Patent ID: 7394865

Claim:
A communication unit comprising: a storage medium for storing a signal constellation, the signal constellation comprising: a plurality of constellation points wherein two constellation points defining a minimum separation from one another are separated by a distance D based on a maximized minimum difference between conditional probability distributions; and at least one of a transmitter or a receiver, wherein the transmitter comprises a mapper for converting an input signal to a plurality of data symbols that each correspond to at least one of the constellation points, a pilot circuit for adding pilot symbols to the data symbols, and a modulator for modulating the data symbols in accordance with a multi-carrier transmission technique, and wherein the receiver comprises a channel estimator for estimating a channel of a multi-carrier system using pilot symbols of a received set of symbols, a demodulator for demodulating at least a portion of the received set of symbols in accordance with a multi-carrier transmission technique, and a de-mapper for converting the demodulated symbols to a plurality of data signals that each alone or in combination correspond to a constellation point; wherein the distance D is the maximized minimum difference, given by: max C = { c 1 , ⋯ ⁢ , c M } 1 M ⁢ ∑ i = 1 M ⁢ ⁢  c i  2 ≤ P av ⁢ ⁢ min i ≠ j ⁢ ⁢ D ( c i ⁢  c j ) , wherein i and j are integer indexes, C is the signal constellation, c i and c j are constellation points, M is the total number of constellation points in the constellation, and P av is one of a constellation power, a ratio of signal power to noise power, a ratio of bit energy to noise power spectral density, or a ratio of symbol energy to noise power spectral density.