Compressive Sampling based Multiple Symbol Differential Detection for UWB Communications

Compressive sampling (CS) based multiple sym- bol differential detectors are proposed for impulse-radio ultra- wideband signaling, using the principles of generalized likelihood ratio tests. The CS based detectors correspond to two communica- tion scenarios. One, where the signaling is fully synchronized at the receiver and the other, where there exists a symbol level synchro- nization only. With the help of CS, the sampling rates are reduced much below the Nyquist rate to save on the high power consumed by the analog-to-digital converters. In stark contrast to the usual compressive sampling practices, the proposed detectors work on the compressed samples directly, thereby avoiding a complicated reconstruction step and resulting in a reduction of the implemen- tation complexity. To resolve the detection of multiple symbols, compressed sphere decoders are proposed as well, for both com- munication scenarios, which can further help to reduce the sys- tem complexity. Differential detection directly on the compressed symbols is generally marred by the requirement of an identical measurement process for every received symbol. Our proposed detectors are valid for scenarios where the measurement process is the same as well as where it is different for each received symbol.