Complex Noise Analysis of DMT

In this paper, we consider discrete multitone (DMT) or baseband orthogonal frequency-division multiplexing (OFDM) modulation and perform a detailed noise analysis which takes into account dependencies and power (variance) differences of real and imaginary part after the complex-valued discrete Fourier transform (DFT). The derivation is based on the so-called pseudocovariance matrix of a complex random vector, which was introduced by Neeser and Massey (1993). We show that the relevant pseudocovariance matrix is not the zero matrix in general, in contrast to pass-band OFDM, for which it can be proven (under certain assumptions) that all occurring pseudocovariance matrices are vanishing. We show that for colored noise rotated rectangular symbol constellations are more appropriate than the common quadratic quadrature amplitude modulation (QAM) symbol constellations with respect to capacity and symbol error probability, and we derive formulas for the rotation angles and constellation sizes/densities. Finally, we extend the results to a multitransceiver [multiple-input-multiple-output (MIMO)] scenario, for which we assume a very general noise model at the inputs of the receivers, allowing correlations between the noise signals of different receivers. This requires the introduction of pseudocross-covariance matrices of complex random vectors, which are the important objects (together with cross-covariance matrices) in the MIMO situation.