Mean Value-Based Power Allocation and Ratio Selection for MIMO Cognitive Radio Systems Kamel Tourki ∗ , Khalid A. Qaraqe ∗ and Mohamed-Slim Alouini ∗∗ ∗ Texas A&M University at Qatar, Education City, Qatar, Email: {kamel.tourki,khalid.qaraqe}@qatar.tamu.edu ∗∗ KAUST, Thuwal, Makkah Province, Kingdom of Saudi Arabia, Email: mohamed.alouini@kaust.edu.sa Abstract—In this paper, we consider a spectrum sharing cognitive radio system with ratio selection using a mean value- based power allocation strategy. We first provide the exact statistics in terms of probability density function and cumulative density function of the secondary channel gain as well as of the interference channel gain. These statistics are then used to derive exact closed form expression of the secondary outage probability. Furthermore, asymptotical analysis is derived and generalized diversity gain is deduced. We validate our analysis with simulation results in a Rayleigh fading environment. I. I NTRODUCTION Cognitive radio (CR) started as a form of intelligent wireless communication in which a transmitter, referred to as secondary user (SU), can detect unused licensed spectrum (known as white space) in order to utilize it and avoid interference with occupied ones [1]. However, the CR must continuously sense the spectrum (link maintenance) it is using in order to detect the reappearance of the licensed user, referred to as primary user (PU). Once the PU activity is detected, the SU should evacuate the band (link release). More recent works focused on spectrum sharing in cognitive networks, where a SU may share the primary spectrum during the PU’s activity on condition that its transmission will not cause harmful interference at the primary receiver [2]–[4]. This may restrain the transmit power in the secondary system especially when the interference channel gain is high and the secondary link is deeply faded. As a consequence, multiple antennas can be used to provide the secondary transmitter more degrees of freedom in space, time, and frequency, so as to balance between maximizing its own transmit rate and minimizing the interference power at the primary receiver [5]. In particular, to enhance the secondary capacity using multiple-input multiple- output (MIMO) systems, the total amount of interference caused by the secondary transmitter is directly controlled by precoding and beamforming [5]–[7]. These schemes typically require complex-valued full channel state information (CSI) and additional computational complexity to generate precoding and beamforming vectors. A. Related Works Recent works have focused on investigating the secondary capacity and adapted power allocation strategy based on the amount of the CSI of the interference channel gain [8]– [10]. More specifically, considering a simple point-to-point secondary system, the author in [9] showed that the secondary capacity performance could benefit more from the flexibility of the average interference power constraint than from its peak interference counterpart. Such conclusions were reconfirmed in [10] where the authors demonstrated that a mean value- based power allocation outperforms an instantaneous outdated channel information-based scheme. On the other hand, more recent works investigated MIMO secondary link to enhance capacity [11]–[14]. In particular in [11], the authors proposed a ratio selection scheme with a conventional power allocation strategy without accounting for the transmit power constraint. This means that the transmit power of the secondary trans- mitter can approach infinity when the interference link is in deep fading. Moreover, the analysis of transmit diversity spectrum sharing system with single antenna receiver at the primary and secondary receivers were provided, where the analytical results were only derived in an approximated form. However, and following the same system model, Wang and Coon proposed a new transmit antenna selection, called as difference antenna selection, under peak and average inter- ference power constraint [12]. They derived closed form expression for the secondary outage probability as function of the difference selection weight and the secondary trans- mit power. Surprisingly, the best performance are achieved when the difference selection reduces to the classical transmit antenna selection (difference selection weight equal to one), in which the transmit antenna selection is reduced to the secondary-to-secondary link only. In [13], the authors analyzed the effect of maximum ratio combining (MRC) diversity on the performance of spectrum sharing systems. Considering transmit and interference power constraints, the results were limited to the asymptotic performance of the system. Finally, the authors in [14] considered a transmit antenna selection using a conventional power allocation scheme. However, they failed to derive a closed form expression for the capacity of a MIMO CR system without relaxing the transmit power constraint. B. Contributions While the use of transmit antenna selection in spectrum sharing systems has been well investigated in the literature, to the best of knowledge of the authors, none of the previous works has derived the statistics of the secondary and inter- ference links when ratio selection is considered. Furthermore, the mean value (MV)-based power allocation scheme is of 978-1-4673-3122-7/13/$31.00 ©2013 IEEE IEEE ICC 2013 - Cognitive Radio and Networks Symposium 1341