DOA ESTIMATION OF MANY W-DISJOINT ORTHOGONAL SOURCESFROM TWO MIXTURES USING

1. ABSTRACT A novel direction of arrival (DOA) technique is presented which constructs estimates of the relative delay mixing parameters associated with each signal by taking the ratio of time-frequency representations of two mixtures. The technique is based on the Degenerate Unmixing and Estimation Technique (DUET))1]. If the sources are W-disjoint orthogonal , meaning that only one signal is active in the time-frequency plane at a given time-frequency, then the ratio only depends on the mixing parameters of one source. The ratio can thus be used to generate estimates of the mixing parameters and these estimates can be clustered to determine both the number of sources present in the mixtures and their associated mixing parameters. The method allows for the estimation of the DOA for many sources using only two receive antennas, whereas traditional techniques require N antennas to estimate N ? 1 angles of arrival. Simulation results are presented and compared to MUSIC, ESPRIT, and other DOA estimation techniques. The goal of accurately estimating the arrival angle of a signal on an antenna array is long standing in the eld of signal processing. Direction of arrival estimation is important for such tasks as tracking the signal emitter and smart antenna array processing for interference reduction in mobile wireless systems. Most DOA techniques require N antennas to estimate N ? 1 angles of arrival. A notable exception to the N ? 1 angles of arrival rule uses forth-order cumulants to estimate three time delays from two mixturess2]. One advantage of the technique presented here is that it requires only two antenna elements to estimate the arrival angle of an arbitrary number of sources. This reduction in the required number of antenna elements is made by assuming the sources are W-disjoint orthogonal. This paper applies the work on the Degenerate Unmix-ing and Estimation Technique(DUET) on W-disjoint orthogonal signals originally proposed in 3] to wireless signals. W-disjoint orthogonal signals have disjoint support for their time-frequency representation. For example, multiple M-ary frequency shift keyed signals are W-disjoint orthogonal , except for the occasional hit when two or more signals transmit at the same frequency at the same time. Another (perhaps surprising) example of W-disjoint orthogonal signals is speech. Tests show that voice data satisses the W-disjoint orthogonality constraint closely enough to allow accurate angle of arrival estimation and blind separationn3, 4]. In essence, the W-disjoint orthogonal assumption assumes that all signals are instantaneously …