# Lower Bound on the Sum-rate of Decremental Beam Selection Algorithm for Beamspace MIMO Systems

## TL;DR

This paper derives a theoretical lower bound on the sum-rate performance of a decremental beam selection algorithm in beamspace MIMO systems at mmWave frequencies, providing insights into the limits of such algorithms.

## Contribution

It introduces a novel sum-rate lower bound for decremental beam selection in beamspace MIMO, linking Frobenius norms of precoding matrices and offering new theoretical insights.

## Key findings

- The bound relates Frobenius norms of full and reduced MIMO precoding matrices.
- It provides a deterministic square-hyperbolic function to estimate sum-rate limits.
- The bound helps understand the performance limits of beam selection algorithms.

## Abstract

In general, the zero-forcing (ZF) precoding suffers from a severe receive signal-to-noise ratio (SNR) degradation in the high interference regime. However, recent evidences from realistic measurements demonstrated that millimeter wave (mmWave) systems are mainly noise-limited as high gain antennas behave as spatial filters to the interference signal. This makes ZF precoding equally attractive as that of other linear precoding counterparts. Considering ZF precoding, this paper aims to derive a lower bound on the sum-rate achieved by a decremental beam selection (BS) algorithm in a beamspace MIMO (B-MIMO) system operating at mmWave frequencies. This bound relates Frobenious norms of precoding matrices of full and reduced dimensional (i.e. after BS) B-MIMO systems through a deterministic square-hyperbolic function. Note that, both ZF precoding and decremental BS are not new concepts. However, the derived sum-rate bound provides a new insight to the topic. Given a particular full dimensional B-MIMO channel, the presented bound can be used to understand limits of BS algorithms.