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Characterization of Capacity and Outage of RIS-aided Downlink Systems under Rician Fading

Kali Krishna Kota, Praful D. Mankar, Harpreet S. Dhillon

Abstract

This letter presents optimal beamforming and outage analysis for a Reconfigurable Intelligent Surface (RIS)-aided multiple input single output downlink system under Rician fading on both the direct and the RIS-assisted indirect links. We focus on maximizing the capacity for two transmitter architectures: fully digital (FD) and fully analog (FA). This capacity maximization problem with optimally configured RIS is shown to be $L_1$ norm-maximization with respect to the transmit beamformer. To obtain the optimal FD beamformer, we propose a complex $L_1$-PCA-based algorithm whose complexity is significantly lower than the existing semi-definite relaxation-based solutions. We also propose a low-complexity optimal beamforming algorithm to obtain the FA beamformer solution. Further, we derive analytical upper bounds on the SNR achievable by the proposed algorithms and utilize them to characterize the lower bounds on outage probabilities. The derived bounds are numerically shown to closely match the achievable performance for a low-rank channel matrix and are shown to be exact for a unit-rank channel matrix.

Characterization of Capacity and Outage of RIS-aided Downlink Systems under Rician Fading

Abstract

This letter presents optimal beamforming and outage analysis for a Reconfigurable Intelligent Surface (RIS)-aided multiple input single output downlink system under Rician fading on both the direct and the RIS-assisted indirect links. We focus on maximizing the capacity for two transmitter architectures: fully digital (FD) and fully analog (FA). This capacity maximization problem with optimally configured RIS is shown to be norm-maximization with respect to the transmit beamformer. To obtain the optimal FD beamformer, we propose a complex -PCA-based algorithm whose complexity is significantly lower than the existing semi-definite relaxation-based solutions. We also propose a low-complexity optimal beamforming algorithm to obtain the FA beamformer solution. Further, we derive analytical upper bounds on the SNR achievable by the proposed algorithms and utilize them to characterize the lower bounds on outage probabilities. The derived bounds are numerically shown to closely match the achievable performance for a low-rank channel matrix and are shown to be exact for a unit-rank channel matrix.
Paper Structure (10 sections, 4 theorems, 28 equations, 1 figure, 2 algorithms)

This paper contains 10 sections, 4 theorems, 28 equations, 1 figure, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. Optimal Beamforming
  4. Optimal RIS phase shifts
  5. Optimal Transmit Beamforming
  6. Digital Beamformer
  7. Analog Beamformer
  8. Outage Probability Analysis
  9. Numerical Results and Discussion
  10. Conclusion

Key Result

Theorem 1

The maximum capacity of a RIS-aided MISO communication system with FA architecture is upper bounded by $\log_2(1+\Gamma^{\rm UB})=\log_2(1+\frac{\gamma}{M}\|\mathbf{G}\|^2_{1,1})$.

Figures (1)

  • Figure 1: Capacity vs. $N$ without DL (left), with either DL or IL (middle bottom), and with both DL and IL (middle top). Outage probability (right).

Theorems & Definitions (7)

  • Remark 1
  • Theorem 1
  • Corollary 1.1
  • Corollary 1.2
  • proof
  • Remark 2
  • Theorem 2