Signal constellations for multi-carrier systems

A communication unit for communicating over a wireless multi-carrier system comprising:

• a storage medium for storing a first signal constellation and a second signal constellation,
• wherein the first signal constellation comprises a plurality of first constellation points of which two nearest first constellation points define a minimum separation distance D from one another that is based on a maximized minimum difference between conditional probability distributions, and wherein the first signal constellation is used for communicating over a wireless multi-carrier system when one of 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 exceeds a threshold value;
• wherein the second signal constellation comprises a plurality of second constellation points of which two nearest second constellation points define a minimum separation distance D from one another that is based on a maximized minimum difference between conditional probability distributions, and wherein the second signal constellation is used for communicating over a wireless multi-carrier system when one of 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 is below the threshold value;
• and at least one of
• a modulator for modulating a signal to be transmitted in accordance with a multi-carrier modulation technique and a mapper for mapping a signal to be transmitted to one of the first or second signal constellations, or
• a demodulator for demodulating a received signal in accordance with a multi-carrier modulation technique and a de-mapper for mapping a received signal from one of the first or second signal constellations;
• wherein for each of the first and second signal constellation, the distance D is the maximized minimum difference, given by:
• max
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• wherein i and j are integer indexes, C is the signal constellation, ci and cj are constellation points, M is the total number of constellation points in the constellation, and Pav is one of a constellation power, the ratio of signal power to noise power, the ratio of bit energy to noise power spectral density, or the ratio of symbol energy to noise power spectral density.

A mobile terminal for communicating over a fast fading, multi-carrier wireless channel, comprising:

• a demodulator for demodulating a signal received from a multi-carrier wireless channel;
• a channel estimator for estimating the multi-carrier wireless channel using at least some pilot signals of the signal received;
• a signal constellation embodied on a computer storage medium, the signal
• constellation comprising a plurality of points exhibiting a minimum separation D
• given by:
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• wherein i and j are integer indexes, C is the signal constellation, ci and cj are constellation points, M is the total number of constellation points in the constellation, and Pav 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;
• and
• computer code embodied on a computer storage medium for matching a symbol of the signal received to the signal constellation.

A method of transmitting a signal over a multi-carrier system comprising:

• mapping a signal to be transmitted to a signal constellation, the signal constellation defining a plurality of constellation points, wherein a minimum separation distance D between two constellation points is based on a maximized minimum difference between conditional probability distributions;
• adding pilot symbols to the signal to be transmitted for aiding in channel estimation;
• and
• modulating the signal to be transmitted in accordance with a multi-carrier modulation technique
• wherein the distance D is the maximized minimum difference, given by:
• max
• C
• =
• {
• c
• 1
• ,
• …
• ⁢
• ,
• c
• M
• }
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• ≤
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• av
• wherein i and j are integer indexes, C is the signal constellation, ci and cj are constellation points, M is the total number of constellation points in the constellation, and Pav 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.