Patent ID: 6449322
Filing Date: 2002-09-10
Classification: H04L

Abstract:
A method of maximum likelihood detection of data symbols in an MPSK data burst comprising the steps of:(a) identifying N MPSK data symbols s1, s2, . . . sN at times 1,2, . . . N along with at least one reference symbol sN+1 at time N+1, where sk=ej&psgr;k for k=1, . . . N, and &phgr;k is uniformly distributed random phase taking values in {0,2&pgr;/M, . . . 2&pgr;(Mâˆ’1)/M}, and for k=N+1, reference symbol sN+1 is an MPSK symbol ej0=1; (b) transmitting said N MPSK symbols over an AWGN channel with unknown phase and modeled as r=sej&thgr;+n, where r, s, and n are N+1 length sequences whose kth components are rk, sk, and nk, k=1, . . . N+1; and (c) finding s which maximized &eegr;(s), where: Î·&af;(s)=&LeftBracketingBar;&Sum;k=1N&it;rk&it;sk*+rN+1â€²&it;sN+1*&RightBracketingBar;2,(c1) defining &PHgr; as the phase vector &PHgr;=(&phgr;1, . . . &phgr;N+1) and |rk|>0, k=1, . . . N, and for a complex number of &ggr;, let arg[&ggr;] be the angle of &ggr;; (c2) let &PHgr;=(&phgr;1, . . . &phgr;N+1) be the unique &PHgr; for which arg[rkeâˆ’j&phgr;k]&egr;[0,2&pgr;M) for k=1, . . . N+1 andzkrkeâˆ’j{tilde over (&psgr;)}k; (c3) for each k, k=1, . . . N+1, calculate arg(zk), and reorder values from largest to smallest, (c4) define a function k(i) as giving a subscript k of zk for the ith list position, i=1, . . . N+1 whereby: 0&leq;arg&af;[zk&af;(N+1)]&leq;arg&af;[zk&af;(N)]&leq;â€¦&leq;arg&af;[zk&af;(1)]<2&it;Ï€M;(c5) for i=1, . . . N+1, let gi=zk(i), and for i satisfying N+1gi=eâˆ’j2&pgr;/Mgiâˆ’(N+1); and(c6) calculate: &LeftBracketingBar;&Sum;i=qq+N&it;gi&RightBracketingBar;2,â€ƒ&it;for&it;â€ƒ&it;q=1,â€¦&it;â€ƒ&it;N+1;â€ƒ&it;and(c7) select the largest value in step (c6).