This letter considers a noncoherent two-user uplink system, where each user has a single antenna and a base station is equipped with a large number of antennas. It is assumed that small scale channel fading is Rayleigh fading and quasi-static in two consecutive time slots and changes to other values independently in the next block. For such massive MIMO uplink system, we propose an orthogonal binary modulation scheme and utilize a noncoherent maximum likelihood receiver rather than a commonly adopted channel orthogonality approximation to analyze its error performance. A fast decoding algorithm is obtained and an exact bit error probability (BEP) formula is derived. When the large scale fading coefficients are available at the transmitters, a closed-form optimal power loading is attained that minimizes a tight upper bound of BEP. Computer simulations demonstrate that in a mild signal-to-noise ratio region, the optimized upper bound is almost equal to the truly optimized BEP. Hence, our derived BEP formula can be used to quantify how many antennas we need for the given BEP. In addition, the extension of all these results to the system with coherence time longer than two is also briefly discussed.
['Gangtao Han', 'Zheng Dong', 'Jian-Kang Zhang', 'Xiaomin Mu']
Orthogonal Binary Modulation Division for Two-User Uplink Massive MIMO Systems With Noncoherent ML Detection