A family of linear complexity likelihood ascent search detectors for CDMA multiuser detection

We propose a family of likelihood ascent search (LAS) detectors that achieve maximum likelihood detection in a subset of hypotheses whereas their expected per-bit computational complexity is linear in the number of users. The LAS detectors monotonically increase likelihood at every search step, and thus monotonically decrease error probability, and converge to a fixed point in a finite number of steps with probability one. It is proved that the thresholds set up in the LAS detectors are necessary and sufficient for monotonic likelihood ascent for an arbitrary signature crosscorrelation matrix with probability one. Among the LAS detectors, the set of wide-sense sequential LAS (WSLAS) detectors is shown to be a set of local maximum likelihood (LML) detectors defined with neighborhood size one. The properties of the fixed points and their observation regions are studied. Simulations are carried out and verify analytical results.