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# Exercise 8 20 We have seen in Figure 813 that at low SNR the bank of linear matched filter achieves capacity of the 8 by 8 iid Rayleigh fading channel in the sense that the ratio of the total

Exercise 8.20 We have seen in Figure 8.13 that, at low SNR, the bank of linear matched filter achieves capacity of the 8 by 8 i.i.d. Rayleigh fading channel, in the sense that the ratio of the total achievable rate to the capacity approaches 1. Show that this is true for general nt  and  nr.

Exercise 8.21 Consider the by i.i.d. flat Rayleigh fading channel. Show that the total achievable rate of the following receiver architectures scales linearly with n: (a) bank of linear decorrelators; (b) bank of matched filters; (c) bank of linear MMSE receivers. You can assume that independent information streams are coded and sent out of each of the transmit antennas and the power allocation across antennas is uniform. Hint: The calculation involving the linear MMSE receivers is tricky. You have to show that the linear MMSE receiver performance, asymptotically for large n, depends on the covariance matrix of the interference faced by each stream only through its empirical eigenvalue distribution, and then apply the large-random matrix result used in Section 8.2.2. To show the first step, compute the mean and variance of the output SINR, conditional on the spatial signatures of the interfering streams. This calculation is done in [132, 123]

Jul 31 2020 View more View Less

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