| Compressed sensing is a new paradigm that exploits the sparsity of signals to reduce the number of measurements required to recover a representation. This is accomplished using the general notion of inner-products as measurements, encapsulated in "measurement matrices." In this work, we focus on designing both measurement matrices as well as compressed sensing recovery algorithms. We consider several measurement code designs and recovery schemes with applications to particular systems. First, we consider chirp-coded compressed sensing measurements which, with a jointly designed recovery algorithm, is designed for computationally efficient recovery. For M measurements, O( M log M) recovery is possible, a significant speed improvement over conventional random signals and recovery methods. Subsequently, we consider OFDM channel estimation in the context of compressed sensing and note that measurement matrices are restricted to the form of sub-Fourier matrices. We provide a method to manifest suitable matrices for recovering sparse channels by deterministically selecting a few pilot tones. Next, we consider how the compressed sensing paradigm can be used to build novel wireless systems. We design a muliuser detection scheme for random access on asynchronous channels. For this system, we develop new compressed sensing recovery theory and design a codebook suitable for the recovery of sparse sets of active users. Finally, we design a virtual full-duplex adhoc wireless network system using half-duplex hardware. In the system, nodes use codes containing "listening symbols" during which the devices sense the wireless channel. When active nodes in the network transmit simultaneously, each node inherits a unique compressed sensing problem to recover the data from its neighbors.;The work in this thesis shows how, with careful consideration of the application, compressed sensing with coded matrices can provide great performance improvements and novel system designs. |
