18. MIMO System Consider the instantaneous MIMO channel matrix H given below and answer the questions...

 

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18. MIMO System Consider the instantaneous MIMO channel matrix H given below and answer the questions that follow. 1 -2 2 H = 2 -1 -2 2 2 1 (a) What property do the columns C1, C2, C3 of this matrix satisfy? (b) Compute the SVD of the above channel matrix. (c) What is the corresponding MIMO zero-forcing receiver matrix ? (d) If the transmit power of BPSK modulated symbols is P = 5 dB per transmit antenna and noise power = 3 dB, what is the instantaneous bit error rate for the zero forcing decoder? (e) If the transmit power of BPSK modulated symbols is P = 5 dB per transmit antenna and noise power = 3 dB, what is the instantaneous bit error rate for the second Multiple-Input Multiple-Output Wireless Communications 227 decoded stream in the V-BLAST decoder, assuming the decoding operation proceeds in the order of the transmit antennas ? Make the simplifying assumption that there is no error propagation. (f) If the transmit power of BPSK modulated symbols is P = 5 dB per transmit antenna and noise power = 3 dB, what is the exact (NOT PEP) instantaneous bit error rate for the maximum likelihood decoder? (g) Considering a transmit power of P = 30 dB, =-3 dB, and BPSK symbols, what is the average BER for zero-forcing with elements of the channel matrix H IID Rayleigh of average power unity? (h) Considering a transmit power of P = 30 dB, =-3 dB, and BPSK symbols, what is the average BER for the second decoded stream in the V-BLAST decoder, assuming the decoding operation proceeds in the order of the transmit antennas, with elements of the channel matrix H IID Rayleigh of average power unity? Make the simplifying assumption that there is no error propagation. 18. MIMO System Consider the instantaneous MIMO channel matrix H given below and answer the questions that follow. 1 -2 2 H = 2 -1 -2 2 2 1 (a) What property do the columns C1, C2, C3 of this matrix satisfy? (b) Compute the SVD of the above channel matrix. (c) What is the corresponding MIMO zero-forcing receiver matrix ? (d) If the transmit power of BPSK modulated symbols is P = 5 dB per transmit antenna and noise power = 3 dB, what is the instantaneous bit error rate for the zero forcing decoder? (e) If the transmit power of BPSK modulated symbols is P = 5 dB per transmit antenna and noise power = 3 dB, what is the instantaneous bit error rate for the second Multiple-Input Multiple-Output Wireless Communications 227 decoded stream in the V-BLAST decoder, assuming the decoding operation proceeds in the order of the transmit antennas ? Make the simplifying assumption that there is no error propagation. (f) If the transmit power of BPSK modulated symbols is P = 5 dB per transmit antenna and noise power = 3 dB, what is the exact (NOT PEP) instantaneous bit error rate for the maximum likelihood decoder? (g) Considering a transmit power of P = 30 dB, =-3 dB, and BPSK symbols, what is the average BER for zero-forcing with elements of the channel matrix H IID Rayleigh of average power unity? (h) Considering a transmit power of P = 30 dB, =-3 dB, and BPSK symbols, what is the average BER for the second decoded stream in the V-BLAST decoder, assuming the decoding operation proceeds in the order of the transmit antennas, with elements of the channel matrix H IID Rayleigh of average power unity? Make the simplifying assumption that there is no error propagation.