[Paper Review] Precoding via Approximate Message Passing with Instantaneous Signal Constraints

Ali Bereyhi, Mohammad Ali Sedaghat+1 more|arXiv (Cornell University)|Jan 8, 2018

Advanced MIMO Systems Optimization13 references8 citations

TL;DR

This paper proposes a low-complexity precoding algorithm, GLSE-GAMP, that leverages Generalized Approximate Message Passing to solve GLSE precoding problems with instantaneous signal constraints—such as peak-to-average power ratio (PAPR) limits and transmit antenna selection—while achieving performance close to the asymptotic GLSE benchmark even with moderate-sized MIMO systems.

ABSTRACT

This paper proposes a low complexity precoding algorithm based on the recently proposed Generalized Least Square Error (GLSE) scheme with generic penalty and support. The algorithm iteratively constructs the transmit vector via Approximate Message Passing (AMP). Using the asymptotic decoupling property of GLSE precoders, we derive closed form fixed point equations to tune the parameters in the proposed algorithm for a general set of instantaneous signal constraints. The tuning strategy is then utilized to construct transmit vectors with restricted peak-to-average power ratios and to efficiently select a subset of transmit antennas. The numerical investigations show that the proposed algorithm tracks the large-system performance of GLSE precoders even for a moderate number of antennas.

Motivation & Objective

• Address the high computational complexity of Generalized Least Square Error (GLSE) precoders in massive MIMO systems with non-convex constraints.
• Overcome the practical limitations of high RF-cost and power amplifier inefficiency due to high PAPR and full-array transmission.
• Develop a low-complexity iterative precoding algorithm that maintains performance close to optimal GLSE precoders under real-world signal constraints.
• Enable efficient transmit antenna selection and PAPR control without significant performance degradation.
• Provide a tuning strategy for GLSE-GAMP parameters using asymptotic fixed-point equations derived from replica theory.

Proposed method

• Adapt the Generalized Approximate Message Passing (GAMP) algorithm to iteratively solve the GLSE optimization problem with generic penalty functions and support sets.
• Use the asymptotic decoupling property of GLSE precoders to derive closed-form fixed-point equations for tuning algorithm parameters.
• Formulate the tuning strategy based on replica method results, relating average power $P$, active antenna fraction $\eta$, and PAPR constraints.
• Introduce parameterized fixed-point equations involving $\xi$, $\lambda$, $\mu$, and $\theta$ to jointly optimize power control and constraint satisfaction.
• Apply the tuned GLSE-GAMP algorithm to two practical scenarios: PAPR-limited transmission and transmit antenna selection.
• Utilize the VAMP algorithm as a potential alternative for ill-conditioned channel matrices where standard GAMP may diverge.

Experimental results

Research questions

• RQ1 Can GLSE-GAMP achieve performance close to the asymptotic GLSE precoder in finite-sized MIMO systems with non-convex constraints?
• RQ2 How can the parameters of the GLSE-GAMP algorithm be tuned to match the large-system performance of GLSE under PAPR and antenna selection constraints?
• RQ3 To what extent does the GLSE-GAMP algorithm reduce PAPR while maintaining low distortion and high spectral efficiency?
• RQ4 Does the proposed tuning strategy based on replica method results yield accurate parameter settings for practical MIMO configurations?
• RQ5 Can GLSE-GAMP be extended to ill-conditioned channel matrices, and if so, how does VAMP improve convergence?

Key findings

• The GLSE-GAMP precoder achieves distortion performance that closely tracks the asymptotic GLSE benchmark, even with $N=64$ antennas and $T=20$ iterations.
• For PAPR-limited transmission, the GLSE-GAMP precoder with PAPR = 3 dB achieves distortion within 1 dB of the unconstrained GLSE case, indicating minimal performance loss.
• When PAPR is increased to 5 dB, the GLSE-GAMP performance becomes nearly indistinguishable from the unconstrained GLSE case, suggesting effective PAPR control with negligible rate penalty.
• The tuning strategy based on fixed-point equations accurately predicts the required parameters for average power $P$ and active antenna fraction $\eta$, enabling reliable implementation.
• The GLSE-GAMP algorithm maintains consistent performance across different load factors $\alpha^{-1} = N/K$, demonstrating robustness to system load variations.
• The GLSE-GAMP approach enables the use of low-efficiency, low-dynamic-range power amplifiers by effectively controlling PAPR, significantly reducing RF-cost in massive MIMO systems.