Capacity of SIMO and MISO Phase-Noise Channels with Common/Separate Oscillators

TL;DR

This paper analyzes the high-SNR capacity of SIMO and MISO phase-noise channels, revealing that while the first-order capacity term is scenario-independent, the second-order phase-noise number varies with oscillator configuration and antenna setup.

Contribution

It provides a detailed comparison of capacity limits for SIMO and MISO channels under common and separate oscillators, highlighting the impact of oscillator configuration on phase-noise gains.

Findings

First-order capacity term is 0.5*ln(SNR) for all scenarios.

SLO configuration offers diversity gain in SIMO channels.

CLO configuration yields higher phase-noise number in MISO channels.

Abstract

In multiple antenna systems, phase noise due to instabilities of the radio-frequency (RF) oscillators, acts differently depending on whether the RF circuitries connected to each antenna are driven by separate (independent) local oscillators (SLO) or by a common local oscillator (CLO). In this paper, we investigate the high-SNR capacity of single-input multiple-output (SIMO) and multiple-output single-input (MISO) phase-noise channels for both the CLO and the SLO configurations. Our results show that the first-order term in the high-SNR capacity expansion is the same for all scenarios (SIMO/MISO and SLO/CLO), and equal to $0.5\ln (\rho)$, where $\rho$ stands for the SNR. On the contrary, the second-order term, which we refer to as phase-noise number, turns out to be scenario-dependent. For the SIMO case, the SLO configuration provides a diversity gain, resulting in a larger phase-noise number than for the CLO configuration. For the case of Wiener phase noise, a diversity gain of at least $0.5 \ln(M)$ can be achieved, where $M$ is the number of receive antennas. For the MISO, the CLO configuration yields a higher phase-noise number than the SLO configuration. This is because with the CLO configuration one can obtain a coherent-combining gain through maximum ratio transmission (a.k.a. conjugate beamforming). This gain is unattainable with the SLO configuration.