[Paper Review] Hybrid Precoding Design for Reconfigurable Intelligent Surface aided mmWave Communication Systems

Chandan Pradhan, Ang Li+3 more|arXiv (Cornell University)|Nov 29, 2019

Advanced Wireless Communication Technologies10 references5 citations

TL;DR

This paper proposes a joint hybrid precoding (HP) and reconfigurable intelligent surface (RIS) phase shift (PS) design for multi-user mmWave systems to minimize mean-squared error (MSE). Using an alternating optimization framework with gradient-projection (GP) to handle constant-modulus constraints, the algorithm converges to a KKT point and achieves significant spectral efficiency gains over baseline schemes with only 6 RF chains.

ABSTRACT

In this letter, we focus on the hybrid precoding (HP) design for the reconfigurable intelligent surface (RIS) aided multi-user (MU) millimeter wave (mmWave) communication systems. Specifically, we aim to minimize the mean-squared-error (MSE) between the received symbols and the transmitted symbols by jointly optimizing the analog-digital HP at the base-station (BS) and the phase shifts (PSs) at the RIS, where the non-convex element-wise constant-modulus constraints for the analog precoding and the PSs are tackled by resorting to the gradient-projection (GP) method. We analytically prove the convergence of the proposed algorithm and demonstrate the desirable performance gain for the proposed design through numerical results.

Motivation & Objective

• Address the challenge of inter-user interference and high path loss in multi-user mmWave systems with limited RF chains.
• Overcome the limitations of fully-digital precoding in mmWave bands due to high hardware cost and power consumption.
• Replace conventional relays with reconfigurable intelligent surfaces (RIS) to enable passive, low-cost, and energy-efficient signal reflection without additional RF chains or noise.
• Jointly optimize hybrid precoding at the base station and phase shifts at the RIS to minimize MSE between transmitted and received symbols.
• Develop a convergent algorithm that handles non-convex, element-wise constant-modulus constraints for both analog precoding and RIS phase shifts.

Proposed method

• Formulate a non-convex optimization problem to minimize MSE by jointly optimizing hybrid precoding at the base station and phase shifts at the RIS.
• Use an alternating optimization framework to iteratively optimize the analog precoder and RIS phase shifts while keeping the other fixed.
• Apply the gradient-projection (GP) method to enforce element-wise constant-modulus constraints on both the analog precoder and RIS phase shifts.
• Prove convergence of the algorithm to a Karush–Kuhn–Tucker (KKT) point using a majorization-minimization approach with a quadratic upper bound on the cost function.
• Implement the algorithm with iterative updates for the analog precoder and RIS phase shifts, using a block-diagonal structure for the analog precoder under the phase codebook selection (PCS) constraint.
• Use a surrogate function to approximate the non-convex cost function and ensure monotonic decrease in the objective value across iterations.

Experimental results

Research questions

• RQ1 Can joint optimization of hybrid precoding and RIS phase shifts significantly improve spectral efficiency in multi-user mmWave systems compared to conventional schemes?
• RQ2 How does the proposed algorithm perform under practical hardware constraints such as limited RF chains and constant-modulus phase shifts?
• RQ3 Does the use of RIS with hybrid precoding outperform traditional relay-based systems in terms of spectral efficiency and energy efficiency?
• RQ4 To what extent does the number of RIS elements (R) and signal-to-noise ratio (SNR) impact the performance of the joint HP-RIS design?
• RQ5 Is the proposed algorithm guaranteed to converge to a stationary point under non-convex constraints?

Key findings

• The proposed joint hybrid precoding and RIS phase shift design achieves significant spectral efficiency gains over benchmark schemes such as hpBS-rndRIS and hpBS-noRIS, especially with increasing RIS element count.
• Spectral efficiency improves with increasing RIS element count (R), demonstrating the value of larger RIS aperture for beamforming gain and interference mitigation.
• At SNR = -10 dB and R = 100, the proposed design achieves a spectral efficiency close to the upper bound (upBound) and fully-digital RIS-optimized benchmark (fdBS-optRIS), despite using only 6 RF chains.
• The algorithm converges to a KKT point, as analytically proven via a majorization-minimization framework with a quadratic upper bound on the cost function.
• The performance loss compared to the fully-digital benchmark is offset by substantial energy efficiency and hardware cost savings due to the use of only 6 RF chains.
• The spectral efficiency increases with higher SNR, confirming the robustness and scalability of the proposed design under varying channel conditions.