[Paper Review] Power Allocation for Discrete-Input Non-Ergodic Block-Fading Channels

Khoa D. Nguyen, Albert Guillén i Fàbregas+1 more|ArXiv.org|May 2, 2007

Advanced Wireless Communication Techniques6 references4 citations

TL;DR

This paper proposes optimal and low-complexity suboptimal power allocation schemes for discrete-input block-fading channels with perfect channel state information at both transmitter and receiver. It shows that the SNR exponent of the optimal short-term scheme achieves the Singleton bound, and long-term power constraints yield significant outage performance gains—up to 12 dB at 10⁻⁴ outage probability—while suboptimal schemes closely match optimal performance with drastically reduced complexity.

ABSTRACT

We consider power allocation algorithms for fixed-rate transmission over Nakagami-m non-ergodic block-fading channels with perfect transmitter and receiver channel state information and discrete input signal constellations under both short- and long-term power constraints. Optimal power allocation schemes are shown to be direct applications of previous results in the literature. We show that the SNR exponent of the optimal short-term scheme is given by the Singleton bound. We also illustrate the significant gains available by employing long-term power constraints. Due to the nature of the expressions involved, the complexity of optimal schemes may be prohibitive for system implementation. We propose simple sub-optimal power allocation schemes whose outage probability performance is very close to the minimum outage probability obtained by optimal schemes.

Motivation & Objective

• To design optimal and low-complexity power allocation schemes for fixed-rate transmission over Nakagami-m block-fading channels with discrete input constellations.
• To analyze the outage performance under both short-term and long-term power constraints, leveraging perfect transmitter and receiver channel state information.
• To demonstrate that long-term power allocation yields substantial performance gains over short-term schemes, especially with discrete inputs.
• To propose suboptimal schemes that closely match optimal performance while significantly reducing computational complexity.

Proposed method

• Derives optimal short-term power allocation via water-filling, showing its SNR exponent matches the Singleton bound.
• Applies results from prior work on parallel channels with arbitrary input distributions to derive optimal long-term power allocation.
• Proposes a refined suboptimal scheme using a reference mutual information function $ I^{\text{ref}}(\rho) $ to approximate $ I_{\mathcal{X}}(\rho) $, enabling simpler computation.
• Introduces a computationally efficient approximation $ \tilde{I}_{\mathcal{X}}(\rho) = M(1 - e^{-c_1\rho^{c_2}})^{c_3} $ for mutual information, with optimized parameters for QPSK.
• Uses a two-stage power allocation rule based on thresholds involving $ \alpha, \beta, \kappa, \eta $, with $ \eta $ chosen to satisfy a rate constraint using the approximated mutual information.
• Employs a non-causal CSI assumption, modeling OFDM systems where channel gains are known before transmission.

Experimental results

Research questions

• RQ1 What is the optimal power allocation strategy for discrete-input block-fading channels under short-term power constraints, and what is its fundamental performance limit?
• RQ2 How do long-term power constraints improve outage performance compared to short-term constraints in non-ergodic block-fading channels with discrete inputs?
• RQ3 Can suboptimal power allocation schemes achieve near-optimal outage performance with significantly reduced complexity?
• RQ4 What approximation of the mutual information function enables low-complexity implementation while maintaining performance close to optimal?

Key findings

• The SNR exponent of the optimal short-term power allocation scheme for discrete inputs is bounded by the Singleton bound, indicating a fundamental limit on diversity gain.
• Long-term power allocation achieves a 12 dB gain over uniform allocation at 10⁻⁴ outage probability in a 4-block Rayleigh-fading block-fading channel with QPSK inputs.
• The proposed suboptimal long-term scheme with refined thresholds ($ \mathbf{p}_{\rm lt}^{\rm ref} $) achieves outage performance within negligible loss of the optimal scheme.
• Using a parametric approximation $ \tilde{I}_{\mathcal{X}}(\rho) $ with $ c_1=0.77, c_2=0.87, c_3=1.16 $, the rate error is bounded at $ \Delta R = 0.0033 $, enabling low-complexity implementation with minimal performance loss.
• The outage performance of the suboptimal scheme using the approximation is nearly indistinguishable from the optimal scheme in simulations, confirming its practical viability.