Performance of PZF and MMSE Receivers in Cellular Networks with Multi-User Spatial Multiplexing

This paper characterizes the performance of cellular networks employing multiple antenna open-loop spatial multiplexing techniques. We use a stochastic geometric framework to model distance depended inter cell interference. Using this framework, we analyze the coverage and rate using two linear receivers, namely, partial zero-forcing (PZF) and minimum-mean-square-estimation (MMSE) receivers. Analytical expressions are obtained for coverage and rate distribution that are suitable for fast numerical computation. In the case of the PZF receiver, we show that it is not optimal to utilize all the receive antenna for canceling interference. With $\alpha$ as the path loss exponent, $N_t$ transmit antenna, $N_r$ receive antenna, we show that it is optimal to use $N_t\left\lceil\left(1-\frac{2}{\alpha}\right) \left( \frac{N_r}{N_t} -\frac{1}{2}\right)\right\rceil$ receive antennas for interference cancellation and the remaining antennas for signal enhancement (array gain). For both PZF and MMSE receivers, we observe that increasing the number of data streams provides an improvement in the mean data rate with diminishing returns. Also transmitting $N_r$ streams is not optimal in terms of the mean sum rate. We observe that increasing the SM rate with a PZF receiver always degrades the cell edge data rate while the performance with MMSE receiver is nearly independent of the SM rate.