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Asymptotic Capacity of 1-Bit MIMO Fading Channels

Sheng Yang, Richard Combes

Abstract

In this work, we investigate the capacity of multi-antenna fading channels with 1-bit quantized output per receive antenna. Specifically, leveraging Bayesian statistical tools, we analyze the asymptotic regime with a large number of receive antennas. In the coherent case, where the channel state information (CSI) is known at the receiver's side, we completely characterize the asymptotic capacity and provide the exact scaling in the extreme regimes of signal-to-noise ratio (SNR) and the number of transmit antennas. In the non-coherent case, where the CSI is unknown but remains constant during T symbol periods, we first obtain the exact asymptotic capacity for T<=3. Then, we propose a scheme involving uniform signaling in the covariance space and derive a non-asymptotic lower bound on the capacity for an arbitrary block size T. Furthermore, we propose a genie-aided upper bound where the channel is revealed to the receiver. We show that the upper and lower bounds coincide when T is large. In the low SNR regime, we derive the asymptotic capacity up to a vanishing term, which, remarkably, matches our capacity lower bound.

Asymptotic Capacity of 1-Bit MIMO Fading Channels

Abstract

In this work, we investigate the capacity of multi-antenna fading channels with 1-bit quantized output per receive antenna. Specifically, leveraging Bayesian statistical tools, we analyze the asymptotic regime with a large number of receive antennas. In the coherent case, where the channel state information (CSI) is known at the receiver's side, we completely characterize the asymptotic capacity and provide the exact scaling in the extreme regimes of signal-to-noise ratio (SNR) and the number of transmit antennas. In the non-coherent case, where the CSI is unknown but remains constant during T symbol periods, we first obtain the exact asymptotic capacity for T<=3. Then, we propose a scheme involving uniform signaling in the covariance space and derive a non-asymptotic lower bound on the capacity for an arbitrary block size T. Furthermore, we propose a genie-aided upper bound where the channel is revealed to the receiver. We show that the upper and lower bounds coincide when T is large. In the low SNR regime, we derive the asymptotic capacity up to a vanishing term, which, remarkably, matches our capacity lower bound.
Paper Structure (39 sections, 26 theorems, 86 equations)

This paper contains 39 sections, 26 theorems, 86 equations.

Table of Contents

  1. Introduction
  2. Problem formulation
  3. Channel model
  4. Coherent communication
  5. Non-coherent communication
  6. Coherent communication
  7. Channel capacity
  8. Asymptotic SNR and $n_\text{t}$ regimes
  9. Non-coherent communication: Special cases with $T=2, 3$
  10. The case $T=2$
  11. The case $T=3$
  12. Non-coherent communication: Arbitrary $T$
  13. Lower bounds
  14. Input distribution
  15. Receiver
  16. ...and 24 more sections

Key Result

Proposition 0

Let ${\pmb{y}}_1,\ldots,{\pmb{y}}_{n_\text{r}}$ be i.i.d. samples from the density $f({\pmb{y}};{\pmb{\theta}})$, ${\pmb{\theta}}\in\Omega$, satisfying some regularity conditions.The conditions are specified in Appendix app:CB_cond. When $n_\text{r}$ is large, for any compact subset ${\mathcal{K}}$ where $\mathrm{dim}({\mathcal{K}})$ is the dimension of the parameter space ${\mathcal{K}}$; $\pmb{

Theorems & Definitions (44)

  • Proposition 0: Clarke and Barron CB94
  • Lemma 1
  • proof
  • Lemma 2
  • Lemma 3
  • proof
  • Proposition 1
  • proof
  • Corollary 1
  • Lemma 4
  • ...and 34 more