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On Analysis of Superimposed Pilot in Multi-User Massive MIMO with Massive Connectivity

Shuxiao Ye, Xianchao Zhang, Neng Ye

TL;DR

This work tackles the challenge of massive connectivity in multi-user MIMO by analyzing a superimposed-pilot (SP) scheme, which allows simultaneous pilot and data transmission when the number of users $K$ exceeds the coherence-time length $L$. It develops a non-asymptotic mutual-information lower bound (MILB) framework and derives an explicit scaling law, along with an analytical method to optimally allocate power between pilots and data. The paper compares SP with regular pilots (RP), deriving MILB expressions for both and showing that SP offers substantial improvements in achievable information rate under realistic system parameters. Numerical results corroborate the theory, highlighting SP’s potential to enhance spectral efficiency in ultra-dense uplink massive-MIMO scenarios and providing practical guidance on power split and pilot design for massive connectivity.

Abstract

The simultaneous transmission of numerous users presents substantial challenges due to the inherent trade-off between channel estimation and information transmission in multi-user multiple-input multiple-output (MIMO) system. In this paper, we explore the use of the superimposed pilot (SP) scheme to tackle the large transmitting users, where the number of users may exceed the coherent time. SP scheme incorporates both transmitted data and noise in the channel estimation process, which is significant different from the counterpart of RP scheme. We provide an in-depth analysis of the interaction between interference caused by channel estimation errors and noise. We then derive the explicit expression for the scaling law of the mutual information lower bound (MILB) in relation to the number of users and the levels of transmitted power. Besides, the optimal power allocation between pilots and data transmission is also derived analytically. The analytical results demonstrate that the SP scheme significantly improves performance compared to traditional RP scheme in our consider case. Numerical results are also presented to validate our theoretical derivations.

On Analysis of Superimposed Pilot in Multi-User Massive MIMO with Massive Connectivity

TL;DR

This work tackles the challenge of massive connectivity in multi-user MIMO by analyzing a superimposed-pilot (SP) scheme, which allows simultaneous pilot and data transmission when the number of users exceeds the coherence-time length . It develops a non-asymptotic mutual-information lower bound (MILB) framework and derives an explicit scaling law, along with an analytical method to optimally allocate power between pilots and data. The paper compares SP with regular pilots (RP), deriving MILB expressions for both and showing that SP offers substantial improvements in achievable information rate under realistic system parameters. Numerical results corroborate the theory, highlighting SP’s potential to enhance spectral efficiency in ultra-dense uplink massive-MIMO scenarios and providing practical guidance on power split and pilot design for massive connectivity.

Abstract

The simultaneous transmission of numerous users presents substantial challenges due to the inherent trade-off between channel estimation and information transmission in multi-user multiple-input multiple-output (MIMO) system. In this paper, we explore the use of the superimposed pilot (SP) scheme to tackle the large transmitting users, where the number of users may exceed the coherent time. SP scheme incorporates both transmitted data and noise in the channel estimation process, which is significant different from the counterpart of RP scheme. We provide an in-depth analysis of the interaction between interference caused by channel estimation errors and noise. We then derive the explicit expression for the scaling law of the mutual information lower bound (MILB) in relation to the number of users and the levels of transmitted power. Besides, the optimal power allocation between pilots and data transmission is also derived analytically. The analytical results demonstrate that the SP scheme significantly improves performance compared to traditional RP scheme in our consider case. Numerical results are also presented to validate our theoretical derivations.
Paper Structure (10 sections, 2 theorems, 43 equations, 3 figures)

This paper contains 10 sections, 2 theorems, 43 equations, 3 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Signal Model
  4. Superimposed Pilot
  5. Regular Pilot
  6. Performance Analysis
  7. Performance of Superimposed Pilot
  8. Performance of Regular Pilot
  9. Numerical Results and Discussion
  10. Conclusion

Key Result

Theorem 1

The variance of element in $\mathbf{V}$ is given by

Figures (3)

  • Figure 1: The structure of transmission signal under RP and SP schemes.
  • Figure 2: The MILB versus the levels of transmitted power $P$ under different users $K$.
  • Figure 3: The MILB versus the number of transmitted users $K$ under different power levels $P$.

Theorems & Definitions (2)

  • Theorem 1
  • Theorem 2