Compressive Sampling of Multi-Channel Data, 16-R8017

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Principal Investigator
Ryan B. Casey

Inclusive Dates:  01/01/09 – 12/31/09

Background - A direction-finding (DF) system uses phase-coherent receivers connected to an array of antenna elements to estimate a received signals direction of arrival (DOA). The increase in signal density resulting from the wireless communications boom is driving the need for a full multi-channel design that enables multi-signal DF techniques and digital beam and null steering to improve collection on the signal of interest when more than one signal is present simultaneously. The limiting factor of a multi-channel system is cost. Radio-frequency components including receivers have not decreased in price as rapidly as digital processing components, and consequently the addition of multiple RF channels can increase system cost dramatically. An alternative to multi-channel systems is to commutate the antenna elements through a single RF channel where a switch selects each antenna in the array, sampling a time series from one antenna at time before moving to the next antenna. The DOA is then estimated by processing the sequenced data along with a reference channel. Compressive sampling is a "new" technique in the field of signal processing and image processing, and may hold the possibility of reconstructing parallel signal channels from a commutated antenna system. Compressive sampling is based on the premise that redundant information is present in virtually all signals, allowing effective sampling to be achieved at a rate considerably lower than what has been historically required. The theory behind compressive sampling has been around for several decades, but the technology for practical and reliable information recovery has only recently been developed.

Approach - The objective of the proposed effort is to investigate a new space-time sampling structure. This structure will reconstruct all multi-channel data from a small number of channels. The sampled channels will be pseudo-randomly chosen from a subset of elements that are simultaneously sampled for a given time interval before switching to another randomly chosen subset of elements. The key area of research is discovering a workable set of pseudo random sampling intervals spatial domain that exploits the redundancy of signal content and reliably enables reconstruction of all antenna responses.

Accomplishments - A compressive sampling model based on a given sensor array geometry, the wave-number vector Fourier transform (WVFT) and a sequencing model were developed. Compressive sensing was applied to the space-time problem using these models in conjunction with known sparse reconstruction algorithms found in the literature. The complete WVFT space was accurately reconstructed from the randomly sampled array. The original WVFT space, the reconstructed space, and the difference are shown in the illustration.

Figure 1.

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