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In this study, a classification algorithm based on complex number feature is proposed. Specifically, the SVM framework is reformulated, so each example would be classified in the unitary space. The cost function is redefined by considering the maximum margin of real and imaginary units of the complex number feature at the same time. The cost function is based on the expectation of the hinge loss, and its derivatives can be calculated in closed forms. Using a stochastic gradient descent (SGD) algorithm, this method allows for efficient implementation. For complex number feature, the example uncertainty is modeled by a sample preprocessing method based on within-class Euclidean distance Gaussian distribution sample (DGS). In addition, a complex number feature selection method based on improved hybrid discrimination analysis (HDA) is proposed by considering the correlation between real and imaginary units of complex number feature. The proposed classification algorithm is tested on synthetic data and three publicly available and popular datasets, namely, MNIST, WDBC, and Voc2012. Experimental results verify the effectiveness of the proposed method. The codes are available: https://github.com/luckysomebody/paper-code.

In this article, we consider the problem of planar graph-based simultaneous localization and mapping (SLAM) that involves both poses of the autonomous agent and positions of observed landmarks. We present complex (CPL)-SLAM, an efficient and certifiably correct algorithm to solve planar graph-based SLAM using the complex number representation. We formulate and simplify planar graph-based SLAM as the maximum likelihood estimation on the product of unit complex numbers, and relax this nonconvex quadratic complex optimization problem to convex complex semidefinite programming (SDP). Furthermore, we simplify the corresponding complex SDP to Riemannian staircase optimization (RSO) on the complex oblique manifold that can be solved with the Riemannian trust region method. In addition, we prove that the SDP relaxation and RSO simplification are tight as long as the noise magnitude is below a certain threshold. The efficacy of this work is validated through applications of CPL-SLAM and comparisons with existing state-of-the-art methods on planar graph-based SLAM, which indicates that our proposed algorithm is capable of solving planar graph-based SLAM certifiably, and is more efficient in numerical computation and more robust to measurement noise than existing state-of-the-art methods. The C++ code for CPL-SLAM is available at https://github.com/MurpheyLab/CPL-SLAM. [ABSTRACT FROM AUTHOR]

In this paper, we expand our recently introduced concept of unique word orthogonal frequency division multiplexing (UW-OFDM). In UW-OFDM the cyclic prefixes (CPs) are replaced by deterministic sequences, the so-called unique words (UWs). The UWs are generated by appropriately loading a set of redundant subcarriers. By that a systematic complex number Reed–Solomon (RS) code construction is introduced in a quite natural way, because an RS code may be defined as the set of vectors, for which a block of successive zeros occurs in the other domain w.r.t. a discrete Fourier transform. (For a fixed block different to zero, i.e., a UW, a coset code of an RS code is generated.) A remaining problem in the original systematic coded UW-OFDM concept is the fact that the redundant subcarrier symbols disproportionately contribute to the mean OFDM symbol energy. In this paper we introduce the concept of non-systematic coded UW-OFDM, where the redundancy is no longer allocated to dedicated subcarriers, but distributed over all subcarriers. We derive optimum complex valued code generator matrices matched to the best linear unbiased estimator (BLUE) and to the linear minimum mean square error (LMMSE) data estimator, respectively. With the help of simulations we highlight the advantageous spectral properties and the superior bit error ratio (BER) performance of non-systematic coded UW-OFDM compared to systematic coded UW-OFDM and to CP-OFDM in additive white Gaussian noise (AWGN ) as well as in frequency selective environments. [ABSTRACT FROM PUBLISHER]

The computation of the arctangent of a complex number, i.e., the atan2 function, is frequently needed in hardware systems that could profit from an optimized operator. In this brief, we present a novel method to compute the atan2 function and a hardware architecture for its implementation. The method is based on a first stage that performs a coarse approximation of the atan2 function and a second stage that improves the output accuracy by means of a lookup table. We present results for fixed-point implementations in a field-programmable gate array device, all of them guaranteeing last-bit accuracy, which provide an advantage in latency, speed, and use of resources, when compared with well-established fixed-point options. [ABSTRACT FROM PUBLISHER]

Presents a study which examined a regular digit-serial complex multiplier architecture suited for very large scale integrator implementations. Discussion on the complex-number representation schemes; Information on the digit-serial complex multiplier.