Standard Principal-Component Analysis (PCA) is known to be very sensitive to outliers among the processed data.1 On the other hand, it has been recently shown that L1-norm-based PCA (L1-PCA) exhibits sturdy resistance against outliers, while it performs similar to standard PCA when applied to nominal or smoothly corrupted data.2, 3 Exact calculation of the K L1-norm Principal Components (L1-PCs) of a rank-r data matrix X∈ RD×N costs O(2NK), in the general case, and O(N(r-1)K+1) when r is fixed with respect to N.2, 3 In this work, we examine approximating the K L1-PCs of X by the K L1-PCs of its L2-norm-based rank-d approximation (K≤d≤r), calculable exactly with reduced complexity O(N(d-1)K+1). Reduced-rank L1-PCA aims at leveraging both the low computational cost of standard PCA and the outlier-resistance of L1-PCA. Our novel approximation guarantees and experiments on dimensionality reduction show that, for appropriately chosen d, reduced-rank L1-PCA performs almost identical to L1-PCA.
KEYWORDS: Signal to noise ratio, Resistance, Sensors, Signal processing, Contamination, Receivers, Electrical engineering, Electronics engineering, Computer engineering, Data analysis
Conventional subspace-based signal direction-of-arrival estimation methods rely on the familiar L2-norm-derived
principal components (singular vectors) of the observed sensor-array data matrix. In this paper, for the first
time in the literature, we find the L1-norm maximum projection components of the observed data and search
in their subspace for signal presence. We demonstrate that L1-subspace direction-of-arrival estimation exhibits
(i) similar performance to L2 (usual singular-value/eigen-vector decomposition) direction-of-arrival estimation
under normal nominal-data system operation and (ii) significant resistance to sporadic/occasional directional
jamming and/or faulty measurements.
A doubly optimal binary signature set is a set of binary spreading sequences that can be used for code division multiplexing purposes and exhibits minimum total-squared-correlation (TSC)and minimum maximum-squared-correlation (MSC) at the same time. In this article,
we focus on such sets with signatures of odd length and we derive closed-form expressions for the signature cross-correlation matrix, its eigenvalues, and its inverse. Then, we derive analytic
expressions for (i) the bit-error-rate (BER) upon decorrelating processing,(ii) the maximum achievable signal-to-interference-plus-noise (SINR) ratio upon minimum-mean-square-error (MMSE) filtering, and (iii) the total asymptotic efficiency of the system. We find that doubly optimal sets with signature length of the form 4m+1, m=1,
2,..., are in all respects superior to doubly optimal sets with signature length of the form 4m-1 (the latter class includes the familiar Gold sets as a small proper subset). "4m+1" sets perform practically at the single-user-bound (SUB) after decorrelating or MMSE
processing (not true for "4m-1" sets). The total asymptotic efficiency of "4m+1" sets is lower bounded by 2/e for any system user load. The corresponding lower bound for "4m-1" sets is zero.
KEYWORDS: Binary data, Signal to noise ratio, Electronic filtering, Signal processing, Digital filtering, Algorithm development, Interference (communication), Receivers, Linear filtering, Data modeling
In direct-sequence code-division-multiple-access (DS-CDMA) systems, the pre-detection signal-to-interference-plus-noise ratio (SINR) at the output of the single-user minimum-mean-square-error (MMSE) filter is a function of the specific user spreading code (signature). In this paper, we consider the adaptive optimization of the user signature assignment such that the output SINR of the MMSE filter is maximized under a transmitter power constraint. In the context of binary signatures, the complexity of the signature optimization procedure is exponential in the processing gain. A low-cost suboptimum adaptive binary signature assignment algorithm is derived based on conditional optimization principles. We use this algorithm to design an efficient system-wide multiuser adaptive signature set assignment scheme. The performance of the proposed scheme is evaluated under asynchronous multipath fading DS-CDMA channel models and is compared to the performance of systems with arbitrarily chosen signature sets.
KEYWORDS: Phase shift keying, Receivers, Linear filtering, Digital filtering, Sensors, Logic, Modulation, Signal to noise ratio, Demodulation, Telecommunications
Second-order multipath channel estimation procedures for direct-sequence code-division-multiple-access communications induce phase ambiguity that necessitates differential phase- shift-keying (DPSK) modulation and detection. The maximum likelihood (ML) single-symbol multiuser DPSK/CDMA detector is derived with direct generalization to multiple-symbol (block) multiuser DPSK/CDMA detection. Exponential complexity requirements limit the use of the ML rule to theoretical lower-bound bit-error-rate benchmarking. Linear filter DPSK demodulators are viewed as a practical alternative. Phase-ambiguous RAKE filtering followed by RAKE-output differential detection is considered. The familiar minimum-variance-distortionless-response (MVDR) PSK/CDMA filter (designed for minimum filter output energy under the constraint of distortionless response in a given RAKE vector direction) adds the valuable feature of active interference suppression; however, minimum disturbance variance at the differential logic output can be claimed formally only in the absence of multipath (no inter-symbol- interference). Short-data-record adaptive alternatives to costly and slow adaptive MVDR implementations are sought in the context of auxiliary-vector filtering. Numerical and simulation studies illustrate the developments.
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