Multiple-input multiple-output (MIMO) antennas can be combined with orthogonal frequency division multiplexing (OFDM) to achieve diversity gain and/or to increase system spectral efficiency through spatial multiplexing. In this letter, we derive the probability density function (pdf) expressions of the condition number (i.e., the maximum-to-minimum-singular-value ratio, MMSVR) of the channel state information (CSI) matrix. We show that this ratio is directly related to the noise enhancement in open-loop MIMO systems and provides a significant insight on the overall system capacity. The pdf of this ratio could be used to predict the relative performances of various MIMO configurations without complex system-level simulations. The pdf can also be used to compute the probability of whether certain channels fail in the high-throughput mode. Extensive simulations are performed to validate the accuracy of the closed-form pdf of the MMSVR derived in this letter

Graphical block diagram simulation tools with highly interactive plotting and visualization capabilities can accelerate and greatly improve DSP and communications education. In this paper, we present several projects given in graduate and senior level undergraduate courses in DSP and communications which use the graphical simulation tool Capsim, and emphasize the importance of true multi-rate signal processing capability for studying DSP. We present a project on integrated design and simulation of network and physical layers in communications systems which also requires asynchronous data flow capability. This project unifies two topics that are traditionally treated separately, and provides important insight for students on error free transmission over noisy channels.>

We present a novel solution to the problem of instability in multiloop /spl Sigma//spl Delta/ modulators (nonlinear oversampled one-bit A/D and D/A converters). /spl Sigma//spl Delta/ modulators are attractive because their SNR is proportional to their oversampling rate which is physically tied to the speed of the VLSI. The problem of instability in traditional higher order (multiloop) /spl Sigma//spl Delta/ modulators is corrected by a new class of self-stabilizing /spl Sigma//spl Delta/ modulators called look-ahead decision-feedback (LADF) /spl Sigma//spl Delta/ modulators. LADF /spl Sigma//spl Delta/ modulators select the output at each time-step to create the optimally stable set of integrator states at the following time-step. Simulation results for up to third order (triple loop) modulators are included.>

The authors consider the derivation of a numerically stable multichannel fast least-squares algorithm, the multichannel general-order fast transversal filter (MCGO-FTF). The new algorithm is derived by using a vector space formulation, and it is a general-order algorithm, i.e. the orders of several input channel joint process filters can be independently and arbitrarily specified. The numerical stability is achieved through feedback of numerical errors. The algorithm is tested in the equalization of mobile communication channels, which is an important application area for the algorithm. The decision feedback equalizer (DFE), which is essential for the equalization of a mobile communications channel, requires the use of a general-order algorithm to mitigate the effect of error propagation in the decision directed mode. Also, the choice of a least-squares algorithm for this application is critical because of its superior convergence properties.>

The authors derive the steady-state mean square prediction error expression for the fixed-point RLS (recursive least squares) algorithm for the case of time-varying channel estimation, which is modeled as a first-order Markov tapped delay line. It is shown that the random variable driving the time-varying system taps affects the prediction error in the same way as does the roundoff error term due to weight update. It causes the error to grow linearly with time when the forgetting factor, lambda , is chosen as 1. For lambda>

A technique for adaptive filtering of nonlinear systems with memory has been developed which combines quantized mean field annealing (QMFA) and conventional recursive-least-squares/fast-transversal filter (RLS/FTF) adaptive filtering. Unlike other methods which rely on Volterra and Wiener models, this technique can efficiently handle large order nonlinearities with or without memory. The nonlinear channel is divided into a memory nonlinearity followed by a dispersive linear system. Assuming that the dispersive linear system is stationary during initialization and the nonlinearity does not change while the dispersive linear system varies with time, QMFA is applied to obtain the coefficients and the order of the memory of the nonlinearity and RLS/FTF is applied to determine the weights of the dispersive linear system. This method was applied to a full duplex digital subscriber loop. Simulations show that the performance of the technique is superior to that of ordinary RLS/FTF and steepest descent algorithms.>

The steady state mean square prediction error is derived for the fixed-point RLS (recursive least squares) algorithm, both for the exponentially windowed RLS (forgetting factor, gamma>

A technique is presented for finding transmitter and receiver filters for a wide class of data transmission systems which minimize the bit error rate (BER). The techniques uses Monte Carlo simulation to estimate the BER, coupled with mean field annealing (MFA) to optimize the pulse shapes. Modeling of the link can be as complex as simulation will allow, while MFA is resistant to the statistical scatter in the BER estimate from the simulation. In a complex example, MFA is coupled with Monte Carlo simulation techniques to find near optimal transmit and receive filters for a satellite communications link, taking 6 CPU hours on a DECstation 3100. The bit error rate of the link is found to be as much as three orders of magnitude lower when using the MFA-constructed optimal filters than when using filters constructed by gradient descent and simulated annealing.>

Three results on Sigma Delta modulation are presented. First, a change of variables is presented that demonstrates that two of the parameters in a Sigma Delta modulator do not affect the system performance. Second, a successive parameterization approach is used to determine the probability density function (PDF) at the input to the quantizer of a second-order Sigma Delta modulator. Third, this calculated PDF is used to determine the minimum mean-square error linearizing gains for a second-order Sigma Delta modulator and an expression for the variance of the noise at the input to the quantizer.>

A technique for finding transmitter and receiver filters for a wide class of digital communication systems which minimize the bit-error rate (BER) is presented. The technique uses Monte Carlo simulation to estimate the BER and mean field annealing (MFA) to optimize the pulse shapes. Modeling of the link can be as complex as simulation will allow, while MFA is resistant to the statistical variation in the BER estimate from the simulation. Initially, the MFA technique was applied to a binary symmetric channel in a nonsimulation environment, and an approximate analysis of the behavior of MFA for this problem was performed. In a more complex example, MFA was coupled with Monte Carlo simulation techniques to find near-optimal transmit and receive filters for a satellite communications link, taking 6 CPU hours on a DECstation 3100. The BER of the link was found to be as much as three orders of magnitude lower when using the MFA-constructed optimal filters than when using filters from other comparison results. For this example, the pulse shapes obtained using MFA exhibit a low BER even as the parameter controlling the nonlinearity of the satellite-link model is varied over a wide range, thus showing the solution is robust.>

ZSIM, a nonlinear Z-domain simulator for sampled-data systems, is presented and verified. ZSIM integrates analytic tools, a difference equation simulator, a table-based nonlinear Z-domain simulator, and digital signal processing into a workstation environment to provide fast and accurate simulation of delta-sigma modulators. The use of table-based simulation allows simulation of circuit nonidealities including clock feedthrough and saturation. Benchmark comparisons of difference equation simulations and table-based simulations are presented for delta-sigma modulators suitable for use in voice-band coders.>

Transversal recursive least-squares (RLS) algorithms estimate filter coefficients which minimize the accumulated sum of the square of the error residuals, termed the error power. The sensitivity of this error power to random perturbations about the optimum filter coefficients is investigated. Expressions are derived for the mean and variance of the deviation from the optimum error power. It is shown that for the prewindowed growing-memory RLS algorithm ( lambda =1), the mean value of the deviation increases linearly with the number of iterations. The variance of the deviation increases in proportion to the square of the number of iterations. Expressions are derived for the variance of correlated signals. These expressions show that the variance of the deviation for correlated signals increases compared to uncorrelated white signals by a term related to the sum of the square of the off-diagonal elements of the sample autocorrelation matrix. Expressions are also derived for the mean and variance of the deviation for the exponentially windowed RLS algorithm ( lambda>

Delta-sigma modulation is gaining widespread use as a monolithic analog-to-digital and digital-to-analog conversion technique in a wide variety of applications. The behavior of delta-sigma modulators depends on the statistics and nature of the input signal. The behavior of the circuit is input-amplitude-dependent, due to the nonlinearity (two-level quantizer). The nonlinear behavior of high-order delta-sigma modulators with bandlimited Gaussian inputs is analyzed.>

The general order, multichannel FTF algorithm is a generalization of the multichannel FTF algorithm in which the orders of the input channels can be independently specified. The algorithm is applied to a special case of a two-input-channel, joint process estimator. One of the input channels is defined as the unit-delayed joint process signal; the configuration is an 'equation error' form for least squares (LS) pole-zero ARMA (autoregressive moving-average) system identification. This form is also used in decision-directed equalization and echo cancellation. For this special two-channel case, a computational savings of 2N+1 operations per recursive update is identified, where N is the total number of filter taps. The saving is proven using the concepts of projection onto a vector space. The reduction is available with any of the order-N 'fast' LS algorithms including the fast Kalman (FK) and FAEST algorithms; this had not been recognized for similar application of the FK algorithm to decision-directed equalization. A summary of the modified algorithm is given, with an operations count for each step.>

This paper introduces a new method of analysis for Delta-Sigma Modulators based on modeling the nonlinear quantizer with a linerized gain, obtained by minimizing a mean-square-error criterion[7], followed by an additive noise source representing distortion components. In the paper, input-signal amplitude dependencies of Delta-Sigma Modulator stability and signal to noise ratio are analyzed. It is shown that due to the nonlinearity of the quantizer, the signal-to-noise ratio of the modulator may decrease as the input amplitude increases prior to saturation. Also, a stable third-order Delta-Sigma Modulator may become unstable by increasing the input amplitude beyond a certain threshold. Both of these phenomenon are explained by the nonlinear analysis of this paper. The analysis is carried out sinusoidal excitations.

A floating point error analysis of the Recursive Least Squares and Least Mean Squares (LMS) algorithms is presented. Both the prewindowed growing memory RLS algorithm (λ=1) for stationary systems and the exponential sliding window RLS algorithm (λ\lambda\rightarrow1. Floating point errors in the calculation of the weight vector correction term, however, do not effect the steady state error and have a transient effect. Similar results are obtained for the LMS algorithm where a tradeoff exists in the choice of the loop gain.

The Fast Pole-Zero (ARMA) Recursive Least Squares Algorithm is derived using geometric projections. The new algorithm has a reduced number of computations compared to the pole-zero fast Kalman algorithm. In particular, four vector inner products and scalar-times-vector operations are eliminated. This is particularly important in multiprocessor implementations of the algorithm. The geometric approach provides insight and useful interpretations of the various filters and residuals that form the algorithm. Simulations verifying the performance of the algorithm are presented where the poles and zeroes of an IIR filter are estimated.