[Paper Review] MIMO Precoding in Underlay Cognitive Radio Systems with Completely Unknown Primary CSI

Amitav Mukherjee, Minyan Pei+1 more|arXiv (Cornell University)|Apr 5, 2012

Advanced MIMO Systems Optimization29 references3 citations

TL;DR

This paper proposes a rank-minimization precoding strategy for MIMO cognitive radio systems with completely unknown primary channel state information (CSI), introducing a novel 'frugal waterfilling' (FWF) algorithm that minimizes transmit power and rank while guaranteeing a target CR rate. FWF achieves higher primary receiver (PR) throughput than conventional waterfilling and heuristic methods despite higher interference temperature, demonstrating that interference temperature is a poor metric and that interference leakage rate is a better indicator of PR performance impact.

ABSTRACT

This paper studies a novel underlay MIMO cognitive radio (CR) system, where the instantaneous or statistical channel state information (CSI) of the interfering channels to the primary receivers (PRs) is completely unknown to the CR. For the single underlay receiver scenario, we assume a minimum information rate must be guaranteed on the CR main channel whose CSI is known at the CR transmitter. We first show that low-rank CR interference is preferable for improving the throughput of the PRs compared with spreading less power over more transmit dimensions. Based on this observation, we then propose a rank minimization CR transmission strategy assuming a minimum information rate must be guaranteed on the CR main channel. We propose a simple solution referred to as frugal waterfilling (FWF) that uses the least amount of power required to achieve the rate constraint with a minimum-rank transmit covariance matrix. We also present two heuristic approaches that have been used in prior work to transform rank minimization problems into convex optimization problems. The proposed schemes are then generalized to an underlay MIMO CR downlink network with multiple receivers. Finally, a theoretical analysis of the interference temperature and leakage rate outage probabilities at the PR is presented for Rayleigh fading channels.We demonstrate that the direct FWF solution leads to higher PR throughput even though it has higher interference "temperature (IT) compared with the heuristic methods and classic waterfilling, which calls into question the use of IT as a metric for CR interference.

Motivation & Objective

• Address the challenge of designing efficient MIMO cognitive radio systems when the cognitive radio transmitter has no knowledge of the primary user's channel state information (CSI), including both instantaneous and statistical knowledge.
• Ensure a minimum quality-of-service (rate) requirement on the cognitive radio's main communication link despite the lack of primary CSI.
• Develop a transmission strategy that minimizes interference to primary users while maximizing primary system throughput under these constraints.
• Re-evaluate the validity of interference temperature (IT) as a metric for cognitive radio interference impact, given its disconnect from actual primary performance.
• Propose and validate an alternative metric—interference leakage rate—that better reflects the true impact of cognitive transmissions on primary users.

Proposed method

• Propose a rank minimization framework for the cognitive radio transmit covariance matrix to reduce spatial degrees of freedom and concentrate interference, thereby improving primary user throughput.
• Introduce the 'frugal waterfilling' (FWF) algorithm, a simple, closed-form solution that achieves the required cognitive rate with minimum power and minimum-rank covariance matrix.
• Adapt two convex relaxation techniques—nuclear norm and log-determinant heuristic—to approximate the non-convex rank minimization problem.
• Generalize the FWF and heuristic strategies to multi-user MIMO underlay downlink scenarios using a modified block-diagonalization (BD) approach.
• Derive theoretical expressions for interference temperature and leakage rate outage probabilities using random matrix theory for Rayleigh fading channels.
• Use empirical complementary cumulative distribution functions (ccdf) to compare the statistical behavior of interference temperature and leakage rate across different algorithms.

Experimental results

Research questions

• RQ1 Can a cognitive radio system achieve high spectral efficiency and minimize interference to primary users when no CSI of the primary links is available?
• RQ2 Does minimizing the rank of the cognitive radio's transmit covariance matrix lead to better primary user performance than spreading power across more spatial dimensions?
• RQ3 How does the performance of the proposed frugal waterfilling (FWF) algorithm compare to conventional waterfilling and heuristic rank approximations in terms of primary user throughput and outage probability?
• RQ4 Is the commonly used interference temperature (IT) metric a reliable indicator of actual interference impact on primary users, or is it misleading?
• RQ5 Can the interference leakage rate serve as a more accurate and meaningful metric for evaluating cognitive radio interference than interference temperature?

Key findings

• The frugal waterfilling (FWF) algorithm achieves the highest primary user (PR) throughput among all tested schemes, even though it results in the highest interference temperature.
• FWF consistently outperforms both conventional waterfilling (CWF) and log-det heuristic methods in terms of average PR rate and PR rate outage probability.
• The interference temperature (IT) metric is shown to be misleading, as higher IT does not correlate with worse PR performance—FWF has the highest IT but the best PR performance.
• The proposed interference leakage rate metric correlates strongly with actual PR performance and is a more accurate indicator of cognitive radio interference impact than IT.
• Theoretical analysis and simulations confirm that rank minimization leads to better PR performance than power spreading across multiple spatial dimensions, even under Rayleigh fading.
• In multi-user MIMO underlay downlink scenarios with three cognitive users, FWF maintains superior PR rate performance across varying transmit power and target rate configurations.