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.

This paper presents an asymptotic analysis of multisignature code-division multiple access (CDMA) in the presence of frequency-selective channels. We characterize the sum spectral efficiency and spectral efficiency regions for both the optimal and linear minimum mean-squared error (MMSE) multiuser receivers. Both independent and identically distributed (i.i.d). signatures and isometric signatures, which are orthogonal at each transmitter, are considered. Our results are asymptotic as the number of signatures per user and processing gain both tend to infinity with fixed ratio. The spectral efficiency of the MMSE receiver is determined from the asymptotic output signal-to-interference-plus noise ratio (SINR). For isometric signatures, our results rely on approximating certain covariance matrices with unitarily invariant matrices that are asymptotically free. This approximation is shown to be very accurate through comparison with both simulation and an "incremental-signature" analysis, which can be used to compute asymptotic moments. Also, a novel proof of the convergence of the empirical spectral distribution of the signal correlation matrix is presented. From these results, we derive the optimal coding-spreading tradeoff, which maximizes the MMSE spectral efficiency, for the case of a single user with multiple i.i.d. signatures. Simulation studies demonstrate that the asymptotic results accurately predict the performance of finite-size systems of interest. The resulting expressions are used to highlight and infer properties of the multisignature CDMA system, including the benefit of orthogonal relative to i.i.d. signatures, and the tradeoff between spectral efficiency and the versatility of providing a variable data rate service through multiple signatures

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 independent, identically distributed (i.i.d.) and random orthogonal precoding. We derive expressions for the asymptotic signal-to-interference-plus-noise ratio (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

Large system analysis has been used extensively in recent years to evaluate the performance of code division-multiple access (CDMA) and multi-input/multi-output (MIMO) communications systems. A key feature of this analysis is application of results on eigenvalue distributions and moments of large random matrices. These results enable the efficient computation of large system performance measures, such as spectral efficiency and probability of error, which are far more difficult to compute for finite-size systems. The large system results typically give an accurate prediction of the performance of finite-size systems, and offer important insights into system behavior. We give an overview of large system results for some different communications system models. Our emphasis is on techniques used previously by the authors to evaluate the performance of multi-carrier CDMA with the optimal linear receiver.

We consider a large system analysis of the minimum-mean-squared-error (MMSE) receiver and the adaptive least-squares (ALS) receiver for a class of random matrix channels. We give a 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, would have an identical transient ALS SINR response

This paper considers properties of the extrinsic information transfer (EXIT) functions of turbo equalized intersymbol interference channels and finite-impulse response precoders. An analytic expression is derived for the maximum value of the EXIT function of the equalizer. Using this parameter, a design strategy is proposed for allocating redundancy between the equalizer and the decoder. The key quantities are pilot-symbol rate and code puncturing, for fixed overall data and symbol rates.

In this paper we derive asymptotic performance measures for multiuser receivers in the uplink of multi-carrier (MC) CDMA communication systems with multiple signatures per user. We examine spectral efficiency regions of multi-signature CDMA, for both the optimal and optimal-linear receivers. We also derive an approximate expression for the asymptotic average signal to interference and noise ratio at the output of the optimal-linear multiuser receiver in the case of two users. Simulation studies demonstrate that the asymptotic results closely predict performance of practical finite systems.

We derive asymptotic performance measures for peer-to-peer multi-carrier CDMA networks with low data rate feedback channels between transmitter-receiver pairs. We derive expressions for the asymptotic average signal to interference and noise ratio at the output of the optimal linear multi-signature receiver using a simple feedback scheme in the single-user case, and an approximate ,expression in the two-user case. The asymptotic results closely predict performance of practical finite systems. We demonstrate that the simple feedback scheme yields most gain for either low system loads or low SNR. The power saving is in the order of 1-2 dB per signature for a wide range of system loads and SNRs.

We characterize the asymptotic spectral efficiency of the linear minimum mean squared error (LMMSE) receiver for multiuser multisignature multicarrier (MC) code-division multiple access (CDMA) communication systems. We consider signatures which are orthogonal at each transmitter. Our results are asymptotic as the number of signatures per user and processing gain both tend to infinity with fixed ratio. Our results rely on approximating covariance matrices with unitarily invariant matrices that are asymptotically free.

This paper considers a multicarrier (MC) code-division multiple-access system where each user employs multiple signatures. The receiver is linear and minimizes the mean square error of the data estimate. Both multiple-user and single-user systems are considered, as well as single and multiple signatures per user. In each case, an asymptotic analysis is used to derive the output signal-to-interference-plus-noise ratio (SINR) as a function of the system loading, the noise power, and the fading properties of the channel. Asymptotic in this case means that the number of independent subcarriers and number of signatures per user each tends to infinity with fixed ratio. The associated bit-error rate (BER) is evaluated for binary phase-shift keying symbols. Simulations show that the asymptotic SINRs and BERs derived in each case are accurate for realistic finite systems.

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 multi-user 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.

The paper considers performance and design issues for turbo equalizers. Analytic expressions are derived for the mutual information convergence point of the turbo equalizer. The BER is then found analytically. Results are obtained for both fixed and fading channels, and in conditions of both perfect channel state information as well as unknown estimated channels. Finally, we introduce design rules for adaptive turbo equalizers based on our analysis. The rules give optimal combinations of pilot rate and code puncturing for a range of fading and SNR conditions.

In this paper we derive asymptotic performance measures for multiuser receivers in multi-carrier CDMA communication systems. We consider both single-code-per-user and multi-code cases. Specifically, we derive the asymptotic average SINR and BER at the output of a multiuser LMMSE receiver. Simulation studies demonstrate that the asymptotic results closely predict performance of practical finite systems.