A stochastic behavior analysis of stochastic restricted-gradient descent algorithm in reproducing kernel Hilbert spaces

This paper presents a stochastic behavior analysis of a kernel-based stochastic restricted-gradient descent method. The restricted gradient gives a steepest ascent direction within the so-called dictionary subspace. The analysis provides the transient and steady state performance in the mean squared error criterion. It also includes stability conditions in the mean and mean-square sense. The present study is based on the analysis of the kernel normalized least mean square (KNLMS) algorithm initially proposed by Chen et al. Simulation results validate the analysis

Coordinated Beamforming with Relaxed Zero Forcing: The Sequential Orthogonal Projection Combining Method and Rate Control

In this paper, coordinated beamforming based on relaxed zero forcing (RZF) for K transmitter-receiver pair multiple-input single-output (MISO) and multiple-input multiple-output (MIMO) interference channels is considered. In the RZF coordinated beamforming, conventional zero-forcing interference leakage constraints are relaxed so that some predetermined interference leakage to undesired receivers is allowed in order to increase the beam design space for larger rates than those of the zero-forcing (ZF) scheme or to make beam design feasible when ZF is impossible. In the MISO case, it is shown that the rate-maximizing beam vector under the RZF framework for a given set of interference leakage levels can be obtained by sequential orthogonal projection combining (SOPC). Based on this, exact and approximate closed-form solutions are provided in two-user and three-user cases, respectively, and an efficient beam design algorithm for RZF coordinated beamforming is provided in general cases. Furthermore, the rate control problem under the RZF framework is considered. A centralized approach and a distributed heuristic approach are proposed to control the position of the designed rate-tuple in the achievable rate region. Finally, the RZF framework is extended to MIMO interference channels by deriving a new lower bound on the rate of each user.Comment: Lemma 1 proof corrected; a new SOPC algorithm invented; K > N case considere

Robust Reduced-Rank Adaptive Processing Based on Parallel Subgradient Projection and Krylov Subspace Techniques

In this paper, we propose a novel reduced-rank adaptive filtering algorithm by blending the idea of the Krylov subspace methods with the set-theoretic adaptive filtering framework. Unlike the existing Krylov-subspace-based reduced-rank methods, the proposed algorithm tracks the optimal point in the sense of minimizing the \sinq{true} mean square error (MSE) in the Krylov subspace, even when the estimated statistics become erroneous (e.g., due to sudden changes of environments). Therefore, compared with those existing methods, the proposed algorithm is more suited to adaptive filtering applications. The algorithm is analyzed based on a modified version of the adaptive projected subgradient method (APSM). Numerical examples demonstrate that the proposed algorithm enjoys better tracking performance than the existing methods for the interference suppression problem in code-division multiple-access (CDMA) systems as well as for simple system identification problems.Comment: 10 figures. In IEEE Transactions on Signal Processing, 201

Adaptive Quadratic-Metric Parallel Subgradient Projection Algorithm and its Application to Acoustic Echo Cancellation

Publication in the conference proceedings of EUSIPCO, Florence, Italy, 200

Detection for 5G-NOMA: An Online Adaptive Machine Learning Approach

Non-orthogonal multiple access (NOMA) has emerged as a promising radio access technique for enabling the performance enhancements promised by the fifth-generation (5G) networks in terms of connectivity, low latency, and high spectrum efficiency. In the NOMA uplink, successive interference cancellation (SIC) based detection with device clustering has been suggested. In the case of multiple receive antennas, SIC can be combined with the minimum mean-squared error (MMSE) beamforming. However, there exists a tradeoff between the NOMA cluster size and the incurred SIC error. Larger clusters lead to larger errors but they are desirable from the spectrum efficiency and connectivity point of view. We propose a novel online learning based detection for the NOMA uplink. In particular, we design an online adaptive filter in the sum space of linear and Gaussian reproducing kernel Hilbert spaces (RKHSs). Such a sum space design is robust against variations of a dynamic wireless network that can deteriorate the performance of a purely nonlinear adaptive filter. We demonstrate by simulations that the proposed method outperforms the MMSE-SIC based detection for large cluster sizes.Comment: Accepted at ICC 201

Distributed Adaptive Learning with Multiple Kernels in Diffusion Networks

We propose an adaptive scheme for distributed learning of nonlinear functions by a network of nodes. The proposed algorithm consists of a local adaptation stage utilizing multiple kernels with projections onto hyperslabs and a diffusion stage to achieve consensus on the estimates over the whole network. Multiple kernels are incorporated to enhance the approximation of functions with several high and low frequency components common in practical scenarios. We provide a thorough convergence analysis of the proposed scheme based on the metric of the Cartesian product of multiple reproducing kernel Hilbert spaces. To this end, we introduce a modified consensus matrix considering this specific metric and prove its equivalence to the ordinary consensus matrix. Besides, the use of hyperslabs enables a significant reduction of the computational demand with only a minor loss in the performance. Numerical evaluations with synthetic and real data are conducted showing the efficacy of the proposed algorithm compared to the state of the art schemes.Comment: Double-column 15 pages, 10 figures, submitted to IEEE Trans. Signal Processin