Low-Complexity Estimation of QAM Symbols and Constellations

摘要

Disclosed are methods and structures for soft symbol and variance estimation for QAM constellations including a big-flipping framework and efficient methods for soft symbol estimation and variance estimation for QAM. Disclosed are efficient Gray mapping which provides a much lower complexity, i.e., log N for N-QAM for both squared and non-squared QAM constellations. Also disclosed is an approximation method that avoids multiplications completely while exhibiting only a slight performance degradation. Finally, a low complexity method for variance estimations, particularly second moment estimations for both squared and non-squared QAM constellations with Gray mapping are disclosed. Advantageously—using the disclosed methods—the complexity of the second moment estimation is reduced to O((log N)̂2) for an N-QAM symbol for both squared and non-squared QAM.

主权项

1. A computer implemented method of producing a soft symbol estimate of a pulse amplitude modulation (PAM) symbol comprising the steps of:
determining from one PAM symbol, sN′ the following relationshipPr(x=sN′)=∏iPbi(1)=∏i1λi+1.; determining, for n=N′−1, . . . , 1, (Pr(x=sn) sequentially from the following relationshipPr(x=sn)=Pr(x=sn+1)πi⋓n+1,sn+1,i⋓n+1,nsn,i⋓n+1,n,; wherein {hacek over (i)}n+1,n denotes the index of the only different bit between a labeling bit sequence of Sn+1 and sn; determining, after determining Pr(x=sn) for all n, the soft PAM estimation according to the followingx~=∑s∈PAMsPr(x=s)=∑n=1N′sn∏i=1QPbi(sn,i), where sn,i is the ith bit value mapped to the PAM symbol sn and Pbi(sn,i) is determined according toPbi(0)=ΔPr(bi=0)=1-λi+1,Pbi(1)=ΔPr(bi=1)=1λi+1.