System Level Modeling and Optimization of the LTE Downlink

A. SNR-independence of the CLSM Precoder ChoiceA. SNR-independence of the CLSMPrecoder ChoiceThis appendix justifies the assumption in Section 3.1.1.3 that the optimum precodermatrix choice can be performed independent of the SNR without any relevant lossof accuracy.Noting as ˜H the effective channel matrix, which is expressed as the channel matrixH multiplied by the precoder W, the post-equalization SINR (γ) for the k-thtransmitted symbol (k-th layer) is expressed asγ ZF,k =1[ ( ) ] −1ρ ˜H H ˜Hkk, (A.1)where ρ denotes the E b /N 0 divided by the number of receive antennas N RX , and[·] kk is the k-th diagonal element of the MSE matrix.The total spectral efficiency, denoted as C is the sum over the K layers, which isexpressed asK∑C = log 2 (1 + γ k ) .k=1(A.2)Via a Singular Value Decomposition (SVD) of H, we can express the effective channelmatrix product ( ˜H H ˜H) asW H H H HW = W H VΛU H UΛV H W = ( W H V )Λ 2 ( W H V ) H, (A.3)} {{ } } {{ }PP H85