Digital signal processing for optimum wideband channel estimation in the presence of noise

Optimal sequences for channel estimation using discrete Fourier transform techniques

“…The channel estimate is obtained as (6) Using (5), and the fact that taking the inverse DFT of the DFT of a sequence recovers the original sequence, we have (7) In the absence of noise, . Also, is an unbiased estimate of , i.e.,…”

“…Specifically, [5]- [9] consider CE given a known training sequence. Following the least-squares (LS) philosophy, [5] presents algorithms for optimal unbiased CE with aperiodic spread spectrum signals for white or nonwhite noise. Optimum unbiased CE given white noise is considered in [6] following a maximum-likelihood (ML) approach.…”

Multistatic adaptive pulse compression

“…4. We examine the performance of the standard matched filter, LS estimator [9][10][11], and the MAPC algorithm when applied to estimate the mainbeam range profile illuminated by radar 1 at the receiver of radar 1. Note that unlike MAPC, the matched filter and least-squares estimator are only appropriate for the extraction of monostatic radar return signals and are thus expected to perform poorly for the multistatic radar scenario.…”

“…For the suppression of range sidelobes, least-squares estimation [9][10][11] has been shown to perform relatively well for the monostatic radar scenario yet it does not account for the presence of multiple received signals and as such can be expected to degrade for the multistatic radar scenario. Hence from a conceptual point of view, it would seem desirable that the receive filter matched to a specific waveform should be adaptive to the actual received signals since the presence of other target returns (from multiple received signals) which may generate masking interference cannot be known a priori and cannot be sufficiently suppressed using standard nonadaptive approaches.…”

Adaptive pulse compression repair processing

“…To suppress range sidelobes, other deterministic alternatives to the matched filter have been devised, which include optimum mismatched filters [2,3] and Least Squares estimation [4,5]. Gabriel [6,7] was the first to consider applying pulse compression in an adaptive manner by computing a sample covariance matrix from the returns of many pulses in order to achieve higher range resolution for Inverse Synthetic Aperture Radar (ISAR).…”