CHAPTER 3 MIMO-OFDM DETECTION

63 CHAPTER 3 MIMO-OFDM DETECTION 3.1 INTRODUCTION This chapter discusses various MIMO detection methods and their performance with CE errors. Based on the fact that the IEEE 80.11n channel models have high SFCF, a low complexity method of implementing the MIMO- OFDM detectors is proposed with no significant performance degradation. The performance analysis is based on simulation which was done for the TGn sync proposal and with various MIMO detection algorithms. The effect of CE on the system performance is also studied. The chapter is organized as follows, the first section discusses the simple MIMO system model with a flat fading channel between the transmitter and receiver antenna pair. In section 3.3. various MIMO detection methods are employed for the system model established and the performance of the schemes are discussed with simulations. Section 3.4 discusses the system model of the MIMO-OFDM system and a low complexity method of implementing the MIMO detectors with representative results. In section 3.5, the performance of the TGn sync system with various CE schemes discussed in chapter is discussed with various MIMO detectors. Finally the performance of the TGn system in terms of packet error rate (PER) is obtained by simulations for the low complexity method.

64 3. MIMO SYSTEM MODEL A simple MIMO system model shown in Figure-3.1 is established for discussing the MIMO detection algorithms and to extend the idea to the MIMO- OFDM system. In Figure-3.1 a system with N t transmit and N r receive antennas is shown. Let us assume that N t =N r = as it is the mandatory mode of operation in the 80.11n proposals. h 11 b 1 (n) MOD x 1 (n) h 1 h 1 w 1 MIMO Detector x 1(n) Demod b 1(n) b (n) MOD x (n) h w x (n) Demod b (n) Figure 3.1: A simple x spatial multiplexing MIMO system The two streams of incoming bits are modulated to symbols and transmitted simultaneously from the two antennas. According to the flat fading channel assumption, there is a single tap between every transmit-receive antenna pair. The channel taps are Rayleigh distributed and independent of each other. The AWGN is added at the front end of the receiver. The received signal on the two antennas are passed into the MIMO detector block, whose function is to separate out the spatially combined signal transmitted from the multiple antennas, with the knowledge of the channel coefficients. The output of the MIMO detector block is passed through the demodulator for obtaining the bits. In these spatial multiplexing systems, no explicit orgthogonalization or coding is necessary at the transmitter for signal decorrelation; instead the propagation medium with rich multipath scattering can be used at the receiver for separating out the spatially combined transmitted streams (Arogyaswami Paulraj et al, 003).

65 The received signal in the matrix form is written as, y1() n h11() n h1() n x1() n w1() n y () n = h () n h () n + x () n w () n 1 (3.1) N t yn ( ) = hi( nx ) i( n) + wn ( ) (3.) i= 1 Where yn ( ) is the N r x1 vector of received signal, hi ( n ) is the i th column of the MIMO channel matrix whose elements are Rayleigh distributed, xi ( n ) is the symbol transmitted from the i th transmit antenna in the nth symbol time and wi ( n ) denotes the N r x1 AWGN vector. The channel information is needed at the receiver for the MIMO detector to decode the streams. 3.3 MIMO DETECTORS The MIMO detectors which are popular in the literature (David Tse, 005) and used in practice are decorrelator, MMSE, successive interference cancellation (SIC), VBLAST, ML method. The decorrelator and the MMSE are linear MIMO detectors, whereas the rest of the methods mentioned are non linear methods. 3.3.1 Decorrelator below, where The received signal vector in equation (3.) can be written as given x k is the desired data stream and it faces interferences from the remaining k-1 streams. The index for symbol period is dropped for simplicity. y= hkxk + hx i i+ w (3.3) i k The interference faced by the k th data stream from the remaining streams can be perfectly cancelled by projecting the received signal onto the subspace orthogonal to the one spanned by h1, h... hk 1, hk+ 1... hnt. Let V k be the basis of the new subspace. The signal vector after projection is given by

66 y' = V y= V hkx + w' (3.4) k k k The demodulation of the k th stream can be performed by match filtering on the signal to get the unquantized estimate of the data symbol on the k th stream, x kuq, and quantization is finally applied to obtain data symbol on the k th stream, x k, which is given below, H kuq, = ( Vk k) Vk k k + ( Vk k) x k = Q( xk, uq) x h h x h w' H (3.5) The combination of projection operation followed by the matched filter is called the decorrelator or zero forcing (ZF) detector. A simple formula for demodulating all the streams at once, is given by H H where = ( ) 1 uq x = HHx+ H w (3.6) H H H H, is the pseudo inverse of H. The ZF detector suffers from noise enhancement especially in the lower SNR range as it tries to completely null out the interference without regard to the loss in energy of the desired stream. 3.3. Linear MMSE As we have already discussed, since the decorrelator completely cancels out the interference, it performs better in higher SNR range. On the other hand, the matched filtering or maximal ratio combining receiver tries to maximize the output SNR of the desired stream. The matched filtering receiver performs well in the lower SNR case where the AWGN is dominant and in the higher SNR range it suffers from heavy inter-stream interference. Thus, there exists a tradeoff between completely eliminating the inter-stream interference and preserving as much energy content of the stream of interest. The linear detector which optimally combines the decorrelator and the matched filter is the MMSE detector, which is shown in the Figure-3..

67 y = H x+ w V mmse x uq - x + e min Figure 3.: A simplified MMSE detector Q (.) x The objective function of the MMSE MIMO detector is given by, V = arg min E x x = E VHx+ V w x (3.7) V V uq arg min { } Using Wiener-Hopf equation and solving for the optimal solution leads to the MMSE solution matrix given by H σ n Vopt = Vmmse = H H H+ I (3.8) σ s The data symbols transmitted on all the streams, x is obtained as follows, 1 1 H H σ n H xuq = ( Vmmse ) y = H H+ I y H σ s x= Q( xuq ) (3.9) From the MMSE solution matrix given in equation (3.8) it can be observed that at higher SNR values it is very close to the pseudo inverse of H matrix, which is the decorrelator. On the other hand, for lower SNR values, the solution is close to the H H, which is the MRC or matched filtering. Thus, the MMSE detector performs better compared to the ZF detector; however, the SNR of operation is required for obtaining the solution matrix. 3.3.3 Successive interference cancellation (SIC) The SIC is a non linear MIMO detection scheme in which a linear detector is used to decode a stream and subtract it off from the received vector and detect the next stream and this process continues till all the data streams are detected. Thus, at each stage the number of interfering streams decreases. The SIC

68 scheme is explained in the flow chart shown in Figure-3.3. The post detection SNR of the i th data stream is defined as, { x i } E ρi = (3.10) σ W i n Input H, y i=1; H 1 =H W i W i = ( Hi ) is the ith row of H i x i = Q( W iyi ) ( ) with dimension N x1 i r matrix i=i+1 Is i = N t Yes [ H] i+1 i [ ] i 1 i i where is the ith column of H matrix H i y = + y x H is obtained by making No zeroing columns 1,,...i+1 of H STOP Figure 3.3: Flow chart of the SIC Decorrelator For the linear detection schemes, the post detection SNR remains the same for all the streams. However, for the SIC method, the post detection SNR of the stream increases in each stage and it is lower bounded by their corresponding post detection SNR obtained without interference cancellation. Thus, the performance of the SIC scheme is better compared to its corresponding linear detection scheme. It is assumed that the stream detected at each stage is perfect, however, the wrong decisions may lead to error propagation. The SIC scheme

69 described here follows an arbitrary ordering; for instance, order can be from stream 1 to N t. 3.3.4 VBLAST The order in which the streams are detected in the SIC impacts the performance as it might lead to error propagation. The VBLAST detection scheme is same as the SIC method except that it follows an order for detection of the streams at each stage. It is also called as ordered SIC (OSIC). It is proved in (Wolniansky et al, 1998) that by simply choosing the best ρ i at each stage in the detection process leads to the globally optimum ordering. The ZF-VBLAST scheme is shown in the flow chart in Figure-3.4, in which the ZF scheme is used for detection. The MMSE-VBLAST is also an ordered SIC, in which the MMSE filter is used for detecting the streams and the ordering is based on the maximum post detection SINR (Hufei zhu, 004). The stream which corresponds to the minimum value in the main diagonal of the matrix, 1 H σ n H H+ I is detected first and the effect of that stream is removed σ s from the received signal and process is iterated to get all streams. The MMSE- VBLAST has the advantage of both MMSE detection and optimal ordering in the SIC maximizing the output SINR at each stage and hence it performs better than the ZF-VBLAST. 3.3.5 Maximum likelihood detection The objective function of the maximum likelihood detection is given as Where x xml = arg min y H x (3.11) x takes all possible combinations of all symbols from all streams. The ML method is the optimal and it chooses the transmit symbol vector

70 which minimizes the Euclidean norm between the received signal and all possible combinations of constellations from multiple transmit antennas. The number of possible combinations is given by M N t, where M is the constellation size. The search space increases exponentially with number of antennas and the constellation size. Though the ML method is the optimal, it is computationally complex. Input: H, r Intialization i=1 G = H 1 k = arg min ( G ) 1 1 j j Where ( G ( ) W = G ki i k i i ) ki correspond to i=i+1 the k i th column of G i ki T ki y = W r a = Q i ( y ) k k i i Is i = N t Yes No Where r = r a i+ 1 i k k i G i+ 1 ( H i ) = H ki ki H is the matrix obtained by zeroing columns k 1,k..k i of H k i + 1 = arg min G i + 1 j j k k k ( ) { 1,.. j} STOP Figure 3.4: Flow chart of the VBLAST scheme

71 3.4 MIMO-OFDM SYSTEM The simplified MIMO-OFDM system is shown in Figure-3.5 with N t =N r =. The incoming symbols are made into a block of size N, where N is the number of subcarriers and OFDM symbols are constructed and transmitted from the antennas. The received signal is obtained by passing the transmitted signals through the multipath channels and AWGN is added at the receivers. h 11 (n) X ( k ) 1 s / p I F F T p / s CP h 1 (n) w 1 (n) CP s / p F F T p / s Y 1 ( k ) X 1 ( k) h 1 (n) MIMO Detector X ( k ) s / p I F F T p / s CP h (n) Multipath channel w (n) Figure 3.5: MIMO-OFDM system CP s / p F F T p / s Y ( k ) X ( k) At the receiver, the typical OFDM receiver operations are done in the two antennas separately to obtain the frequency domain signals. The MIMO detector is applied at each subcarrier to detect the data transmitted on that subcarrier. Thus, the MIMO-OFDM system can be viewed as N parallel MIMO systems with flat fading channel coefficients and the detection has to be performed on each subcarrier independently (Allert Van Zelst, 004). The system forms the basis for the IEEE 80.11n standard proposals. 3.4.1 Mean square error of detection The mean square error (MSE) between the transmitted data symbols and the output of the detection algorithm is a good measure for the performance of MIMO detection algorithms though there is no simple relation with BER or PER. Since the MSE can be derived for the MIMO detection algorithms, we use the MSE as performance metric for comparing the various MIMO detection

7 processes. However, the entire system performance result including the effects of the encoder etc., can be obtained in terms of the BER and PER and we also show these simulation results in section 3.4.4. It has been seen in simulations and in other studies that a reduction in MSE leads to a reduction in the BER. The system model is shown in Figure-3.5. The MSE is given as follows, MSE= E { xn ( ) xn ( ) } (3.1) The closed form MSE for the decorrelator and the MMSE detector is derived in Appendix and is given as follows, decorr H H { } MSE = E w V V w (3.13) { ( 1) } { ( ) } Re { ( 3) } MSEmmse = Ntσu + NtσuE trace G + NtσnE trace G Ntσ u E trace G (3.14) 3.4. Low complexity MIMO detection In a MIMO-OFDM system with N subcarriers typically, we need to employ N independent MIMO detectors. The system complexity increases with the increasing number of antennas and particularly in OFDM systems, the complexity is still more as we might need to employ N parallel MIMO detectors. In this work, a low complexity solution for a certain type of MIMO detectors is proposed. The idea is to reduce the number of MIMO detectors applied for detecting the data in all the subcarriers. As previously discussed, the IEEE 80.11n channel models have significant amount of correlation across subcarriers. This frequency correlation among the adjacent subcarrier can be used to reduce the complexity of the MIMO-OFDM system. Since the channel matrices for adjacent subcarriers are similar, instead of independently employing MIMO detectors in all the subcarriers, only the solution for the MIMO detector on alternate subcarrier positions are found. The solution for the other subcarriers is

73 found by interpolating the solutions obtained for the neighboring subcarriers. Linear interpolation using weights which are simple to implement can be used. Let k-1 and k+1 be the subcarrier positions where the direct solution for MIMO detection is obtained and let k be the subcarrier position in which the solution is obtained by linear interpolation as given by, + = V V k 1 k+ 1 V k (3.15) Where V k is the matrix solution for MIMO detection. If the number of complex multiplications is L for a single MIMO detector, the number of complex multiplications for applying the MIMO detector independently on each subcarrier is NxL and with this low complexity method, it becomes (NxL)/. Thus, there is a 50% reduction in the complexity when compared to the normal MIMO-OFDM detection methods. Another notable advantage of this method is that there is no need for the channel estimates on alternate subcarriers. This idea can be used for ZF, MMSE, MMSE-SIC, ZF-SIC detection method. It cannot be directly applied to the VBLAST based detection schemes, since the order in which the detection is performed varies for each subcarrier. 3.4.3 Complexity comparison The computational effort needed for the MIMO detectors so far discussed is shown in the Table-3.1. The number of complex multiplications tabulated here is calculated by considering detection on all the streams and on all the N subcarrier (Mohammed Alamgir, 003). The computations required for various MIMO detection methods is plotted for,3,4 transmit and receive antennas is plotted in Figure-3.6. The value of N assumed is 56. The decorrelator/zf solution is the pseudoinverse of the channel matrix. The MMSE solution requires matrix multiplications and a normal matrix inverse. The number of complex operations of the MMSE method is less than that

74 of the ZF since the pseudoinverse requires more computations. The non-linear methods such as ZF/MMSE-VBLAST require more amount of computations as compared to linear methods as SIC is done and the ordering and filters need to be calculated for every transmit stream, but as the iteration progresses the number of complex operations per iteration decreases, because of the reduced (deflated) channel matrix as there is a decrease in inter-stream interference. The ZF- VBLAST requires more complexity than the MMSE-VBLAST for the reason mentioned earlier (Pseudoinverse requires more complexity than normal inversion). From Figure-3.6 it can be seen that the low complexity detectors LC- ZF/LC-MMSE have almost half the complexity reduced because of using interpolated solutions. The complex operations for finding the interpolated solutions are also included, however, the complexity is drastically reduced, since the linear interpolation (or) simple averaging doesn t increase the computations. The ML detection requires huge amount of complexity which increases exponentially with more number of transmit and receive antennas since the search space increases drastically. Thus, ML is generally not preferred for implementation as compared to other non linear schemes like ZF/MMSE- VBLAST. Table 3.1: Complexity comparison MIMO detector No. of. Complex operations Decorrelator 3 N( 5Nr Nt + Nt + Nt ) MMSE N( 5N 3 t + N t N r + N t ) LC-ZF LC-MMSE ZF-VBLAST MMSE-VBLAST N N N N N N N 3 ( 5 r t + t + t + t r) N N N N N N N 3 ( 5 t + t r + t + t r) N t N N i i N i= 1 ( 5 3 r + + t ) N t N i N i N i i= 1 3 ( 5 r + r + )

75 18 x 104 No.of. COMPLEX MUL and ADD 16 14 1 10 8 6 4 ZF LC-ZF MMSE LC-MMSE ZF-VBLAST MMSE-VBLAST 0 3 4 No.of. Antennas Nt=Nr Figure 3.6: Comparison of computational complexity for various MIMO detection schemes 3.4.4 Simulation results and discussion This subsection presents the simulation results for the MIMO detection algorithms discussed so far and the effect of CE on the system performance. The system model assumed for the simulation is shown in Figure-3.5. As already discussed, the MIMO detection schemes discussed in section 3. is applicable to the MIMO-OFDM system at the subcarrier level. The system parameters used are given as follows; the number of subcarriers, N is 64, the CP 16 samples, the bandwidth is equal to 0MHz, and QPSK modulation is used. The TGn channel model D in NLOS condition is considered here. All results are obtained for 10000 independent realizations of channel and AWGN. Ideal synchronization is assumed between the transmitter and the receiver. The MSE of the MIMO detection scheme for a x system is shown in Figure-3.7 for decorrelator/zf, MMSE, ML, VBLAST-ZF and VBLAST-MMSE detection methods. From the figure it can be observed that the MSE performance

76 of the ML detector is better than that of all the other schemes. However, the ML method is computationally complex. The MSE of the ZF detector is directly proportional to the noise variance and it decreases linearly as the Eb/No increases. The MMSE detector has a small value MSE in lower Eb/No region compared to that of the ZF detector since it does not lead to noise enhancement. However, as Eb/No increases, the MSE tends to approach the MSE of the ZF detector. This is because in the higher Eb/No region, the performance degradation is mainly due to inter stream interference. The VBLAST-ZF/MMSE has better MSE performance compared to the normal ZF/MMSE method because of the OSIC. 10 10 1 10 0 ZF MMSE VBLAST-ZF VBLAST-MMSE ML 10-1 MSE 10-10 -3 10-4 10-5 10-6 0 5 10 15 0 5 30 35 Eb/N0 in db Figure 3.7: MSE performance of various MIMO detection schemes for x system in channel D, NLOS A similar plot for 4x4 system is shown in Figure-3.8. It can be observed from the figure that VBLAST-ZF & VBLAST-MMSE perform well. This is because the OSIC for 4 streams cancels the interference in successive stages to get more diversity advantage as discussed in section 3.3.

77 10 10 1 ZF MMSE VBLAST-ZF VBLAST-MMSE 10 0 MSE 10-1 10-10 -3 10-4 0 5 10 15 0 5 30 35 Eb/N0 in db Figure 3.8: MSE performance of various MIMO detection schemes for 4x4 uncoded system in channel D, NLOS 10 10 1 LC-ZF LC-MMSE ZF MMSE 10 0 MSE 10-1 10-10 -3 0 5 10 15 0 5 30 35 Eb/N0 in db Figure 3.9: MSE performance of various low complexity MIMO detection schemes for x uncoded system in channel D, NLOS

78 The MSE performance of the low complexity MMSE and decorrelator is plotted in Figure-3.9. The figure shows that the low complexity MMSE/decorrelator method performs very close to normal MMSE/decorrelator method till a point in SNR of 10 db and has an error floor thereafter and it is because of using the interpolated solutions on alternate subcarrier positions as explained in section 3.4. The BER performance of the MIMO detection schemes is plotted in Figure-3.10. We can observe that the performance of the MIMO detection schemes in BER terms is in accordance with their MSE performance i.e., the order in which the schemes perform is same both in terms of the BER and the MSE. The LC-ZF/LC-MMSE detector performs close to ZF/MMSE till about 15dB of Eb/N0 and has an error floor of 10 - in BER, which is quite high. Thus, the LC-ZF/LC- MMSE are not suitable for uncoded systems, however, it performs well in IEEE 80.11n systems which will be discussed in later sections. 10 0 10-1 10 - BER 10-3 10-4 10-5 ZF MMSE VBLAST-ZF VBLAST-MMSE ML LC-ZF LC-MMSE 10-6 0 5 10 15 0 5 30 35 Eb/N0 in db Figure 3.10: BER performance of various MIMO detection schemes for x uncoded system in channel D, NLOS

79 The performance of the system is affected by the errors in CEs. The following simulation results show the effect of different CE schemes on the system performance in terms of BER. The preamble used here is of the TO type which is discussed in chapter. The estimation schemes used are LS, LMMSE, TMMSE with complex weights, and LCCE. The MMSE MIMO detector is used. The BER plot for x system for the different CE schemes is shown in Figure- 3.11. The BER performance of the system with LMMSE CE scheme is very close to that of the system with ideal estimation and TMMSE3 with complex weights and LCCE schemes have almost similar effect on the BER performance which is quite closer to that of the LMMSE CE. The LS CE results in 3 db loss in system performance compared to that of the ideal estimation. 10 0 10-1 Ideal LS LCCE LMMSE TMMSE 10 - BER 10-3 10-4 10-5 0 5 10 15 0 5 30 35 40 45 SNR per Rx.antenna in db Figure 3.11: BER performance of MMSE detection with different CE schemes for x system in channel D, NLOS 3.5 TGn SYNC SYSTEM This section discusses the TGn sync proposal for 80.11n (TGn sync proposal, 004). We study the effect of CE on the system performance using the LC-ZF/LC-MMSE MIMO detection methods.

80 3.5.1 System model The system model of the TGn sync proposal is shown in the Figure- 3.1. The mandatory mode requires the use of x antennas in a 0 MHz bandwidth. Channel encoder + puncturring S / P Frequency interleaver across 48 data tones Frequency interleaver across 48 data tones Modulation mapper Modulation mapper IFFT (0MHz) 48 data 4 - pilots IFFT (0MHz) 48 data 4 - pilots Insert GI Insert GI RF BW ~17MHz RF BW ~17MHz Figure 3.1.1: TGn sync transmitter Tx., 0 MHz BW Remove GI FFT (0MHz) MIMO Detector Modulation De-mapper Deinterleave S C Depuncture + Viterbi decoder Remove GI FFT (0MHz) Modulation De-mapper Deinterleave Figure 3.1.: A typical receiver for TGn sync x, 0 MHz BW The transmitter architecture with spatial streams in the basic MIMO mode is shown in Figure-3.1.1. In the basic MIMO mode the number of spatial streams is equal to the number of transmit antennas. The scrambled information bits are first passed through a convolutional encoder from which the other rates are derived by puncturing. The output of the puncturing block feeds the coded bits into the spatial parser (SP), which creates several spatial streams in a round robin fashion. The frequency interleaver interleaves the bits to be loaded in one OFDM symbol for subcarriers and constellation positions as given in the standards. The interleaved bits are then mapped to constellation points. The resulting QAM symbols are fed as a block of data to the IFFT to create the time domain signal.

81 The pilot tones are also inserted in the frequency domain. The cyclic prefix (CP) is inserted in the time domain and the windowing of the OFDM symbols is also performed in the time domain. A typical receiver for a x system is shown in the Figure-3.1.. The CP is removed from the received signal on the two antennas, which are then passed through the FFT block to create a frequency domain signal. The received signal on each subcarrier from the two antennas is passed through the MIMO detector, which separates out the transmitted streams. Demodulation is done on each stream, followed by the deinterleaving operation. The spatial combiner (SC) multiplexes the two streams in a round robin fashion and the bits or the soft values are passed through the viterbi decoder after suitable depuncturing, which is then passed through the descrambler to obtain the information bits. 3.5. Effect of CE on system performance In the previous section, we have discussed the effect of CE on the uncoded MIMO-OFDM systems and the performance of the low complexity MIMO detection schemes. It is very important to know the amount of performance degradation due to the CE in terms of BER and PER for IEEE 80.11n. The TGn sync proposal is taken as reference. The CE schemes considered here are the LS, LMMSE, LCCE and TMMSE. The performance measure of the system is presented in terms of both BER and PER. The PER is defined as the ratio between the number of packets received with alteast one bit error to the total number of packets transmitted. The CEs are obtained from HTLTF symbols as outlined in the earlier chapter. 3.5.3 Simulation results and discussion The simulation model used is given in Figure-3.13. and the simulation parameters are summarized in Table 3.. The IEEE 80.11n TGn sync channel model is used and ideal synchronization is assumed.

8 Info bits TGn sync Tx TGn sync Rx. Est bits Channel Figure 3.13: Simulation model Channel Estimation using preambles Parameter CR Modulation N t x N r Payload Table 3.: Simulation parameters Value ½ QPSK x 1000 bytes The BER and PER performance of all the MIMO detection scheme is plotted in Figure-3.14 and 3.15. From Figure-3.14 it can be seen that the order in which the schemes perform better is the VBLAST-MMSE, MMSE, VBLAST-ZF and the ZF detector. The MMSE detector performs better than the VBLAST-ZF in coded system, whereas in uncoded system VBLAST-ZF performs slightly better than the MMSE detector The same trend is observed in the PER plot shown in Figure-3.15. Of all the schemes discussed here, the MMSE detector has a reasonable performance both in terms of BER and PER with less computational complexity compared to other non-linear schemes and it is used in most practical system implementations. In practice a PER of 10 - is considered to be a good operational point. It can be seen that all the schemes except ZF offers 10 - within 0dB of Eb/N0.

83 10 0 10-1 ZF MMSE ZF-VBLAST MMSE-VBLAST 10 - BER 10-3 10-4 10-5 10-6 5 10 15 0 5 30 Eb/N0 in db Figure 3.14: BER performance of various MIMO detection schemes for x TGn sync system in channel D, NLOS 10 0 10-1 ZF MMSE ZF-VBLAST MMSE-VBLAST PER 10-10 -3 10-4 0 5 10 15 0 5 30 Eb/N0 in db Figure 3.15: PER performance of various MIMO detection schemes for x TGn sync system in channel D, NLOS

84 The BER and PER performance of the LC MMSE/ZF scheme with BPSK modulation for x case is shown in the Figure-3.16 and 3.17. From the BER, PER performance plots it can be observed that the LC MMSE/ZF perform very close to ZF/MMSE schemes. An error floor less than 10-5 and 10 - in BER and PER, respectively, is observed for the LC MMSE/ZF schemes. Thus, the LC MMSE/ZF does not have performance loss in the useful Eb/N0 region but has a 50% reduction in complexity. The results follow similar trend for 3x3 and 4x4. 10 0 10-1 ZF MMSE LC-ZF LC-MMSE 10-10 -3 BER 10-4 10-5 10-6 10-7 0 5 10 15 0 5 30 Eb/N0 in db Figure 3.16: PER performance of LC-MIMO detection schemes for x TGn sync system in channel D, NLOS The following simulation results show the effect of different CE schemes on the system performance in terms of BER and PER. We use LS, LCCE, TMMSE, and LMMSE CE schemes for the TGn sync preamble with MMSE MIMO detector. The BER and PER performance for x system for the different CE schemes in channel D, NLOS are plotted in Figure-3.18 and Figure- 3.19. From Figure-3.18 it can be observed that the LMMSE CE scheme has the performance very close to that of the ideal CE. The TMMSE with complex

85 weights and the LCCE schemes have almost similar effect on the BER performance which is quite close to that of the LMMSE CE. The LS CE results in a.75 db loss in performance compared to that of the ideal CE. From Figure-3.19 it can be seen that at 10-1 PER the LC CE leads to a performance loss of about.5 db, the LCCE and RMMSE schemes perform almost same having a loss less than 1 db, and the performance of LMMSE scheme is almost close to that of the ideal CE. 10 0 10-1 ZF MMSE LC-ZF LC-MMSE PER 10-10 -3 10-4 0 5 10 15 0 5 30 Eb/N0 in db Figure 3.17: BER performance for various CE schemes with MMSE detection for x TGn sync system in channel D, NLOS

86 10 0 10-1 10 - LS LCCE LMMSE TMMSE Ideal 10-3 BER 10-4 10-5 10-6 10-7 0 5 10 15 0 5 30 Eb/N0 in db Figure 3.18: PER performance for various CE schemes with MMSE detection for x TGn sync system in channel D, NLOS 10 0 10-1 LS LCCE LMMSE TMMSE Ideal PER 10-10 -3 10-4 5 10 15 0 5 30 Eb/N0 in db Figure 3.19: PER performance of LC MIMO detection schemes for x TGn sync system in channel D, NLOS.

87 The performance gap (G p ) in db between the ideal CE and the other CE schemes at 10-5 BER point is plotted in Figure-3.0 for B to F channel models in NLOS condition. As we move from channel B to F, the G p increases for the CE schemes which use the frequency correlation. i.e., the G p corresponding to channel B is lesser than that of channel F, since the correlation across the frequency response of the channel is more for channel B, which could be used to get better estimates. 3.5 3 Performance Loss, Gp.5 1.5 1 LMMSE TMMSE LCCE LS 0.5 0 B C D E F Channel models Figure 3.0: G p Loss in performance of 10-5 BER for different CE method on all channel models 3.6 SUMMARY In this chapter various MIMO detectors are discussed and their performance in uncoded system in terms of MSE and BER is presented based on simulation. The effect of CE on the performance of uncoded MIMO system is also presented. A low complexity solution for MIMO-OFDM detection is proposed and it reduces the computational complexity by 50%. The performance of the TGn sync system is presented for various MIMO detection methods in terms of BER

88 and PER. It is shown by simulations that the LC MIMO detectors result in very less performance degradation for practical channel conditions. Thus, the LC MIMO detectors can be used for IEEE 80.11n proposals as they reduce the computational complexity load at the receiver. The effect of various CE schemes on the performance of IEEE 80.11n TGn sync proposal is presented in terms of BER and PER. The results indicate that the LS scheme results in about 3 db loss in performance at 10-5 BER point, while the low complexity CE schemes such as LCCE, TMMSE have less performance degradation. Thus, the TMMSE and LCCE CE schemes can be used for IEEE 80.11n proposals leading to fewer computations and less performance degradation.