We present a unified large system analysis of linear receivers for a class of random matrix channels.The technique unifies the analysis of both the minimum-mean-squared-error (MMSE) receiver and the adaptive least-squares (ALS) receiver, and also uses a common approach for both random i.i.d. and random orthogonal precoding. We derive expressions for the asymptotic signal-to-interference-plusnoise (SINR) of the MMSE receiver, and both the transient and steady-state SINR of the ALS receiver, trained using either i.i.d. data sequences or orthogonal training sequences. The results are in terms of key system parameters, and allow for arbitrary distributions of the power of each of the data streams and the eigenvalues of the channel correlation matrix. In the case of the ALS receiver, we allow a diagonal loading constant and an arbitrary data windowing function. For i.i.d. training sequences and no diagonal loading, we give a fundamental relationship between the transient/steady-state SINR of the ALS and the MMSE receivers. We demonstrate that for a particular ratio of receive to transmit dimensions and window shape, all channels which have the same MMSE SINR have an identical transient ALS SINR response. We demonstrate several applications of the results, including an optimization of information throughput with respect to training sequence length in coded block transmission.

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This paper uses an incremental matrix expansion approach to derive asymptotic eigenvalue distributions (a.e.d.'s) of sums and products of large random matrices. We show that the result can be derived directly as a consequence of two common assumptions, and matches the results obtained from using R-and S-transforms in free probability theory. We also give a direct derivation of the a.e.d. of the sum of certain random matrices which are not free. This is used to determine the asymptotic signalto-interference-ratio of a multiuser CDMA system with a minimum mean-square error linear receiver.

In this paper we present an asymptotic analysis of a multi-signature Multi-Carrier CDMA communications system. Such a system is suited to scalable data rate services with decentralized control. Specifically, we derive the asymptotic SINR at the output of a multiuser Linear Minimum Mean Squared Error (LMMSE) receiver and the asymptotic sum spectral efficiency of both the LMMSE and optimal receivers. Simulation studies demonstrate that the asymptotic results closely predict the performance of practical finite systems.

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