Statistical CSI-based Design for Reconfigurable Intelligent Surface-aided Massive MIMO Systems with Direct Links

I. INTRODUCTION

• Earlier RIS research covered passive and active beamforming, multicell MIMO, SWIPT, RIS-versus-relaying analysis, and Rician-channel indoor and outdoor settings.The cited works are –.Source: §I · p. 1
• Prior studies exploited statistical CSI to design RIS phase shifts, which can greatly reduce channel-estimation overhead and computational complexity, for single-user, location-based, multi-user, and massive-MIMO systems –.Source: §I · p. 1
• Direct links may be common in sub-6 GHz massive MIMO, yet strong direct signals can weaken RIS influence while the shared RIS–BS link leaves multi-user interference relevant under MRC.The paper frames whether RIS can still benefit massive MIMO with direct links as an open question.Source: §I · p. 1
• The work models direct-link effects in RIS-aided massive MIMO, derives a closed-form uplink ergodic-rate expression, and uses a genetic algorithm to design phase shifts from statistical CSI.The authors state that RIS-aided massive-MIMO systems could outperform traditional systems even with simple MRC.Source: §I · p. 1

II. SYSTEM MODEL

• The uplink has a BS with M antennas serving K single-antenna users through an RIS and direct links.The RIS has N reflecting elements, and its phase-shift configuration has unit reflection amplitude.Source: §II · pp. 1–2, Figure 1 · p. 2
• The user–RIS and RIS–BS links follow Rician fading, while the direct BS–user links follow Rayleigh fading.The cascaded channel is G = H2ΦH1; direct links are represented by D.Source: §II · p. 2
• The received signal combines the cascaded and direct channels, user transmit powers and symbols, and receiver noise.The model writes y = (G + D)Px + n, with P containing square-root transmit powers, x the symbol vector, and n the receiver-noise vector.Source: §II · p. 2
• The BS forms an MRC matrix from its estimate of the overall channel G + D and processes the uplink signal with that receiver.The model assumes perfect instantaneous channel estimates, described as an upper bound for practical systems; imperfect CSI is left for future work.Source: §II · p. 2
• The paper expresses each user's ergodic rate as the expected log2(1 + SINR_k), using the user's received signal and SINR.The cascaded channel for user k is g_k = H2Φh_k.Source: §II · p. 2

• Theorem 1 gives an approximate uplink ergodic-rate expression for RIS-aided mMIMO with direct links, based on statistical rather than fast-varying CSI.The expression depends on slowly changing AoA/AoD, path-loss coefficients, and Rician factors; RIS phase updates based on statistical CSI are needed only over a long timescale.Source: §III · pp. 2–3
• With simple MRC, signal and interference terms both scale as O(M^2) in RIS-aided systems, so their ratio converges to a constant as M grows.In traditional mMIMO, the interference power is negligible compared with the signal at large M.Source: §III · p. 3
• For pure-NLoS cascaded channels, RIS phase shifts need not be designed, and the rate can grow without bound as both N and M increase.The paper identifies rich scattering as favorable for multi-user RIS systems because it can provide spatial multiplexing gains.Source: §III · p. 3
• In rich-scatter two-user settings, RIS-aided mMIMO outperforms non-RIS systems at low SNR, with large N, or with weak direct links.The analysis attributes these conditions to interference at high SNR, passive beamforming gain from large N, and relatively smaller cascaded-link contributions when direct links are strong.Source: §III · p. 3
• The GA evaluates each individual by the sum of users’ rates and returns the chromosome with the highest fitness.The described procedure uses elites, mutation, and two-point crossover to evolve the population.Source: §III · p. 4
• With random RIS phases and N → ∞, RIS-aided mMIMO beats traditional systems in the low-SNR regime, but meeting the condition remains challenging for large M.The random-phase case assumes phase shifts are set randomly in each time block.Source: §III · pp. 3–4

IV. NUMERICAL RESULTS

• The simulations use a GA-based method to design optimal RIS phase shifts from Eq. (7), with M = N = 49 and four users unless stated otherwise.Users are evenly placed on a 20 m-radius circle centered at the RIS; the RIS-BS distance defaults to 1000 m.Source: §IV · p. 4
• At low SNR, statistical CSI-based RIS improves rate with MRC; as SNR rises, conventional mMIMO outperforms random-phase RIS and can surpass optimal-phase RIS at extremely high SNR.The reported high-SNR comparison is attributed to multi-user interference.Source: §IV · p. 4
• Optimal RIS phase shifts significantly improve rate over traditional mMIMO in both figures, and the improvement persists with large M.The figures vary ergodic rate with N and M at dIB = 1000 m and 700 m.Source: §IV · p. 4, Figure 4 · p. 4
• When direct links are strong or M is large, non-RIS mMIMO performs better than random-phase RIS; the authors recommend many RIS elements for cell-edge users and identify low SNR as a significant-gain regime.Smaller dIB corresponds to stronger direct links.Source: §IV · p. 4

V. CONCLUSION

• With low-complexity MRC beamforming, RIS-aided mMIMO can outperform non-RIS systems in the low-SNR regime.The paper reports that simulations verify its analytical results.Source: §V · p. 4
• The study considers RIS-aided mMIMO systems with direct links.Source: §V · p. 4
• The authors derive a closed-form ergodic-rate expression for the system.Source: §V · p. 4

APPENDIX A

• The derivation approximates the ergodic rate Rk = E {log2 (1+ SINRk)} by applying [15, Lemma 1].Source: Appendix A · p. 4
• The proof uses independence between dk, gk, and di for i ≠ k when deriving the noise term.Source: Appendix A · pp. 4–5
• The derivation obtains the signal and interference terms, then combines the resulting expressions to complete the rate-expression proof.Source: Appendix A · p. 5