Relay precoding for multiple-input and multiple-output (MIMO) relay networks has been approached by either optimizing the efficiency performance with given power consumption constraints or minimizing the power consumption with quality-of-service (QoS) requirements. For the later type design, previous works has worked on minimizing the approximated power consumption. In this paper, exact power consumption for all relays is derived into a quadratic form by diagonalizing the minimum-square error (MSE) matrix, and the relay precoding matrix is designed by optimizing this quadratic form with the help of semidefinite programming (SDP) relaxation. Our simulation results show that such a design can achieve a gain of around 3 dB against the previous design, which optimized the approximated power consumption.

In this paper, a unified generalized eigenvalue based spectrum sensing framework referred to as Generalized mean detector (GMD) has been introduced. The generalization of the detectors namely (i) the eigenvalue ratio detector (ERD) involving the ratio of the largest and the smallest eigenvalues; (ii) the Geometric mean detector (GEMD) involving the ratio of the largest eigenvalue and the geometric mean of the eigenvalues and (iii) the Arithmetic mean detector (ARMD) involving the ratio of the largest and the arithmetic mean of the eigenvalues is explored. The foundation of the proposed unified framework is based on the calculation of exact analytical moments of the random variables of test statistics of the respective detectors. In this context, we approximate the probability density function (PDF) of the test statistics of the respective detectors by Gaussian/Gamma PDF using the moment matching method. Finally, we derive closed-form expressions to calculate the decision threshold of the eigenvalue based detectors by exchanging the derived exact moments of the random variables of test statistics with the moments of the Gaussian/Gamma distribution function. The performance of the eigenvalue based detectors is compared with the traditional detectors such as energy detector (ED) and cyclostationary detector (CSD) and validate the importance of the eigenvalue based detectors particularly over realistic wireless cognitive environments. Analytical and simulation results show that the GEMD and the ARMD yields considerable performance advantage in realistic spectrum sensing scenarios. Moreover, our results based on proposed simple and tractable approximation approaches are in perfect agreement with the empirical results.

In a cognitive relay system, the secondary user is permitted to transmit data via a relay when licensed frequency bands are detected to be free. Previous studies mainly focus on reducing or limiting the interference of the secondary transmission to the primary users. On the other hand, however, the primary user traffic also affects the data transmission performance of the secondary users. In this paper, we mainly investigate the impact of the primary user traffic on the bit error rate (BER) of the secondary transmission, when the secondary user adopts adaptive transmission with a partially selected relay. In addition, the average collision time and the average collision probability have been used to measure the interference level caused by the secondary transmission to the primary users. Based on some selected numerical results, we can see that the primary user traffic seriously degrades the average BER. The worse-link partial selection can perform almost as well as the global selection when the channel conditions of the source-relay links and the relay-destination links are quite different. Although the relay selection improves the spectral efficiency of the secondary transmission, numerical results show that it only has slight impact on the overall average BER, which implies that the robustness of the system will not be affected by the relay selection.

Eigenvalue Ratio (ER) detector based on the two extreme eigenvalues of the received signal covariance matrix is currently one of the most effective solution for spectrum sensing. However, the analytical results of such scheme often depend on asymptotic assumptions since the distribution of the ratio of two extreme eigenvalues is exceptionally complex to compute. In this paper, a non-asymptotic spectrum sensing approach for ER detector is introduced to approximate the marginal and joint distributions of the two extreme eigenvalues. The two extreme eigenvalues are considered as dependent Gaussian random variables such that their joint probability density function (PDF) is approximated by a bivariate Gaussian distribution function for any number of cooperating secondary users and received samples. The PDF approximation approach is based on the moment matching method where we calculate the exact analytical moments of joint and marginal distributions of the two extreme eigenvalues. The decision threshold is calculated by exploiting the statistical mean and the variance of each of the two extreme eigenvalues and the correlation coefficient between them. The performance analysis of our newly proposed approximation approach is compared with the already published asymptotic Tracy-Widom approximation approach. It has been shown that our results are in perfect agreement with the simulation results for any number of secondary users and received samples.

Previous works in cooperative spectrum sensing assumed that the channels for sensing and reporting are independent identically distributed (i.i.d). A more practical and appropriate assumption, however, should be that the sensing channels and reporting channels are independent but not necessarily identically distributed (i.n.i.d). In this paper, we derive the false-alarm probability and the detection probability of cooperative spectrum sensing with energy fusion over i.n.i.d Nakagami fading channels. Selected numerical results show that cooperative spectrum sensing still gives considerably better performance results even over i.n.i.d fading channels.

Different from previous works in cooperative spectrum sensing that assumed the sensing channels independent identically distributed (i.i.d.), we investigate in this paper the independent but not identically distributed (i.n.i.d.) situations. In particular, we derive the false-alarm probability and the detection probability of cooperative spectrum sensing with the scheme of energy fusion over i.n.i.d. Rayleigh, Nakagami, and Rician fading channels. From the selected numerical results, we can see that cooperative spectrum sensing still gives considerably better performance even over i.n.i.d. fading environments.