DATOS PERSONALES

Cognitive Radio: This is a state-of-the-art research area for application of the recent communications and signal processing techniques. Apart from the underlay paradigm employed in Chapter 4, intelligent signal processing has been proposed as another prototype for cognitive radio [20]. The principle is to make cognitive radio an intelligent device such that it is adapt to the wireless environment by proper spectrum sensing and correct decision making of the transmit parameters. In order to have intelligence, like human beings, memory has to be introduced into signal modelling. Memory can be modeled as, e.g., a matrix containing state information changing with time. This matrix will be updated according to the dynamics of the communication environment. The intelligent algorithms can be referred to, e.g., Kalman …lter and Bayesian …lter, for online data processing. From another angle, the adaptive signal processing is evolving into intelligent signal processing under the background of cognitive radio.

Particle Filters: In many application areas, e.g., the econometrics, dy- namic spectrum access, airborne target tracking and missile guidance, elements of non-linearity and non-Gaussianity have to be considered in order to accu- rately model the underlying dynamics of a physical system. Particle …lters [80], which are the sequential Monte Carlo methods based on representations of posterior probability densities, can be applied to any state-space model. In

5. Conclusions and Future Work 117

addition to that, particle …lters are a generalization of the traditional Kalman …ltering methods. It would be bene…cial to introduce particle …lters into array processing for rapid adaptation to changing signal characteristics in the pres- ence of non-linearity and non-Gaussianity. For example, a cognitive radio can employ particle …lters for its antenna array tracking system to …nd a piece of spectrum among many existing radios.

Convex Optimisation: Convex optimisation has now emerged as an e¢ cient signal processing tool that has made a signi…cant impact on numerous problems previously considered NP-hard. Its recent development has been introduced in a series of articles [77]-[85]. Considering from the second order statistics, a typical convex optimisation based beamforming can be formulated in the quadratic form. The argument of interest is the covariance matrix of beam- formers. Given the covariance matrix of channel and the received signal vector, an optimisation problem with respect to positive semi-de…nite matrix can be formed. Such a problem can be e¢ ciently solved using many well-developed convex optimisation packages. The main advantage of convex optimisation lies on its computational e¢ ciency to NP-hard MIMO detection problem [77] (e.g., N(Tx) _{= N}(Rx) _{= 40, which is also a dimensionality reduction problem), corre-} spondingly a tradeo¤ of accuracy but good approximation. Typical research directions in this area for beamforming [83] involve downlink beamforming, downlink-uplink duality beamforming and robust beamforming.

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