http://ieeexplore.ieee.org TOC Alert for Publication# 78 2012 February 10 60 3 C1 C4 186 60 3 C2 C2 40 60 3 997 1009 3148 $k$-sparse $n$-dimensional real vector from $m=4klog(n)$ noise-free linear measurements obtained through a random Gaussian measurement matrix with a probability that approaches one as $nrightarrowinfty$. This work strengthens this result by showing that a lower number of measurements, $m=2klog(n-k)$ , is in fact sufficient for asymptotic recovery. More generally, when the sparsity level satisfies $k_{min}leq kleq k_{max}$ but is unknown, $m=2k_{max}log(n-k_{min})$ measurements is sufficient. Furthermore, this number of measurements is also sufficient for detection of the sparsity pattern (support) of the vector with measurement errors provided the signal-to-noise ratio (SNR) scales to infinity. The scaling $m=2klog(n-k)$ exactly matches the number of measurements required by the more complex lasso method for signal recovery with a similar SNR scaling.]]> 60 3 1010 1021 2755 60 3 1022 1031 3690 60 3 1032 1049 6767 $k$-factors of the two input variables. We derive an upper bound on the truncation error and use this to present an adaptive computational approach that selects the minimum number of terms required for accuracy. We also present the PDF for the special case where either one or both of the input complex Gaussian random variables is zero-mean. We demonstrate the relevance of our results by deriving the optimal Neyman–Pearson detector for a time reversal detection scheme and computing the receiver operating characteristics through Monte Carlo simulations, and by computing the symbol error probability (SEP) for a single-channel $M$-ary phase-shift-keying (M-PSK) communication system.]]> 60 3 1050 1063 3914 60 3 1064 1074 2648 60 3 1075 1086 812 $L^{2}$ -distances between nonparametric trend estimators and their average. A central limit theorem is obtained for the test statistic and the test's consistency is established. We propose a simulation-based approximation to the distribution of the test statistic, which significantly improves upon the normal approximation. The test is also applied to devise a clustering algorithm. Finally, the finite-sample properties of the test are assessed through simulations and the test methodology is illustrated by a cell phone download data collected in the United States.]]> 60 3 1087 1097 3005 60 3 1098 1107 2172 60 3 1108 1120 3012 60 3 1121 1133 3574 60 3 1134 1148 3480 60 3 1149 1158 2814 60 3 1159 1173 3441 60 3 1174 1183 1361 $alpha$, defined as the argument of the log in the $alpha$ -order Renyi entropy, has been successfully used as an information theoretic criterion for supervised adaptive system training. In this paper, we use the survival function (or equivalently the distribution function) of an absolute value transformed random variable to define a new information potential, named the survival information potential (SIP). Compared with the IP, the SIP has some advantages, such as validity in a wide range of distributions, robustness, and the simplicity in computation. The properties of SIP and a simple formula for computing the empirical SIP are given in the paper. Finally, the SIP criterion is applied in adaptive system training, and simulation examples on FIR adaptive filtering, kernel adaptive filtering, and time delay neural networks (TDNNs) training are presented to demonstrate the performance.]]> 60 3 1184 1194 2820 60 3 1195 1204 2939 60 3 1205 1214 2606 60 3 1215 1228 2628 60 3 1229 1240 3804 60 3 1241 1252 2763 $(2q)$ cumulants of the received data have been proposed, giving rise to new DOA estimation algorithms, namely the $2q$ MUSIC algorithm. In particular, it has been shown that the $2q$ MUSIC algorithm can identify $O(N^{q})$ statistically independent non-Gaussian sources. However, in this paper, it is demonstrated that the processing power of the $2q$th-order cumulant based methods can potentially be even larger. It will be shown that the $2q$th-order cumulant matrix of the data is directly related to the concept of a $2q$th-order difference co-array which can potentially have $O(N^{2q})$ virtual sensors, leading to identification of $O(N^{2q})$ statistically independent non-Gaussian sources using $2q$ th-order cumulants. However, the number of actually realizable virtual elements in the $2q$ th-order difference co-array depends on the geometry of the physical array. In order to ensure that the co-array indeed has the desired degrees of freedom, a new generic class of linear (one dimensional) nonuniform arrays, namely the $2q$th-order nested array, is proposed, whose - tex Notation="TeX">$2q$ th-order difference co-array is proved to contain a uniform linear array with $O(N^{2q})$ sensors. In order to exploit these increased degrees of freedom of the co-array, a new algorithm for DOA estimation is also developed, which acts on the same $2q$ th-order cumulant matrix as the earlier methods and can yet identify $O(N^{2q})$ sources. It is proved that the proposed method can identify the maximum number of sources among all methods that use $2q$ th-order cumulants.]]> 60 3 1253 1269 3366 60 3 1270 1282 3499 60 3 1283 1294 4227 , IEEE Trans. Signal Process., vol. 53, no. 10, pp. 3791–3803) and the uniform channel decomposition (UCD) schemeThroughout this paper, the GMD and UCD schemes mean GMD-VBLAST in and UCD-VBLAST in , respectively. (Jiang , IEEE Trans. Signal Process., vol. 53, no. 11, pp. 4283–4294) in BER performance.]]> 60 3 1295 1306 2682 60 3 1307 1318 3128 60 3 1319 1330 2415 60 3 1331 1341 1832 60 3 1342 1351 2683 60 3 1352 1365 3948 60 3 1366 1382 3527 60 3 1383 1396 2040 $K$ single-antenna source-destination pairs communicating through several half-duplex amplify-and-forward MIMO relays where each source is targeting only one destination. The relay beamforming matrices are designed in order to minimize the total power transmitted from the relays subject to quality of service constraints on the received signal to interference-plus-noise ratio at each destination node. Due to the nonconvexity of this problem, several approximations have been used in the literature to find a computationally efficient solution. A novel solution technique is developed in which the problem is decomposed into a group of second-order cone programs (SOCPs) parameterized by $K$ phase angles; each associated with one of the constraints. An iterative algorithm is proposed to search for the phase angles and the relay beamforming matrices sequentially. However, convergence to the global optimal beamforming matrices cannot be guaranteed. Two methods for searching for the optimal values of the phase angles are proposed (from which the optimal beamforming matrices can be obtained) using grid search and bisection and the convergence of these methods to the global optimal solution of the problem is proved. Numerical simulations are presented showing the superior performance of the proposed algorithms compared to earlier suboptimal approximations at the expense of a moderate increase in the computational complexity.]]> 60 3 1397 1408 3458 60 3 1409 1419 2371 60 3 1420 1431 983 60 3 1432 1445 2204 60 3 1446 1459 3370 $O(log^{2} n)$ bound on the adaptive expected regret with $O(n^{2})$ time-complexity, where $n$ is the length of the signal; the bound implies that, regardless of the underlying signal, the expected MSE of our filter universally converges to that of the best switching FIR filters, if the number of switches is $o({{n} over {log^{2}n}})$ . The experimental results show that our filter outperforms its stationary counterpart particularly when the underlying signal has time-varying characteristics. We also show a heuristic scheme with $O(n)$ time-complexity works well without losing too much of the filtering performance.]]> 60 3 1460 1464 411 $K$-sparse representation with respect to a known dictionary ${bf D}$ . The proposed analysis is based on the RIP, establishing a near-oracle performance guarantee for each of these algorithms. Beyond bounds for the reconstruction error that hold with high probability, in this work we also provide a bound for the average error.]]> 60 3 1465 1468 202 60 3 1469 1473 294 60 3 1473 1477 221 $l_{p}$ norm relying on the convex combination of two recursive least $p$ -norm $({rm RL}p{rm N})$ filters is presented. The approach is of interest when the noise is not Gaussian, for instance in the presence of impulsive or alpha-stable $(alpha {hbox{-}}{rm S})$ distributed noise. In these cases, the ${rm RL}p{rm N}$ algorithm, aiming at recursively minimizing the $l_{p}$ norm, offers a more stable and robust solution than adaptive filtering schemes based on the minimization of the squared error. However, since the ${rm RL}p{rm N}$ solution cannot be obtained in closed form for $pne 2$, it is necessary to introduce some approximations that critically affect the filter behavior. The main observed drawback is a poor convergence rate in nonstationary scenarios, especially in the presence of abrupt changes in the model. In this correspondence, we show how this problem can be overcome by relying on convex combinations of two ${rm RL}p{rm N}$ filters with long and short memories. The proposed methods are empirically shown to outperform state-of-the-art methods for this problem, requiring just slightly higher computation than its close competitors.]]> 60 3 1478 1482 403 60 3 1482 1486 211 60 3 1487 1492 704 60 3 1493 1498 280 60 3 1498 1501 355 60 3 1502 1508 378 $tau^{ast}rightarrow 0$. Unfortunately, Ding and Kay have erroneously concluded that the minimum description length (MDL) principle also leads to inconsistent estimates of model order in this setting by equating BIC with MDL. This correspondence shows that only the earlier MDL criterion based on asymptotic assumptions has this problem, and proves that the new MDL linear regression criteria based on normalized maximum likelihood and Bayesian mixture codes satisfy the notion of consistency as $tau^{ast}rightarrow 0$. The main result may be used as a basis to easily establish similar consistency results for other closely related information theoretic regression criteria.]]> 60 3 1508 1510 133 , where the gradient dimension reflects the number of relays.]]> 60 3 1511 1516 266 60 3 1517 1522 477 ${hbox{SNR}}_{c}$ with corresponding variations in loop performance. A model is presented which reflects this signal-to-noise ration (SNR)-sensitivity and, thus, facilitates accurate loop design.]]> 60 3 1522 1527 857 $(d_{min})$ of two received vectors is studied. This criterion leads to a nondiagonal precoding scheme and allows achieving a full diversity order. However, the optimized solution for MIMO systems using a high-order QAM modulation is rather complex and changes for different constellations. Therefore, we propose herein a general form of minimum Euclidean distance based precoders for all rectangular QAM modulations. It is shown that the new solution optimizes the distance $d_{min}$ for small and large dispersive channels.]]> 60 3 1527 1533 897 60 3 1533 1538 482 60 3 1539 1540 520 60 3 1540 1541 422 60 3 1542 1542 30 60 3 1543 1544 46 60 3 C3 C3 33