Iterative water-filling for Gaussian vector multiple-access channels

This paper proposes an efficient numerical algorithm to compute the optimal input distribution that maximizes the sum capacity of a Gaussian multiple-access channel with vector inputs and a vector output. The numerical algorithm has an iterative water-filling interpretation. The algorithm converges from any starting point, and it reaches within 1/2 nats per user per output dimension from the sum capacity after just one iteration. The characterization of sum capacity also allows an upper bound and a lower bound for the entire capacity region to be derived.     

Asymptotically optimal block quantization

In 1948 W. R. Bennett used a companding model for nonuniform quantization and proposed the formulaD : = : frac{1}{12N^{2}} : int : p(x) [ É(x) ]^{-2} dxfor the mean-square quantizing error whereNis the number of levels,p(x) is the probability density of the input, andE prime(x) is the slope of the compressor curve. The formula, an approximation based on the assumption that the number of levels is large and overload distortion is negligible, is a useful tool for analytical studies of quantization. This paper gives a heuristic argument generalizing Bennett's formula to block quantization where a vector of random variables is quantized. The approach is again based on the asymptotic situation whereN, the number of quantized output vectors, is very large. Using the resulting heuristic formula, an optimization is performed leading to an expression for the minimum quantizing noise attainable for any block quantizer of a given block sizek. The results are consistent with Zador's results and specialize to known results for the one- and two-dimensional cases and for the case of infinite block length(k rightarrow infty). The same heuristic approach also gives an alternate derivation of a bound of Elias for multidimensional quantization. Our approach leads to a rigorous method for obtaining upper bounds on the minimum distortion for block quantizers. In particular, fork = 3we give a tight upper bound that may in fact be exact. The idea of representing a block quantizer by a block "compressor" mapping followed with an optimal quantizer for uniformly distributed random vectors is also explored. It is not always possible to represent an optimal quantizer with this block companding model.     

Asymptotically optimal quantizers (Corresp.)

Asymptotically accurate approximations for quantizer performance were developed by Gish and Pierce. Variational techniques were used to obtain asymptotically optimal performance. In this correspondence, optimal performance is demonstrated simply without variational techniques using Holder's and Jensen's inequalities.     

Asymptotically optimal blind estimation of multichannel images.

Optimal estimation of a two-dimensional (2-D) multichannel signal ideally decorrelates the data in both channel and space and weights the resulting coefficients according to their SNR. Many scenarios exist where the required second-order signal and noise statistics are not known in which the decorrelation is difficult or expensive to calculate. An asymptotically optimal estimation scheme proposed here uses a 2-D discrete wavelet transform to approximately decorrelate the signal in space and the discrete Fourier transform to decorrelate between channels. The coefficient weighting is replaced with a wavelet-domain thresholding operation to result in an efficient estimation scheme for both stationary and nonstationary signals. In contrast to optimal estimation, this new scheme does not require second-order signal statistics, making it well suited to many applications. In addition to providing vastly improved visual quality, the new estimator typically yields signal-to-noise ratio gains 12 dB or higher for hyperspectral imagery and functional magnetic resonance images.     

Asymptotically optimal blind fractionally spaced channel estimationand performance analysis

When the received data are fractionally sampled, the magnitude and phase of most linear time-invariant FIR communications channels can be estimated from second-order output only statistics. We present a general cyclic correlation matching algorithm for known order FIR blind channel identification that has closed-form expressions for calculating the asymptotic variance of the channel estimates. We show that for a particular choice of weights, the weighted matching estimator yields (at least for large samples) the minimum variance channel estimator among all unbiased estimators based on second-order statistics. Furthermore, the matching approach, unlike existing methods, provides a useful estimate even when the channel is not uniquely identifiable from second-order statistics     

Asymptotically optimal cooperative wireless networks with reduced signaling complexity

This paper considers an orthogonal amplify-and-forward (OAF) protocol for cooperative relay communication over Rayleigh-fading channels in which the intermediate relays are permitted to linearly transform the received signal and where the source and relays transmit for equal time durations. The diversity-multiplexing gain (D-MG) tradeoff of the equivalent space-time channel associated to this protocol is determined and a cyclic-division-algebra-based D-MG optimal code constructed. The transmission or signaling alphabet of this code is the union of the QAM constellation and a rotated version of QAM. The size of this signaling alphabet is small in comparison with prior D-MG optimal constructions in the literature and is independent of the number of participating nodes in the network     

Asymptotically optimal soft decision decoding algorithms for Hamming codes

Asymptotically optimal soft decision decoding algorithms for d = 3 and d = 4 Hamming codes are given and analysed. Only error sequences with probability exponent larger than that of maximum-likelihood decoding are corrected. Upper bounds on the block error probability for the Gaussian channel are given.     

Asymptotically optimal classification for multiple tests withempirically observed statistics

The decision problem of testing M hypotheses when the source is Kth-order Markov and there are M (or fewer) training sequences of length N and a single test sequence of length n is considered. K, M, n, N are all given. It is shown what the requirements are on M , n, N to achieve vanishing (exponential) error probabilities and how to determine or bound the exponent. A likelihood ratio test that is allowed to produce a no-match decision is shown to provide asymptotically optimal error probabilities and minimum no-match decisions. As an important serial case, the binary hypotheses problem without rejection is discussed. It is shown that, for this configuration, only one training sequence is needed to achieve an asymptotically optimal test     

The capacities of frequency-hopped code-division multiple-accesschannels

This correspondence investigates and compares the capacities of two types of frequency-hopped code-division multiple-access (FH-CDMA) communications systems; namely, multilevel on-off keying (OOK) and MFSK, in particular BFSK. In our multiuser channel model, we assume a random hopping pattern is used for each transmitter-receiver pair, and that the ith receiver is only interested in the message transmitted by ith transmitter. The degradation in AWGN and nonselective Rayleigh fading environments of both types of FH systems is also investigated and compared     

Asymptotically optimal design of congestion control for high speeddata networks

The basic mechanism of sliding windows for the congestion control of virtual circuits is examined. A problem concerning the optimal design of windows is formulated and formulas for basic quantities of interest, such as throughput, delay and moments of packet queues, in the optimal operating regime as well as in other regimes, are obtained. All results are asymptotic, in which the main parameter is λ, the delay-bandwidth product. It is shown that K*~λ+O(√λ), where K* is the optimum window size. Also, in the optimal operating regime, the steady-state mean and standard deviation of the queued packets at individual nodes O(√/λ). The design consequences are examined in the contexts of adaptive dynamic windowing, buffer sizing, and shared versus separate buffers in the case of multiple virtual circuits     

Asymptotically optimal detection for additive watermarking in the DCT and DWT domains

Most of the watermarking schemes that have been proposed until now employ a correlation detector (matched filter). The current paper proposes a new detector scheme that can be applied in the case of additive watermarking in the DCT (discrete cosine transform) or DWT (discrete wavelet transform) domain. Certain properties of the probability density function of the coefficients in these domains are exploited. Thus, an asymptotically optimal detector is constructed based on well known results of the detection theory. Experimental results prove the superiority of the proposed detector over the correlation detector.     

Codecell convexity in optimal entropy-constrained vector quantization

Properties of optimal entropy-constrained vector quantizers (ECVQs) are studied for the squared-error distortion measure. It is known that restricting an ECVQ to have convex codecells may preclude its optimality for some sources with discrete distribution. We show that for sources with continuous distribution, any finite-level ECVQ can be replaced by another finite-level ECVQ with convex codecells that has equal or better performance. We generalize this result to infinite-level quantizers, and also consider the problem of existence of optimal ECVQs for continuous source distributions. In particular, we show that given any entropy constraint, there exists an ECVQ with (possibly infinitely many) convex codecells that has minimum distortion among all ECVQs satisfying the constraint. These results extend analogous statements in entropy-constrained scalar quantization. They also generalize results in entropy-constrained vector quantization that were obtained via the Lagrangian formulation and, therefore, are valid only for certain values of the entropy constraint.     

Asymptotically optimal pattern recognition procedures with density estimates (Corresp.)

The asymptotic optimality of pattern recognition procedures derived from pointwise consistent density estimates is established.     

Asymptotically optimal nonlinear MMSE multiuser detection based on multivariate Gaussian approximation

In this paper, a class of nonlinear minimum mean-squared error multiuser detectors is derived based on a multivariate Gaussian approximation of the multiple-access interference for large systems. This approach leads to expressions identical to those describing the probabilistic data association (PDA) detector, thus providing an alternative analytical justification for this structure. A simplification to the PDA detector based on approximating the covariance matrix of the multivariate Gaussian distribution is suggested, resulting in a soft interference-cancellation scheme. Corresponding multiuser soft-input, soft-output detectors delivering extrinsic log-likelihood ratios are derived for application in iterative multiuser decoders. Finally, a large-system performance analysis is conducted for the simplified PDA, showing that the bit-error rate (BER) performance of this detector can be accurately predicted and related to the replica method analysis for the optimal detector. Methods from statistical neurodynamics are shown to provide a closely related alternative large-system prediction. Numerical results demonstrate that for large systems, the BER is accurately predicted by the analysis and found to be close to optimal performance.     

Asymptotically optimal quantizers for detection of i.i.d

The asymptotic probability of error for quantization in maximum-likelihood tests is analyzed. The authors assume quantizers with large numbers of levels generated from a companding function. A theorem that relates the companding function to the asymptotic probability of error is proved. The companding function is then optimized     

Feedback strategies for a class of two-user multiple-accesschannels

Feedback strategies are presented for the class of two-user discrete memoryless multiple-access channels for which one of the inputs to the channel is determined by the second input and the channel output. The strategies achieve any rate point inside the capacity region of these channels     

Asymptotically optimal detector of memory p for k-dependent random signals (Corresp.)

A general method for discriminating between twokdependent stationary discrete random variables using marginal statistics and their first-order correlations is described.     

Asymptotically optimum estimation of signal waveform in the presence of uncertainties about the steering vector

The problem of signal waveform estimation using an antenna array in case of uncertainties about the steering vector is considered. New asymptotically (in sample size) optimum estimators are derived. In contrast to the known optimal solutions, the employed method of synthesis yields non-iterative direct-form estimators. Simulation results are provided to evaluate the performance of the synthesized estimators. It is shown that the proposed asymptotic estimators perform as well as the iterative optimal estimators and they outperform the MVDR estimator in a wide range of input signal-to-noise and uncertainty ratios.     

On water-filling precoding for coded single-carrier systems

We study the spectrum shaping gain in single carrier systems through water-filling precoding. We show that water-filling precoding outperforms other existing alternatives when iterative linear minimum mean square error (LMMSE) detection is involved, which is confirmed by both evolution analysis and simulation results. This technique does not incur any extra receiver cost when it is used together with frequency domain equalization (FDE).     

认知MIMO MAC最优迭代注水算法

研究发送功率以及干扰温度约束下的认知多入多出多址接入信道(MIMO MAC)的速率和最大化问题。通过部分对偶分解技术松弛干扰温度约束,原始问题被分解为较易处理的子问题,并提出一种迭代算法,通过交替进行对偶变量更新与迭代注水运算求解使得速率和最大的最优发送协方差矩阵。最后通过仿真表明算法的有效性。