Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Optimal Transmitter Design and Pilot Spacing in MIMO Non-Stationary Aging Channels

Sajad Daei, Gabor Fodor, Mikael Skoglund

TL;DR

This work proposes a beamforming framework to capture spatial correlations and introduces a deterministic expression that approximates the average sum-capacity of all users, and obtains the optimal values of pilot spacing and beamforming vectors upon maximizing this expression.

Abstract

This work considers an uplink wireless communication system where multiple users with multiple antennas transmit data frames over dynamic channels. Previous studies have shown that multiple transmit and receive antennas can substantially enhance the sum-capacity of all users when the channel is known at the transmitter and in the case of uncorrelated transmit and receive antennas. However, spatial correlations stemming from close proximity of transmit antennas and channel variation between pilot and data time slots, known as channel aging, can substantially degrade the transmission rate if they are not properly into account. In this work, we provide an analytical framework to concurrently exploit both of these features. Specifically, we first propose a beamforming framework to capture spatial correlations. Then, based on random matrix theory tools, we introduce a deterministic expression that approximates the average sum-capacity of all users. Subsequently, we obtain the optimal values of pilot spacing and beamforming vectors upon maximizing this expression. Simulation results show the impacts of path loss, velocity of mobile users and Rician factor on the resulting sum-capacity and underscore the efficacy of our methodology compared to prior works.

Optimal Transmitter Design and Pilot Spacing in MIMO Non-Stationary Aging Channels

TL;DR

This work proposes a beamforming framework to capture spatial correlations and introduces a deterministic expression that approximates the average sum-capacity of all users, and obtains the optimal values of pilot spacing and beamforming vectors upon maximizing this expression.

Abstract

This work considers an uplink wireless communication system where multiple users with multiple antennas transmit data frames over dynamic channels. Previous studies have shown that multiple transmit and receive antennas can substantially enhance the sum-capacity of all users when the channel is known at the transmitter and in the case of uncorrelated transmit and receive antennas. However, spatial correlations stemming from close proximity of transmit antennas and channel variation between pilot and data time slots, known as channel aging, can substantially degrade the transmission rate if they are not properly into account. In this work, we provide an analytical framework to concurrently exploit both of these features. Specifically, we first propose a beamforming framework to capture spatial correlations. Then, based on random matrix theory tools, we introduce a deterministic expression that approximates the average sum-capacity of all users. Subsequently, we obtain the optimal values of pilot spacing and beamforming vectors upon maximizing this expression. Simulation results show the impacts of path loss, velocity of mobile users and Rician factor on the resulting sum-capacity and underscore the efficacy of our methodology compared to prior works.
Paper Structure (7 sections, 3 theorems, 17 equations, 3 figures)

This paper contains 7 sections, 3 theorems, 17 equations, 3 figures.

Table of Contents

  1. Introduction
  2. System model
  3. Proposed approach
  4. Numerical Results
  5. Conclusion
  6. Proof of Theorem \ref{['thm.Instantanous_SINR']}
  7. Proof of Theorem \ref{['thm.stiel']}

Key Result

Lemma 1

The covariance matrix of the LMMSE channel estimate at data time slot $i$ of frame $m$ corresponding to user $k$ based on the received measurements at pilot time slots of previous and next frames is provided by: where and $\sigma_{{\rm p},k}^2$ is the variance of each element of $\widetilde{\mathbf{e}}_{{\rm p},k}$ and $\delta_m\mathbin{\setstackgap{S}{0pt} = }\sum_{l=1}^m q_l +1$.

Figures (3)

  • Figure 1: A diagram illustrating multi-frame data transmission for each user, where $q_1, ..., q_M$ represent the data length of frames $1, ..., M$. The initial time slot of each frame is designated for pilot transmission and contains $\tau_{\rm p}$ symbols in the frequency domain.
  • Figure 2: Left Image: SSE versus number of transmit antennas. Right image: SSE versus Doppler frequency. The used parameters are $K=3, f_c=1000, PL_i=0, q_{\max}=5, M=1, N_r=10, {K_f}_i=0, {{{P_{{\rm p},i}}}}_{\max}={{P_{{\rm d},i}}}_{\max}=1, \sigma_d^2=0.01, N_r=10, \tau_p=2, \rho_{\rm T}=0.9, \rho_{\rm R}=0$, with the exception of ${f_d}_i=0.1$ in the left image.
  • Figure 3: Left image: SSE versus Rician Factor. Right image: SSE versus path loss. The used parameters are $K=3, f_c=1000, {f_d}_i=0.1, PL_i=0, q_{\max}=5, M=1, N_r=10, {{{P_{{\rm p},i}}}}_{\max}={{P_{{{\rm d},i}}}}_{\max}=1, \sigma_d^2=0.01, N_r=10, \tau_p=2, \rho_{\rm T}=0.9, \rho_{\rm R}=0$, with the exception of ${\rm PL}_i=0$ in the left image and ${K_f}_i=0$ in the right image.

Theorems & Definitions (3)

  • Lemma 1
  • Theorem 1
  • Theorem 2