AN OPTIMUM PULSE AMPLITUDE MODULATION SYSTEM.
CRUFT LAB HARVARD UNIV CAMBRIDGE MASS
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The optimum minimum mean square error linear receiver and transmitter waveform has been jointly determined. The performance of this system is compared with that of the matched filter and the optimum constrained receiver on both a mean square error MSE and probability of error PE basis. Using the optimum MSE system, performance curves for uncorrelated message sequences are compared with those of correlated sequences. These performance curves are graphs of MSE and PE versus signal to noise SN ratio. Approximating the intersymbol interference distribution with a Gaussian distribution gives PE within a few percent of the exact value. It is found that, for sequences with the same information rate, the correlated sequences have smaller error at low SN, but at high SN, the reverse is true. Results are obtained which indicate that, in the absence of accurate information about the message correlation, it is best to design the receiver for an uncorrelated message sequence. The signal energy required to maintain a PE of 0.000001 versus data rate, 1T, is presented for 2,3, and 4 level data. Finally, it is shown that a channel with colored noise of spectral density Nf a b numerical value of Hf to the 2nd power where Hf is the frequency response of the channel, has the same performance as a channel with white noise with spectral density Nf a b and an appropriately chosen channel frequency response function. Author
- Non-Radio Communications