[Paper Review] Error Probability Analysis and Power Allocation for Interference Exploitation Over Rayleigh Fading Channels

Abdelhamid Salem, Christos Masouros|arXiv (Cornell University)|Oct 7, 2019

Advanced MIMO Systems Optimization4 citations

TL;DR

This paper presents the first statistical analysis of constructive interference (CI) precoding in MU-MIMO systems over Rayleigh fading channels with M-PSK signaling. It derives exact and asymptotic expressions for the moment generating function (MGF) and symbol error probability (SEP), enabling optimized power allocation that achieves up to 13 dB SNR gain over equal power allocation and up to 20 dB gain over ZF precoding in SEP performance.

ABSTRACT

This paper considers the performance analysis of constructive interference (CI) precoding technique in multi-user multiple-input multiple-output (MU-MIMO) systems with a finite constellation phase-shift keying (PSK) input alphabet. Firstly, analytical expressions for the moment generating function (MGF) and the average of the received signal-to-noise-ratio (SNR) are derived. Then, based on the derived MGF expression the average symbol error probability (SEP) for the CI precoder with PSK signaling is calculated. In this regard, new exact and very accurate asymptotic approximation for the average SEP are provided. Building on the new performance analysis, different power allocation schemes are considered to enhance the achieved SEP. In the first scheme, power allocation based on minimizing the sum symbol error probabilities (Min-Sum) is studied, while in the second scheme the power allocation based on minimizing the maximum SEP (Min-Max) is investigated. Furthermore, new analytical expressions of the throughput and power efficiency of the CI precoding in MU-MIMO systems are also derived. The numerical results in this work demonstrate that, the CI precoding outperforms the conventional interference suppression precoding techniques with an up to 20dB gain in the transmit SNR in terms of SEP, and up to 15dB gain in the transmit SNR in terms of the throughput. In addition, the SEP-based power allocation schemes provide additional up to 13dB gains in the transmit SNR compared to the conventional equal power allocation scheme.

Motivation & Objective

• To provide the first exact statistical characterization of the received SNR in constructive interference (CI) precoded MU-MIMO systems over Rayleigh fading channels.
• To derive analytical expressions for the moment generating function (MGF) and average SNR to enable performance evaluation of CI precoding with M-PSK signaling.
• To develop power allocation schemes that minimize total or maximum symbol error probability (SEP) to enhance system reliability.
• To derive explicit analytical expressions for throughput and power efficiency of CI precoding in MU-MIMO systems.
• To evaluate the performance gains of CI precoding over conventional zero-forcing (ZF) precoding in terms of SEP, throughput, and power efficiency.

Proposed method

• Derives exact closed-form expressions for the moment generating function (MGF) and average received SNR of CI-precoded MU-MIMO systems with M-PSK inputs over Rayleigh fading channels.
• Uses the derived MGF to compute the exact average symbol error probability (SEP) and provides a highly accurate asymptotic approximation for SEP.
• Proposes two power allocation schemes: Min-Sum (minimizing total SEP) and Min-Max (minimizing maximum SEP) to improve error performance.
• Derives explicit analytical expressions for system throughput and power efficiency based on the CI precoding model and channel statistics.
• Validates analytical results through numerical simulations across various SNR regimes, modulation orders, and system configurations.
• Compares performance against conventional ZF precoding and equal power allocation to quantify gains in SEP, throughput, and power efficiency.

Experimental results

Research questions

• RQ1 What is the exact statistical distribution of the received SNR in CI-precoded MU-MIMO systems with M-PSK signaling over Rayleigh fading channels?
• RQ2 How accurate are the asymptotic approximations for the average symbol error probability (SEP) of CI precoding with M-PSK?
• RQ3 To what extent can power allocation schemes based on minimizing total or maximum SEP improve system performance compared to equal power allocation?
• RQ4 How does CI precoding compare to conventional ZF precoding in terms of SEP, throughput, and power efficiency across different SNR and modulation levels?
• RQ5 How does the number of base station antennas and transmit power affect the power efficiency of CI precoding in MU-MIMO systems?

Key findings

• CI precoding achieves up to 20 dB gain in transmit SNR over conventional ZF precoding in terms of symbol error probability (SEP).
• The proposed Min-Sum and Min-Max power allocation schemes provide up to 13 dB additional SNR gain over equal power allocation in SEP performance.
• Throughput performance of CI precoding outperforms ZF by up to 15 dB in transmit SNR for a given target throughput across all modulation orders.
• Power efficiency is higher for lower-order modulations (e.g., QPSK) at low SNR and small numbers of base station antennas, while higher-order modulations (e.g., 32-PSK) become more efficient at high SNR and large antenna arrays.
• The asymptotic approximation for SEP is highly accurate, especially at high SNR, enabling reliable performance prediction without Monte Carlo simulations.
• As the number of users or base station antennas increases, the SEP performance of CI precoding improves, demonstrating scalability and robustness in dense multi-user scenarios.