# Zero Forcing Detection For Short Packet Transmission Under Channel Estimation Errors

## TL;DR

This paper analyzes a multiuser MIMO system with short-packet transmission under Rayleigh fading, deriving exact formulas for outage probability and goodput while considering channel estimation errors as a signal, providing new insights into system performance.

## Contribution

It introduces a novel analytical approach that treats channel estimation errors as a signal, leading to exact expressions for outage and goodput in short-packet MIMO systems.

## Key findings

- Channel estimation errors can be exploited as a signal to improve performance.
- Derived closed-form expressions for outage probability and goodput.
- Insights on how antennas, power, and coding rate affect system performance.

## Abstract

A multiuser multiple-input multiple-output wireless communication system is analytically studied under the short-packet transmission regime. The practical scenario of channel estimation errors is adopted when the signals undergo Rayleigh channel fading conditions. Unlike most previous works, the channel estimation error term is treated as a signal rather than interference or noise, which may further enhance the overall system performance. The spatial multiplexing mode of transmit operation is considered, while the zero-forcing detection is applied at the receiver. New and exact closed-form expressions for the outage probability and total system goodput are derived. Capitalizing on the analytical results, some new engineering insights are also presented; such as the impact of channel estimation errors with respect to the number of antennas, transmit power, and/or coding rate.