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364 CHAPTER 8 Multiuser MIMO Receiver Processing for Time-Varying Channels The complexity for a data block of length K - J is given by C soft = c QR + (4M T + 1) kP c soft [k] and can be upper bounded using (8.46). 8.7 SIMULATION RESULTS To compare the performance of the presented multiuser detection algorithms, we resort to numeric simulations. Realizations of the time-varying frequency-selective channel h u,t,r [l, m], sampled at the chip rate 1/T c , are generated using an exponentially decaying power delay profile 2 [k] = e - 4 K-1 k =0 k e - 4 k with root mean square delay spread T d = 4T c = 1 µ s for a chip rate of 1/T c = 3.84 · 10 6 s -1 (Correia, 2001). We assume M = 15 resolvable paths. The autocorrelation for every channel tap is given by the classical Clarke spectrum (Clarke, 1968). The system operates at carrier frequency f c = 2 GHz, and there are U = 32 users moving with velocity = 70 km/h. This gives a Doppler bandwidth of B D = 126 Hz. We use M T = 4 transmit antennas per user and M R = 4 receive antennas at the base station. The number of subcarriers is L = 64, and the OFDM symbol with cyclic prefix has length P = L + G = 79. The data block consists of K = 256 OFDM symbols including J = 60 pilot symbols. The system is designed for max = 102.5 km/h, which results in a dimension of D = 3 for the Slepian basis expansion. In order to analyze the diversity gain of the receiver only, the MIMO channel taps are normalized according to E M R M T M-1 |h u,t,r [l, m]| 2 = 1. r=1 t=1 m=0 No antenna gain is present due to this normalization. For data transmission, a convolutional, nonsystematic, nonrecursive, 4 state, rate R c = 1/2 code with code generators [101] and [111] (denoted (5, 7) 8 in octal notation) is used (Hanzo, Liew, & Yeap, 2002). All results shown are obtained by averaging over 100 independent channel realizations. The QPSK symbol energy is normalized to 1. The SNR is defined as E b 1 P K = , N 0 2R c z 2 L K - J which takes into account the loss due to coding, pilots, and cyclic prefix. The noise variance z 2 is assumed to be known at the receiver. 8.7.1 Bit Error Rate Comparison In Fig. 8.7, we compare the BER performance of all presented multiuser detection methods. In addition, we show the performance obtained with LMMSE multiuser detection and perfect channel knowledge