29 illustrates the link-level performance of a 12 x 2 MIMO system with a ZF receiver. It is shown that the performance is close to that of a SISO system since the diversity order is one. The MMSE receiver balances multi-stream interference mitigation and noise enhancement effect and minimizes the total error, and is given by: GMMSE = argmin G E Gy (10-41) where I is an Nr X Nr identity matrix. In low signal-to-interference plus noise ratios (i.e., SINR < 0 dB), the performance of the MMSE receiver approaches that of a matched-filter receiver, out- performing the ZF detector which tends to enhance noise. In high signal-to-interference plus noise N=1,N,=1 (Theory) Nt=1,N,=2 (MRC) N,=2,N,=2 (ZF) Eb/No (dB) FIGURE 10-29 Link-level performance of 2 X 2 MIMO with ZF equalizer (Rayleigh channel and BPSK modulation) 10.4 Multi-antenna transmission schemes ratios; however, the performance of the MMSE receiver approaches that of a ZF receiver, and therefore realizes N - N + 1 order diversity for each data stream. In Maximal Ratio Combining (MRC), the output is a weighted sum of all receiver branches, thus the coefficients aji = 1,2,...,N, are all non-zero. The signals are co-phased and Ai = Bie-joi i = 1,2, ...,Nr where Ai is the phase of the received signal on the ith branch (see Figure 10-30). The magnitude of the combined output can be written as y = Let's assume that the noise power spectral density is No/2 in each branch, which yields the combined noise at the output n = 2N The SNR at the output of the combiner is given as: (10-42) The objective is to find aji = 1,2, Nr which maximizes the output SNR. It can be understood that branches with higher SNR are weighted more than those with lower SNR; therefore, the coefficients Ai,i = 1,2, Nr are proportional to the branch SNRs. The coefficients are found by taking partial derivatives of the output SNR expression and solving the resulting equations for the optimal weights which yields Ai = r2/No, = 2, Nr, and the output SNR will be the sum of the SNRs of the receiving bran