Finding the sparsest solution to underdetermined systems of linear equations y = Φx is NP-hard in general. We show here that for systems with ‘typical’/‘random ’ Φ, a good approximation to the sparsest solution is obtained by applying a fixed number of standard operations from linear algebra. Our proposal, Stagewise Orthogonal Matching Pursuit (StOMP), successively transforms the signal into a negligible residual. Starting with initial residual r0 = y, at the s-th stage it forms the ‘matched filter ’ Φ T rs−1, identifies all coordinates with amplitudes exceeding a specially-chosen threshold, solves a least-squares problem using the selected coordinates, and subtracts the leastsquares fit, producing a new residual. After a fixed number of stages (e.g. 10), it stops. In contrast to Orthogonal Matching Pursuit (OMP), many coefficients can enter the model at each stage in StOMP while only one enters per stage in OMP; and StOMP takes a fixed number of stages (e.g. 10), while OMP can take many (e.g. n). StOMP runs much faster than competing proposals for sparse solutions, such as ℓ1 minimization and OMP, and so is attractive for solving large-scale problems. We use phase diagrams to compare algorithm performance. The problem of recovering a k-sparse vector x0 from (y, Φ) where Φ is random n × N and y = Φx0 is represented by a point (n/N, k/n)

Abstract—This paper studies randomly spread code-division multiple access (CDMA) and multiuser detection in the large-system limit using the replica method developed in statistical physics. Arbitrary input distributions and flat fading are considered. A generic multiuser detector in the form of the posterior mean estimator is applied before single-user decoding. The generic detector can be particularized to the matched filter, decorrelator, linear minimum mean-square error (MMSE) detector, the jointly or the individually optimal detector, and others. It is found that the detection output for each user, although in general asymptotically non-Gaussian conditioned on the transmitted symbol, converges as the number of users go to infinity to a deterministic function of a “hidden ” Gaussian statistic independent of the interferers. Thus, the multiuser channel can be decoupled: Each user experiences an equivalent single-user Gaussian channel, whose signal-to-noise ratio (SNR) suffers a degradation due to the multiple-access interference (MAI). The uncoded error performance (e.g., symbol error rate) and the mutual information can then be fully characterized using the degradation factor, also known as the multiuser efficiency, which can be obtained by solving a pair of coupled fixed-point equations identified in this paper. Based on a general linear vector channel model, the results are also applicable to multiple-input multiple-output (MIMO) channels such as in multiantenna systems. Index Terms—Channel capacity, code-division multiple access (CDMA), free energy, multiple-input multiple-output (MIMO) channel, multiuser detection, multiuser efficiency, replica method, statistical mechanics. I.

We present simple, practical codes designed for the binary and Gaussian dirty-paper chan-nels. We show that the dirty paper decoding problem can be transformed into an equivalent multiple-access decoding problem, for which we apply superposition coding. Our concept is a generalization of the nested lattices approach of Zamir, Shamai and Erez. In a theoretical setting, our constructions are capable of achieving capacity using random component codes and maximum-likelihood decoding. We also present practical implementations of the con-structions, and simulation results for both dirty-paper channels. Our results for the Gaussian dirty-paper channel are on par with the best known results for nested-lattices. We discuss the binary dirty-tape channel, for which we present a simple, effective coding technique. Finally, we propose a framework for extending our approach to general Gel’fand-Pinsker channels. Index Terms- dirty paper, dirty tape, multiple-access channel, side information, superposition coding.

This paper analyzes the convergence behavior and performance of iterative successive interference cancellation (SIC) for a CDMA system with random spreading using the so-called multi-user efficiency (MUE). The goal of such an analysis is the optimization of the detection scheme. Moreover, an optimized power allocation of the users at the transmitter is an important means for enhancing the convergence behavior of the detector and is based on the possibility of prediction. While this analysis has only been applied to parallel interference cancellation (PIC) we will generalize it in this paper also for SIC. It will be shown that the achievable system load can be significantly increased. 1.

In this paper, a class of nonlinear MMSE multiuser detectors are derived based on a mul-tivariate Gaussian approximation of the multiple access interference. 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. Correspond-ing 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 performance of this detector can be accurately predicted and related to the replica method analysis for the optimal detector. Methods from statistical neuro-dynamics are shown to provide a closely related alternative large system prediction. Numerical results demonstrate that for large sys-tems, the bit error rate is accurately predicted by the analysis and found to be close to optimal performance.

Abstract—In this paper, a class of nonlinear MMSE multiuser detectors are derived based on a multivariate Gaussian approximation of the multiple access interference. This approach leads to identical expressions as 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 softinput, soft-output detectors delivering extrinsic log-likelihood ratios are derived for application in iterative multiuser decoders. Numerical results demonstrate that for large systems, the bit error rate is accurately predicted by the analysis and found to be close to optimal performance. Keywords — Code-division multiple access, multiuser detection, optimum detection, Gaussian approximation, large system analysis. I.

Abstract — We consider a multiuser detector based on modelling the multiple-access interference (MAI) as a vector of Gaussian random variables. This approach leads to the probabilistic data association (PDA) multiuser detector, which outputs good approximations to marginal posterior-mode optimal decisions. A simplification to the PDA detector is suggested, leading to a soft interference cancellation scheme. In the large system limit, the bit error rate performance of this detector can be accurately predicted, and shown to be identical to the optimal detector. I. Summary Consider nonlinear minimum mean squared error (NMMSE) estimation in a synchronous code-division multiple-access system with K users. This problem involves solving a set of K optimization problems, namely minmk x (xk −mk) k 2 P(xk|r), for k = 1, 2,..., K, where mk is the NMMSE estimate for user k, xk is the binary information bit from user k and r is the chip-matched filter output. Also, let sµk ∈ {±1} be the µth spreading chip for user k. From Bayes ’ law, we find that P(xk|r) = P(x � k)p(r|xk) x P(x k k)p(r|xk). Computing p(r|xk) involves a sum over 2 K−1 terms. To reduce complexity, the sum is replaced by integration, assuming the probability density function of the MAI, ∆µk = � l�=k sµlxl / √ N, is Gaussian with mean value wµk = E[∆µk] = � l�=k sµlml / √ N and covariance value COV[∆µk∆νk] = � l�=k sµlsνl(1 − m 2 l)/N. This, in turn, leads to p(r|xk) ∝ exp xk (r − wk) T C −1 k sk / √ � N, where we define Ck = (Ωk + σ 2 I), Ωk = COV[∆k ∆ T k], ∆k = (∆1k,..., ∆Nk) T and wk = (w1k, w2k,..., wNk) T. Now, the NMMSE estimate is mk = � x xkP(xk|r) = k

Abstract — In this paper, a class of nonlinear MMSE 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 performance of this detector can be accurately predicted and related to the replica method analysis for the optimal detector. Methods from statistical neuro-dynamics are shown to provide a closely related alternative large system prediction. Numerical results demonstrate that for large systems, the bit error rate is accurately predicted by the analysis and found to be close to optimal performance. Index Terms — Code-division multiple access, multiuser detection, optimum detection, Gaussian approximation, large system analysis. I.

This paper introduces an optimization of the received power profile for iterative parallel and successive interference cancellation (PIC/SIC) in coded CDMA systems. The basic approach is an optimization algorithm called Differential Evolution (DE). An optimized power allocation of the users at the transmitter is an important means for enhancing the convergence behavior of the detector. Either the supportable load can be significantly increased or the required transmit power is decreased by several dB. Furthermore any additional constraint regarding the modelling of realistic communication systems can be implemented very easily. In this paper the number of needed iterations is dramatically decreased. Computational complexity is reduced while the needed power is barely increased. Another constraint which is also considered is the near-far-effect that degenerates system performance. The maximum received power is limited for some users that are assumed to be at the cell border or who suffer from fading. The precondition for this optimization is the analysis of the iterative detection scheme. This is done by a parameter called multi-user efficiency (MUE). 1

Communications in dispersive direct-sequence code-division multiple-access channels suffer from intersymbol and multiple-access interference, which can significantly impair performance. Joint maximum a posteriori probability equalization and multiuser detection with error control decoding can be used to mitigate this interference and to achieve the optimal bit error rate. Unfortunately, such optimal detection typically requires prohibitive computational complexity. This problem is addressed in this paper through the development of a reduced state trellis search detection algorithm, based on decision feedback from channel decoders. The performance of this algorithm is analyzed in the large-system limit. This analysis and simulations show that this reduced complexity algorithm can exhibit near-optimal performance under moderate signal-to-noise ratio and attains larger system load capacity than parallel interference cancellation. I.