On linear structure and phase rotation invariant properties of block 2(sup l)PSK modulation codes
Abstract
Two important structural properties of block 2(l)ary PSK (phase shift keying) modulation codes, linear structure and phase symmetry, are investigated. For an additive white Gaussian noise (AWGN) channel, the error performance of a modulation code depends on its squared Euclidean distance distribution. Linear structure of a code makes the error performance analysis much easier. Phase symmetry of a code is important in resolving carrier phase ambiguity and ensuring rapid carrier phase resynchronization after temporary loss of synchronization. It is desirable for a code to have as many phase symmetries as possible. A 2(l)ary modulation code is represented here as a code with symbols from the integer group. S sub 2(l) PSK = (0,1,2,...,2(l)1), under the modulo2(l) addition. The linear structure of block 2(l)ary PSK modulation codes over S sub 2(l)ary PSK with respect to the modulo2(l) vector addition is defined, and conditions under which a block 2(l)ary PSK modulation code is linear are derived. Once the linear structure is developed, phase symmetry of a block 2(l)ary PSK modulation code is studied. It is a necessary and sufficient condition for a block 2(l)PSK modulation code, which is linear as a binary code, to be invariant under 180 deg/2(lh) phase rotation, for 1 is less than or equal to h is less than or equal to l. A list of short 8PSK and 16PSK modulation codes is given, together with their linear structure and the smallest phase rotation for which a code is invariant.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 January 1990
 Bibcode:
 1990STIN...9019429L
 Keywords:

 Binary Codes;
 Phase Deviation;
 Phase Error;
 Phase Shift;
 Phase Shift Keying;
 Signal Encoding;
 Symmetry;
 White Noise;
 Communications and Radar