Special issue on compressive sensing in communications

Compressive sensing, also known as compressive sampling, has made a tremendous impact on signal processing and statistical learning, and has facilitated numerous applications in areas ranging frommedical imaging and computational biology to astronomy. Recently, there has been a growing interest in applying the principles of compressive sensing to an even wider range of topics, including those in communications and networking. The basic thesis of compressive sensing – and its powerful appeal for many applications – is that under certain conditions it suffices to collect only a small number of signal observations (e.g., pixels of an image) and still be able to reconstruct the signal in its entirety when the signal admits a sparse representation in a basis or a frame. This statement has a profound impact on the way in which a communication system can be designed. From data compression in band-limited systems to estimation of communication channels that are naturally sparse; from active or passive delay, angle, and Doppler estimation of specific targets to distributed sensing of sparse fields, the principles of compressive sensing canbe applied to provide system designs that are more efficient than the traditional ones. This special issue is devoted to those areas of communication system and network design where compressive sensing brings new insights and tools to yield effective solutions for the problems of interest. The issue contains eleven high-quality papers whose topics range from signal detection and channel estimation to radio spectrum sensing and information gathering in energyconstrained sensor networks, offering innovative methodologies, algorithms, and theoretical results by using the existing results of compressive sensing or by extending them. The first paper in this issue, ‘‘Measurement Design for Detecting Sparse Signals’’ [1], addresses the problem of binary hypothesis testingwhen it is known that the observed signal is sparse in some domain. The question of measurement matrix design is posed, with the goal of maximizing the signal-to-noise ratio at the input to the detector. Two optimization frameworks are considered—maximization of the worst case and of the average minimum signalto-noise ratio, yielding respective performance bounds. The customized, deterministic measurement matrices are