Switched-Array DF

LSAP: Laboratory for Sensor and Array Processing

A conceptually straightforward implementation of a direction-finding (DF) system involves a dedicated signal acquisition channel (receiver, A/D, etc.) for each element of the array. The signals impinging on all antennas are observed simultaneously and sophisticated algorithms exist for extracting source angle-of-arrival (AOA) information. Another possible structure, however, involves using an antenna switch to multiplex N antenna outputs into two acquisition channels. In this type of system, the incoming signals are observed in a pairwise manner over several different antenna pairs in a sequence. The primary advantage of a switched system is reduced hardware costs since these systems require fewer signal acquisition channels. Another advantage is that a switched system can be simpler to calibrate. The dominating disadvantage of a switched system versus a full-channel implementation is a time-accuracy tradeoff resulting from the smaller quantity of data observed by the two-channel system over the same collection time.  A block diagram of a switched-element DF system is shown in Figure 1.

Figure 1.  Switched-element DF system: block diagram.

A switched-element system also impacts how the received data may be processed. Since at any given time data are only collected from a single pair of antennas, we are only able to compute a single 2x2 sample covariance matrix from each switch configuration.  Furthermore, since different antenna pairs will be separated by different distances and possibly orientations, the covariance matrices formed from different pairs cannot be directly combined. If multiple non-coherent sources are present, a 2x2 covariance matrix does not have a noise-only subspace; therefore, MUSIC and other subspace algorithms cannot be directly implemented. 

In this research we evaluate several different processing approaches for narrowband DF on a linear, switched-element array. Using the maximum likelihood (ML) estimator, we have compared the performance of switched and full-channel systems under three different data collection equivalences - equal collection time, equal number of data snapshots, and equal snapshots per configuration. This analysis quantifies the time-accuracy tradeoff inherent in the switched implementation.  Figures 2-4 show these comparisons.  In Figure 2, the switched-element and full-channel system collect data over the same absolute time.  Since the full-channel system has eight antennas and the switched-element system collects data on two channels at a time, the full-channel system essentially collects four times more data.  In Figure 3, the total number of snapshots collected by the two systems are the same.  In Figure 4, the number of snapshots per switch configuration is the same as the number of snapshots collected by the full-channel system.

Figure 2. Full vs. switched ML performance for equal collection time.

Figure 3. Full vs. switched ML performance for equal total snapshots.

Figure 4. Full vs. switched ML performance for equal snapshots per configuration.

We have used the covariance matrices of individual antenna pairs to assemble an equivalent full-channel covariance matrix that can be used with existing algorithms such as root-MUSIC and root-MVDR. The equivalent full-channel covariance matrix is called the composite covariance matrix (CCM). Finally, we have also derived a root-MVDR technique that can be implemented without forming the CCM. This last approach is interesting because the CCM implementations require the system to switch through every possible antenna pair. If the CCM is not required, it may be possible to optimize the number of snapshots collected by each antenna pair, which could cause some pairs to be skipped altogether. One can even envision an adaptive switching scheme whereby antenna selection is based on previously received data.

We are currently studying source detection techniques, methods for dealing with coherent signals, and interesting details of the CCM that seem to cause asymptotically biased estimates.