MULTIPLE-PHASE CODES FOR DETECTION WITHOUT CARRIER PHASE REFERENCE

We consider the construction and analysis of linear block codes for M- ary Phase-Shift Keying that can be decoded without carrier phase synch ronization Under these circumstances, the function that has a signific ant impact on performance is the noncoherent distance, analogously to the Euclidean distance for the coherent case. The major difficulty in constructing and analyzing such codes lies in the fact that the noncoh erent distance is not a true metric. For this reason, prior work mainl y relies on numerical approaches to search for good codes and to deter mine the corresponding minimum noncoherent distance. In this paper, we first present a theorem that links the noncoherent distance with the Euclidean and Lee distances, This theorem allows us to construct good codes and determine their minimum noncoherent distances analytically, Based on this theorem, we classify the codes whose duals consist of a cyclic group, These codes are of minimum redundancy. We further invest igate codes with the flavor of Hamming and shortened Hamming codes. Ma ny of these new codes provide significantly larger coding gains than p reviously known codes. Linear codes derived from Code-Division Multipl e-Access (CDMA) sequences are considered as well. These codes in gener al provide rather large coding gains. Finally, an algorithm is introdu ced that can be appended to any suboptimal decoding technique to enhan ce performance.