Wireless Communications Research Group
Convex Optimisation for Cognitive Radio Systems
This research focuses on the application of convex optimisation to spectrum sharing cognitive radio systems. Convex optimisation methods are widely used in the design and analysis of communications systems. Many problems that arise in communications signal processing can be cast or converted into convex optimisation problems which allow analytical or numerical solutions to be calculated easily.
The problems considered are optimum power control, robust cognitive distributed beamforming and robust cognitive multi-antenna beamforming.
The power control problem considers a cognitive radio system with $N$ secondary user (SU) pairs sharing spectrum with a pair of primary users (PU). The SU power allocation problem is formulated as a capacity maximisation problem under PU and SU quality of service and SU peak power constraints. We show our problem formulation is a geometric program and can be solved with convex optimisation techniques. We examine the effect of PU transmissions in our formulations. Solutions for both low- and high- signal-to-interference-and-noise ratio (SINR) scenarios are provided. We show that including the PU capacity in the optimisation problem in some circumstances leads to increased PU performance while not significantly degrading SU capacity. In a practical wireless communications system, accurate channel state information (CSI) is not often available hence we formulate power allocation problems with both perfect and imperfect CSI and analyse the performance loss incurred due to imperfect CSI. Furthermore, we present a novel method of detecting and removing infeasible SU quality of service constraints from the SU power allocation problem that results in considerably improved SU performance. Cumulative distribution functions of capacity for various Rayleigh fading channels are presented.
The distributed beamforming problem considers a cognitive radio (CR) relay network consisting of a cognitive source, a cognitive destination and a number of cognitive relay nodes that share spectrum with a primary transmitter and receiver. Due to poor channel conditions, the cognitive source is unable to communicate directly with the cognitive destination and hence employs the cognitive relays for assistance. We assume that the CR has a very loose cooperation with the primary network and therefore, only partial channel state information is available. Under these assumptions, we propose a new statistically robust CR cooperative relay beamformer where either the total relay transmit power or the cognitive destination signal-to-interference-and-noise ratio (SINR) is optimised subject to primary receiver outage probability constraint. We formulate the robust total relay power and the cognitive destination SINR optimisation problems as a convex second order cone program and a convex feasibility problem, respectively, that provide near optimum results. We also present efficient iterative algorithms that provide the optimum results.
The robust cognitive beamforming problem considers a cognitive radio (CR) network consisting of a secondary user transmitter (SU-Tx) equipped with multiple antennas and a secondary user receiver (SU-Rx) that share spectrum with multiple primary user transmitter (PU-Tx) and receiver (PU-Rx) pairs. We assume that the CR has a loose cooperation with the primary network and therefore, only partial channel state information of each of the PU-Tx to PU-Rx and SU-Tx to each PU-Rx links is available. Furthermore, we assume that the SU-Tx to SU-Rx link CSI is imperfect, with the channel error modelled as additive Gaussian noise. Under these assumptions, we propose a new statistically robust CR beamformer where the total SU-Tx transmit power is minimised subject to PU-Rx and SU-Rx outage probability constraints. We present expressions for PU-Rx and SU-Rx outage probabilities and formulate the robust beamformer optimisation problem as a convex semidefinite program (SDP). SU-Tx transmit power, PU-Rx signal-to-interference-and-noise ratio (SINR) and SU-Rx signal-to-noise (SNR) cumulative distribution functions (CDFs) are obtained through solution of our optimisation problem.
 S. Singh, P. Teal, P. Dmochowski, A. Coulson, "Statistically Robust Cognitive Radio Beamforming", in Proc. Australian Communications Theory Workshop (AusCTW), 2013
 S. Singh, P. Teal, P. Dmochowski, A. Coulson, "Statistically Robust Cooperative Beamforming for Cognitive Radio Networks", IEEE International Conference on Communications (ICC 2013). (accepted)
 S. Singh, P. Teal, P. Dmochowski, A. Coulson, "Interference Management in Cognitive Radio Systems with Feasibility Detection", IEEE Transactions on Vehicular Technologies, 2013. (accepted)
 S. Singh, P. Teal, P. Dmochowski, A. Coulson, "Power Allocation in Underlay Cognitive Radio Systems with Feasibility Detection", in Proc. Australian Communication Theory Workshop (AusCTW), 2012, pp. 135-139.
 S. Singh, P. Teal, P. Dmochowski, A. Coulson, "Interference Management in Cognitive Radio Systems - a Convex Optimisation Approach", in Proc. IEEE International Conference on Communications (ICC), 2012, pp. 1884-1889
 Mitola, J.; Maguire, G.Q., Jr., "Cognitive radio: making software radios more personal," Personal Communications, IEEE , vol.6, no.4, pp.13,18, Aug 1999
 Ghasemi, A.; Sousa, E.S., "Fundamental limits of spectrum-sharing in fading environments," Wireless Communications, IEEE Transactions on , vol.6, no.2, pp.649,658, Feb. 2007
 Palomar, D.P.; Cioffi, J.M.; Lagunas, Miguel-Angel, "Joint Tx-Rx beamforming design for multicarrier MIMO channels: a unified framework for convex optimization," Signal Processing, IEEE Transactions on , vol.51, no.9, pp.2381,2401, Sept. 2003
 Zhi-Quan Luo; Wei Yu, "An introduction to convex optimization for communications and signal processing," Selected Areas in Communications, IEEE Journal on , vol.24, no.8, pp.1426,1438, Aug. 2006
 Mung Chiang; Chee-wei Tan; Palomar, D.P.; O'Neill, D.; Julian, D., "Power Control By Geometric Programming," Wireless Communications, IEEE Transactions on , vol.6, no.7, pp.2640,2651, July 2007
 V. Havary-Nassab, S. Shahbazpanahi, A. Grami, and Z. Luo, "Distributed beamforming for relay networks based on second-order statistics of the channel state information," IEEE Trans. Signal Proc., vol. 56, no. 9, pp. 4306-4316, Sept. 2008.
 M. Bengtsson and B. Ottersten, Handbook on Antennas in Wireless Communications. CRC, 2002, ch. Optimal and suboptimal transmit