Patent ID: 7336750

Claim:
A method for an optimal one-shot phase and frequency estimation for timing acquisition for signals transmitted over a communications channel, the method comprising: sampling a preamble comprising a known string of data bits; estimating the sampled preamble ( Y ), the estimated preamble further comprising an estimated amplitude (Â), an estimated frequency ({circumflex over (f)}), and an estimated phase ({circumflex over (Φ)}); calculating a cost function (C({circumflex over (f)}, {circumflex over (Φ)})) as a function of the estimated frequency ({circumflex over (f)}) and the estimated phase ({circumflex over (Φ)}); varying at least one of the estimated frequency ({circumflex over (f)}) or estimated phase ({circumflex over (Φ)}) to calculate a plurality of cost functions; and selecting the cost function (C({circumflex over (f)}, {circumflex over (Φ)})) having a minimum value, wherein said cost function having the minimum value is a function of an optimal estimated frequency ({circumflex over (f)}) and an optimal estimated phase ({circumflex over (Φ)}), wherein selecting the minimum value cost function further comprises selecting a plurality of first minimum cost functions such that each of the first minimum cost functions has a different estimated frequency ({circumflex over (f)}).