ed power of the MMSE channel estimate, where ECSI = 1 represents perfect CSI. Note that the numerator of the logarithm argument increases proportionally with respect to NTX due to the array gain 584 Chapter 4 and that the denominator represents the interference plus noise. While the generic theory of massive MIMO systems assumed single-antenna terminals, the technology can support term- inals with N'RX antennas. In this case, Nuser denotes the number of simultaneous data streams and the preceding equation describes the spectral efficiency per stream. These streams can be divided over anything from Nuser/N'RX to Nuser terminals [16,52]. We discussed the capacity of MIMO systems earlier in this chapter, which can be written as follows: min(Nrx,NRX) In the preceding equation, it is assumed that transmitter has the full knowledge of CSI and that the channel matrix H can be decomposed using SVD method, where o?'s are the eigen- values of HH In the preceding equation, if the SNR r is extremely small, the capacity asymptotically approaches C7-0~~NRx/ In 2, which is independent of NTX, thus, even under the most favorable propagation conditions, the multiplexing gains are lost, and from the perspective of achievable rate, multiple transmit antennas are of no value. Next, let the number of transmit antennas grow large while keeping the number of receive antennas con- stant. We further assume that the row vectors of the channel matrix are asymptotically orthogonal, CNTX>>NRX NRx10g2(1+y). Then, let the number of receive antennas increase while keeping the number of transmit antennas constant. We also assume that the column vectors of the channel matrix are asymptotically orthogonal, NTxlog2 (1 + yNRx/ NTx). Therefore, an excess number of transmit or receive antennas, combined with asymptotic orthogonality of the propagation vectors, constitutes a highly desirable scenario. Additional receive antennas continue to improve the effective SNR and could in theory compensate for a low SNR and restore multiplexing gains that would 