[Paper Review] Turbo Coded Single User Massive MIMO

K. Vasudevan, A. Phani Kumar Reddy+2 more|arXiv (Cornell University)|Jul 6, 2021

Advanced MIMO Systems Optimization45 references17 citations

TL;DR

This paper proposes turbo-coded single-user massive MIMO (SU-MMIMO) with and without precoding to maximize spectral efficiency under fixed total antenna count. It derives upper bounds on average SNR per bit and spectral efficiency, demonstrating that BER remains insensitive to transmit antenna count and re-transmissions when total antennas are large, enabling near-optimal spectral efficiency for a given BER and total antenna budget.

ABSTRACT

This work deals with turbo coded single user massive multiple input multiple output (SU-MMIMO) systems, with and without precoding. SU-MMIMO has a much higher spectral efficiency compared to multi-user massive MIMO (MU-MMIMO) since independent signals are transmitted from each of the antenna elements (spatial multiplexing). MU-MMIMO that uses beamforming has a much lower spectral efficiency, since the same signal (with a delay) is transmitted from each of the antenna elements. In this work, expressions for the upper bound on the average signal-to-noise ratio (SNR) per bit and spectral efficiency are derived for SU-MMIMO with and without precoding. We propose a performance index $f(N_t)$, which is a function of the number of transmit antennas $N_t$. Here $f(N_t)$ is the sum of the upper bound on the average SNR per bit and the spectral efficiency. We demonstrate that when the total number of antennas ($N_{\mathrm{tot}}$) in the transmitter and receiver is fixed, there exists a minimum value of $f(N_t)$, which has to be avoided. Computer simulations show that the bit-error-rate (BER) is nearly insensitive to a wide range of the number of transmit antennas and re-transmissions, when $N_{\mathrm{tot}}$ is large and kept constant. Thus, the spectral efficiency can be made as large as possible, for a given BER and $N_{\mathrm{tot}}$.

Motivation & Objective

• To analyze spectral efficiency and SNR performance in turbo-coded single-user massive MIMO (SU-MMIMO) systems with and without precoding.
• To identify optimal configurations of transmit and receive antennas that maximize spectral efficiency under a fixed total number of antennas ($N_{\text{tot}}$).
• To propose a performance index $f(N_t)$ combining upper bound on average SNR per bit and spectral efficiency to guide system design.
• To demonstrate that bit-error rate (BER) is nearly insensitive to variations in $N_t$, $N_r$, and number of re-transmissions ($N_{rt}$) when $N_{\text{tot}}$ is large and constant.
• To show that spectral efficiency can be maximized for a given BER and $N_{\text{tot}}$ by selecting appropriate $N_t$ and $N_{rt}$.

Proposed method

• Derives upper bounds on average SNR per bit and spectral efficiency for SU-MMIMO with and without precoding over Rayleigh flat fading channels.
• Introduces a performance index $f(N_t)$ as the sum of the upper bound on average SNR per bit and spectral efficiency, dependent on the number of transmit antennas $N_t$.
• Uses an ideal receiver model with turbo coding and iterative detection, assuming perfect channel state information (CSI) at the transmitter for precoding.
• Employs a precoding scheme that mitigates inter-channel interference (ICI) by exploiting CSI, enhancing SNR performance.
• Conducts computer simulations over $10^4$ frames using the turbo encoder from [19], evaluating BER and spectral efficiency across various $N_t$, $N_r$, and $N_{rt}$ configurations.
• Compares performance with and without precoding under identical $N_{\text{tot}}$ to isolate the impact of precoding on spectral efficiency and SNR gain.

Experimental results

Research questions

• RQ1 How does precoding affect the upper bound on average SNR per bit and spectral efficiency in single-user massive MIMO systems with fixed total antennas?
• RQ2 What is the optimal distribution of transmit and receive antennas ($N_t$, $N_r$) that maximizes spectral efficiency for a given BER and fixed $N_{\text{tot}}$?
• RQ3 How sensitive is the bit-error rate (BER) to variations in the number of transmit antennas ($N_t$) and re-transmissions ($N_{rt}$) when $N_{\text{tot}}$ is held constant?
• RQ4 Can spectral efficiency be made arbitrarily large for a given BER by adjusting $N_t$ and $N_{rt}$ while keeping $N_{\text{tot}}$ fixed?
• RQ5 What is the performance trade-off between spectral efficiency and required SNR per bit in turbo-coded SU-MMIMO with and without precoding?

Key findings

• For $N_{\text{tot}} = 1024$, the highest spectral efficiency of 312 bits/sec/Hz is achieved with $N_t = 400$, $N_{rt} = 1$, and an SNR per bit upper bound of 1.09 dB.
• With $N_{\text{tot}} = 1024$, the lowest spectral efficiency of 0.25 bits/sec/Hz is achieved with $N_t = 1023$, $N_{rt} = 2$, and an SNR per bit upper bound approaching infinity.
• For $N_{\text{tot}} = 32$, the BER at 3.5 dB SNR per bit is approximately $2 \times 10^{-6}$ with precoding and $10^{-6}$ without precoding, showing significant improvement over SISO systems.
• The BER is nearly insensitive to changes in $N_t$, $N_r$, and $N_{rt}$ when $N_{\text{tot}}$ is large and fixed, indicating robustness to antenna allocation.
• The highest spectral efficiency of 256 bits/sec/Hz is achieved without precoding at $N_t = 512$, $N_{rt} = 1$, with an SNR per bit upper bound of 3.03 dB.
• The performance index $f(N_t)$ reveals a minimum value that must be avoided, indicating a non-monotonic trade-off between spectral efficiency and SNR gain as $N_t$ varies.