Capacity scaling in a Non-coherent Wideband Massive SIMO Block Fading Channel

TL;DR

This paper analyzes how the capacity of non-coherent wideband SIMO channels scales with bandwidth and antennas, revealing a threshold beyond which pilot-assisted methods cannot exploit additional spectrum for capacity gains.

Contribution

It characterizes the capacity scaling behavior in wideband SIMO channels without CSI at the transmitter, identifying a threshold bandwidth related to the number of antennas.

Findings

No capacity gap below the threshold bandwidth.

A capacity scaling gap exists above the threshold.

Pilot-assisted schemes cannot exploit excess spectrum beyond the threshold.

Abstract

The scaling of coherent and non-coherent channel capacity is studied in a single-input multiple-output (SIMO) block Rayleigh fading channel as both the bandwidth and the number of receiver antennas go to infinity jointly with the transmit power fixed. The transmitter has no channel state information (CSI), while the receiver may have genie-provided CSI (coherent receiver), or the channel statistics only (non-coherent receiver). Our results show that if the available bandwidth is smaller than a threshold bandwidth which is proportional (up to leading order terms) to the square root of the number of antennas, there is no gap between the coherent capacity and the non-coherent capacity in terms of capacity scaling behavior. On the other hand, when the bandwidth is larger than this threshold, there is a capacity scaling gap. Since achievable rates using pilot symbols for channel estimation are subject to the non-coherent capacity bound, this work reveals that pilot-assisted coherent receivers in systems with a large number of receive antennas are unable to exploit excess spectrum above a given threshold for capacity gain.