Power Scaling of Uplink Massive MIMO Systems with Arbitrary-Rank Channel Means

TL;DR

This paper derives analytical expressions for uplink achievable rates in massive MIMO systems with arbitrary-rank Ricean fading channels, revealing how transmit power scales with the number of antennas under different CSI conditions.

Contribution

It provides new tractable formulas and scaling laws for uplink rates in massive MIMO with arbitrary-rank channels, extending prior work to more general channel models.

Findings

Transmit power can be scaled down proportionally to 1/M with perfect CSI.

Power scaling is limited to 1/√M in Rayleigh fading with imperfect CSI.

Uplink rates converge to fixed values as Ricean K-factor increases.

Abstract

This paper investigates the uplink achievable rates of massive multiple-input multiple-output (MIMO) antenna systems in Ricean fading channels, using maximal-ratio combining (MRC) and zero-forcing (ZF) receivers, assuming perfect and imperfect channel state information (CSI). In contrast to previous relevant works, the fast fading MIMO channel matrix is assumed to have an arbitrary-rank deterministic component as well as a Rayleigh-distributed random component. We derive tractable expressions for the achievable uplink rate in the large-antenna limit, along with approximating results that hold for any finite number of antennas. Based on these analytical results, we obtain the scaling law that the users' transmit power should satisfy, while maintaining a desirable quality of service. In particular, it is found that regardless of the Ricean $K$-factor, in the case of perfect CSI, the approximations converge to the same constant value as the exact results, as the number of base station antennas, $M$, grows large, while the transmit power of each user can be scaled down proportionally to $1/M$. If CSI is estimated with uncertainty, the same result holds true but only when the Ricean $K$-factor is non-zero. Otherwise, if the channel experiences Rayleigh fading, we can only cut the transmit power of each user proportionally to $1/\sqrt M$. In addition, we show that with an increasing Ricean $K$-factor, the uplink rates will converge to fixed values for both MRC and ZF receivers.