Down link performance for a Time Division Duplex broadcast network: Refined asymptotics for the power normalization constant

A TDD OFDM scheme for broadcasting using a Massive MIMO array to a group of mobiles is considered. Asymptotic formulas are developed (fixed number of users K, M antennas going to ∞) for the constant χM used to normalise the Zero Forcing (ZF) matrix. This quantity is the reciprocal square root of the trace of a generalized Wishart matrix. Its asymptotic distribution is shown to be normal and approximations are obtained for its mean and variance. In some transmission schemes it may be necessary to estimate or track the mean of χ which appears in the channel model after zero forcing. The results show that this quantity varies as the 4th moment of the fading amplitude.