Design and Analysis of Novel Precoding Scheme for LSAS Using Power Allocation

Abstract

Massive MIMO systems (also known as “large-scale antenna system” and “full-dimension MIMO”) significantly reduce air interface latency by using a large excess of service antennas over active terminals and time-division duplex operation. We consider the downlink of a time-division duplexing multicell multiuser MIMO system in which the base transceiver stations are equipped with a very large number of antennas. Assuming channel estimation through uplink pilots, arbitrary antenna correlations, and user distributions, we derive approximations of achievable rates with linear precoding techniques—namely, zero forcing, matched filtering, eigen-beamforming (EBF), and regularized zero-forcing (RZF). The approximations are tight in the large system limit with an infinitely large number of antennas and user terminals, but they match our simulations for realistic system dimensions. We further show that a simple EBF precoding scheme can achieve the same performance as RZF with one order of magnitude fewer antennas in both uncorrelated and correlated fading channels. Our simulation results show that our proposed precoding scheme is better than the conventional scheme. Moreover, we have used two channel environments for further analysis of our algorithm—long-term evolution advanced and millimeter wave mobile broadband channels.

Appendix

When the massive MIMO system adopts precoding, the approximate power allocation vector achieving the optimal PA is

$$P^{o} = \left[ {\tilde{H}^{ - 1} b} \right]^{ + }$$

where

$$\left[ x \right]^{ + } = max\left\{ {0,x_{i} } \right\}, b = \left[ {b_{1} ,b_{2} , \ldots ,b_{K} } \right]^{T} ,$$

and

$$b_{k} = \frac{{\eta \left\| {h_{k} } \right\|^{2} }}{{\eta_{PE}^{o} ln2}} - \frac{{\sigma^{2} }}{{\beta_{k} }}$$

$$\tilde{H} = \left[ {\begin{array}{*{20}c} {\left\| {h_{1} } \right\|^{2} /\mu } & 1 & \cdots & 1 \\ 1 & {\left\| {h_{2} } \right\|^{2} /\mu } & \cdots & 1 \\ \vdots & \vdots & \ddots & \vdots \\ 1 & 1 & \cdots & {\left\| {h_{k} } \right\|^{2} /\mu } \\ \end{array} } \right]$$

where $\tilde{H} = {\text{diag}}\left\{ {\left\| {h_{1} } \right\|^{2} ,\left\| {h_{2} } \right\|^{2} , \ldots ,\left\| {h_{K} } \right\|^{2} } \right\}/\mu + 1_{K \times K} - I_{K \times K}$ and ${\text{b}} = \left[ {b_{1} ,b_{2} , \ldots ,b_{K} } \right]^{ }$, $b_{K} = \frac{{\eta \left\| {h_{K} } \right\|^{2} }}{{\mu \eta_{PE}^{o} ln2}} - \frac{{\sigma^{2} }}{{\beta_{k} }}.$ $\eta_{PE}^{o}$ unique globally optimal power allocation. As the independence of ${\text{h}}_{l} \left( {l = 1,2, \ldots ,K} \right)$, the rank of the matrix $\tilde{H}$ is K. Therefore,$\tilde{H}$ is invertible and the power allocation is expressed as

$$P^{o} = \left[ {\tilde{H}^{ - 1} b} \right]^{ + }$$