Wide-Band Cyclic Cross-Correlation Processing

The wide-band cyclic cross-correlation function (WB-CCCF) is introduced for finite average-power signals. It is the cyclic cross-correlation of a signal and a time-scaled version of another signal. Input-output relationships in terms of WBCCCFs are derived for the wide-band Doppler channel, that is, the channel that introduces a complex gain, a delay, a frequency shift, and a time-scale factor on the complex envelope of the input signal. These relationships are exploited to design new algorithms for estimating time-difference-of-arrival, frequency-difference-of- arrival, and time-scale ratio of the signals impinging on a pair of sensors when the transmitter is a high-speed—possibly hypersonic—source emitting a wide-band radio-frequency signal. In the presence of severe noise and interference environments, the proposed algorithms exhibit the typical signal-selectivity property of cyclostationarity-based estimation techniques. Moreover, unlike existing methods, they provide satisfactory performance when the so called narrow-band condition is not satisfied, that is when the product of signal bandwidth and length of the observation interval is not much smaller than the ratio of medium propagation speed and source radial speed. The new techniques are exploited for the problem of locating a very low Earth orbit satellite and a hypersonic re-entry vehicle.