting antennas (2 in this paper). X ( m ) Serial to Parallel Space-Freq Encoder X 1 (n) X 2 (n) IDFT & Cyclic Prefix IDFT & Cyclic Prefix Tx Tx h1(n) h2(n) Rx X % ( m) Parallel to Serial Space-Freq Decoder Y(n) Prefix Removal & DFT xe xo X 1 ( n) = X 2 (n) = x o xe Channel Estimator Figure 1: Block diagram of space-frequency coded MIMO-OFDM transmitter diversity system. Therefore, a signal vector S = {s[0], s[1],, s[n t 1]} is provided as the input to of SFBC encoder where N t is equal to the number of transmitting antenna. Let us define sub-blocks s 1 [k] and s 2 [k] as s 1 [k]=(s[2k] -s [2k +1]) and s 2 [k]=(s[2k +1] s [2k]) respectively (Figure 1). Then, the orthogonal block code for two transmit antennas can be written as SFBC provides two blocks S 1 and S 2, each of the length N, for OFDM at the transmitter. In order to utilize the space-frequency diversity, the input blocks are encoded as shown in table 3. After applying the SFBC-OFDM with cyclic prefix, which maps each symbol at a particular subcarrier, the OFDM symbols are transmitted from each antenna through the time varying multipath fading channel. The received signal from two receiving antennas after OFDM demodulation are sent to linear combiner, which combine the input signals to form composite output signal, ( j i ) The combining scheme for system in figure1 is suggested by Alamouti [2]. Let H diag H [ k] j, i, N 1 = is an N N diagonal matrix with elements corresponding to the DFT of the channel response between the i-th transmit and j-th receive antennas. Under the assumption that the CSI is known at the receiver, the different detection scheme and equalizer can be used for decoding the received signal. This detection scheme can be written as: N r S% [ k] = ( h,1 2n r 2n h,2 2n r 2n 1 j 1 j j + j j + = N r S% [2k + 1] = ( h,2 2n 1 r 2n h,1 2n 1 r 2n 1 j 1 j + j j + j + = [ ] [ ] [ ] [ ] (1) [ ] [ ] [ ] [ ] (2) k = 0
4 Design Error Performance of Space-Frequency Block Coded OFDM Systems with Different Equalizers and For Different Modulation Schemes The combined signal is then equalized by applying different equalizers like Zero-forcing (ZF), Decision feedback equalization (DFE) and Maximum likelihood (ML) detector which are discussed in section 3. A. Equalization The inter-symbol interference (ISI) caused by multipath MIMO channels distorts the MIMO-OFDM transmitted signal which causes bit errors at receiver. To minimize this ISI equalization [13] is needed. Equalizer minimizes the error between actual output and desired output by continuous updating its filter coefficients. Equalization can be done in both time and frequency domain. Equalization in frequency domain is simpler to use as compared to time domain. In this paper various equalizers like ZFE, DFE and ML detection are implemented in frequency domain and their performance evaluation is done in terms of bit error rates (BER). 1) Zero-Forcing (ZF) Equalization In ZF equalizer [14] the coefficients are chosen to force the samples of the combined channel and equalizer impulse response to zero. The combined response of the channel with the equalizer is given by (3) ( ) ( ) H f H f = 1 (3) channel equalizer Where H channel (f) is folded frequency response of the MIMO-channel and H equalizer (f) is frequency response of equalizer. Equations (1) and (2) show the combined MIMO-OFDM symbols at receiver 1 and 2. ZF equalizer can be realized by multiplying the (1) and (2) by vector 1/H(k).Where H (k) is the normalized MIMO-channel vector which can be formed as shown in (4). H = H 11. H 12 + H 21. H 22 (4) In this case, the equalizer filter compensates for the channel-induced ISI as well as the ISI brought about by the transmitter and receiver filters. Zero-Forcing filter designed using the equation above does not eliminate all ISI because the filter is of finite length. 2) Decision Feedback Equalizer (DFE) In DFE [15] once an input symbol has been detected, the ISI that it induces on future symbols is estimated and subtracted out before detection of subsequent symbols. DFE is realized in direct transversal form which consists of feed forward filter (FFF) and a feedback filter (FBF) as shown in Fig. 2. The FBF [15] is driven by decision on the output of the detector, and its coefficients are adjusted to cancel out the ISI on the current symbol from past detected symbols.
5 IJECSE,Volume1,Number 1 Rijhun Tripathi et al. 88 Input Transversal Filter + Adaptive Weight Algorithm - Desired Response Figure 2: Schematic of Decision Feedback Equalizer RLS (recursive least squares) algorithm is used for determining the coefficient of an adaptive filter [16]. RLS algorithm uses information from all past input samples to estimate the autocorrelation matrix of the input vector. To decrease the influence of input samples, a weighting factor for the influence of each sample is used. First process is the filtering in which RLS computes the output of a linear filter in response to an input signal and generates an estimation error. Second is the adjustment of parameters of the filter in accordance with the estimation error. Reconsider equation 3 and multiply it with weight vector w yields (5). ( ) ( ) ( ) r n w H n C n = (5) Equation (5) describes the filtering portion of the algorithm. Transversal filter is excited to compute error estimates given by (6). All subscripts are omitted for simplification ( ) ( ) ( ) e n d n r n = (6) Where nr is the desired response and is given by (7).Equation (8) describes the adaptive operation in which the tap-weight vector is updated by incrementing its old value by an amount equal to the complex conjugate of the estimation error. d ( n) = w r ( n) (7) w( nr + 1 ) = w ( nr ) + µ C (n) e (n) (8) Where nr is number of iterations and µ is step size, which controls the convergence and stability of algorithm. 3) Maximum Likelihood (ML) Detection In more practical situations we choose ML [16, 17] based equalizer which tests all possible data sequences and chooses the data sequence with the maximum probability as the output. It requires knowledge of channel characteristics in order to compute the metrics for making decisions. It also requires knowledge of statistical distribution of the noise, which determines the form of metric for optimum demodulation of the received signal. Assuming that perfect channel state information is available, the receiver chooses S = (s 1, s 2,., s N ) from the transmission constellation C that minimizes the following decision metric (9): Nr L N 2 2 t r Hs = d rt, m, hn, ms n, t m= 1 t= 1 n= 1 (9) The minimization of (1, 2) results in a ML decoding, which can alternatively be represented by
6 Design Error Performance of Space-Frequency Block Coded OFDM Systems with Different Equalizers and For Different Modulation Schemes 2 sˆ = arg min r Hs s C 2 Where A denotes the Euclidean norm of matrix A defined by ( H ) ( ) (10) A tr A A, tr A and A H =, respectively, denotes the trace and Hermitian transpose of matrix A, and d 2 (a,b) is the squared Euclidean distance between signals a and b calculated by 2 (, ) ( )( ) 2 d a b = a b = a b a b (11) Above equations holds good for all data sequences. Decoding complexity increases exponentially by increasing number of transmitting and receiver antennas in such cases joint detection will be used like sphere decoding [9]. B. Quadrature amplitude modulation (QAM) "Q-A-M" is both an analog and a digital modulation scheme. It conveys two analog message signals, or two digital bit streams, by changing (modulating) the amplitudes of two carrier waves, using the amplitude-shift keying (ASK) digital modulation scheme or amplitude modulation (AM) analog modulation scheme. The two carrier waves, usually sinusoids, are out of phase with each other by 90 and are thus called quadrature carriers or quadrature components hence the name of the scheme. The modulated waves are summed, and the resulting waveform is a combination of both phase-shift keying (PSK) and amplitude-shift keying (ASK), or (in the analog case) of phase modulation (PM) and amplitude modulation. In the digital QAM case, a finite number of at least two phases and at least two amplitudes are used. PSK modulators are often designed using the QAM principle, but are not considered as QAM since the amplitude of the modulated carrier signal is constant. QAM is used extensively as a modulation scheme for digital telecommunication systems. Spectral efficiencies of 6 bits/s/hz can be achieved with QAM. QAM modulation is being used in optical fiber systems as bit rates increase QAM16 and QAM64 can be optically emulated with a 3-path interferometer 1) QAM comparison with other modes As there are advantages and disadvantages of using QAM it is necessary to compare QAM with other modes before making a decision about the optimum mode. Some radio communications systems dynamically change the modulation scheme dependent upon the link conditions and requirements - signal level, noise, data rate required, etc. The table below compares various forms of modulation: Modulation Bits per symbol Error margin Complexity OOK 1 1/2 0.5 Low BPSK Medium QPSK 1 1 / Medium 16 QAM 4 2 / High 64QAM 6 &radic / High
7 IJECSE,Volume1,Number 1 Rijhun Tripathi et al. 90 III. SIMULATION RESULTS AND DISCUSSION Simulation results are plotted for BER with variation in signal to noise ratio (SNR) in MIMO-OFDM system. Simulation are carried out in two phases, in first phase results are plotted considering 2 transmit and 1 receiving antenna and in second phase results are plotted considering 2 transmit and 2 receiving antenna. The channel experienced by each transmitting antenna is considered to be independent of each other. It is also assumed that transmitting power of each transmitting antenna is same. Further, we assume that the receiver has perfect knowledge of the channel. Figure 3 (a) and 3 (b) shows BER performance for 2 1 MIMO-OFDM system using BPSK and 2 2 MIMO- to 10-4 at SNR of 16dB in OFDM system using 16-QAM data modulation techniques. Using BPSK BER gets reduced first sub-plot and around 10-3 at SNR of 11 and 10 db in subsequent sub plots. Whereas using 16-QAM BER reduced to 10-3 at SNR of around 25 in first sub-plot and around 18 and 14 db in other sub-plots. Thus BER performance is comparatively better in BPSK than 16-QAM. Comparing Figure 3 (a) and (b) it can be clearly observed that employing 2 receivers greatly enhance the system performance. Among equalizers ML equalizers dominates other mentioned equalizers. Fig. 3 (a) BER performance for 2 1 MIMO-OFDM system using BPSK
8 Design Error Performancee of Space-Frequency Block Coded OFDM Systems with Different Equalizers and For Different Modulation Schemes Fig. 3 (b) BER performance for 2 2 MIMO-OFDM system using 16 QAM IV. CONCLUSION In this paper, we studied 2 1 and 2 2 MIMO-OFDM system performance under mobile radio channel using Alamouti based SF coding. Further, the system performance is compared with different equalizers in frequency domain. A significant performancee gain is observed by employing equalizers along with Alamouti scheme. It is already mentioned that the diversity gain as reference to Fig. 1 is 4. Mentioned system does not showing full-diversity so research is going for full-diversity rate 1 codes. Rate can be further enhanced by employing algebraic SF codes. The high-rate SFBC mostly relies on joint detection and thus increases the decoding complexity. This decoding burden can be alleviated by an approximate ML decoding, known as sphere decoding. System performance can further be improved by extending coding in three dimension i.e. space, time and frequency such codes are called STF codes. STF codes further increase the complexity of the system. V- REFERENCES [1] P. W. Wolniansky, G. J. Foschini, G. D. Golden and R. A. Valenzuela, V-Blast: An architecture for realizing very high data rates over the rich scattering wireless channels, Proc. of URSI Intl. Sym. on Signals, Systems, and Electronics, pp , [2] S. M. Alamouti, A simple transmitter diversity scheme for wireless communications, IEEE J. Select. Areas Communication, vol.16, pp , [3] V. Tarokh, H. Jafarkhani and A. R. Calderbank, Space-time block codes from orthogonal designs, IEEE Trans. on Information Theory vol.45, pp , 1999.
9 IJECSE,Volume1,Number 1 Rijhun Tripathi et al. 92 [4] K. F. Lee, D. B. Williams, A space-time coded transmitter diversity technique for frequency selective fading channel, Proc. of IEEE Sensor Array and Multichannel Signal Proc. Workshop, vol.1, pp , [5] H. Bolcskei, A. Paulraj, Space-frequency codes for broadband fading channels, Proc. of IEEE Int. Communication Conf.(ICC), pp , [6] Y. Li and G. L. Stüber, Orthogonal Frequency Division Multiplexing for Wireless Communications, Springer, [7] H. Bölcskei, MIMO-OFDM Wireless Systems: Basics, Perspectives and Challenges, IEEE Wireless Commun., vol. 13, no 4.,pp Apr [8] S. N. Diggavi et al., Great Expectations: the Value of Spatial Diversity in Wireless Networks, in Proc. IEEE, vol. 92, no. 2, pp , Feb [9] J. Ylioinas and M. Juntti, Iterative Joint Detection, Decoding, and Channel Estimation in Turbo-Coded MIMO-OFDM IEEE Trans. Veh. Technol., vol. 58, no. 4, pp , Apr [10] P. Elia et al., Explicit Space-Time Codes Achieving the Diversity-Multiplexing Gain Trade-Off, IEEE Trans. Inf. Theory., vol. 52, no. 9, pp , Sep [11] Andreas A. Huttera, Selim Mekrazib, Beza N. Getuc and Fanny Platbrooda, Alamouti-Based Space-Frequency Coding for OFDM, in Springer journal of wireless personal communications., vol. 35, no. 1-2, pp , [12] Zhang Wei, Gen Xia Xiang and K. Ben Letaief, Space-time/frequency coding for MIMO-OFDM in next generation broadband wireless systems, in IEEE Wireless Commun., vol. 14, no. 3, pp , June [13] Philip Schniter, Low-Complexity Equalization of OFDM in Doubly Selective Channels, IEEE Trans. Signal Process., vol. 52, no. 4, pp , Apr [14] Rui Zhang and J.M Cioffi, Approaching MIMO-OFDM Capacity With Zero-Forcing V-BLAST Decoding and Optimized Power, Rate, and Antenna-Mapping Feedback, IEEE Trans. Signal Process., vol. 56, no. 10, pp , Oct [15] Rih-Lung Chung, Chin-Wen Chang and Jeng-Kuang Hwang, Bidirectional decision feedback equalization for mobile MIMO-OFDM systems, in proc., of international Symposium son Information Theory and its Applications (ISITA), pp , [16] Hun-Hee Lee, Myung- MIMO Sun Baek, Jee-Hoon Kim and Hyoung-Kyu Song, Efficient detection scheme in OFDM for high speed wireless home network system, IEEE Trans. Consum. Electron., vol. 55, no. 2, pp , Feb [17] Tsung Hui Chang, Wing-Kin Ma and Chong-Yung Chi, Maximum-Likelihood Detection of Orthogonal Space-Time Block Coded OFDM in Unknown Block Fading Channels IEEE Trans. Signal Proces., vol. 56, no. 4, pp , Apr
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