Blind joint information and spreading sequence estimation for short-code DS-SS signal in asynchronous and synchronous systems

In this paper an efficient method is proposed for blind estimation of short-code direct sequence spread spectrum (DS-SS) signal in synchronous system. This method is based on hill-climbing algorithm (HC), which is developed to estimate the spreading sequence for the capability of efficiency and speediness local optimization search. Firstly, The fitness function is constructed to value the quality of candidate sequence. Secondly, the feasibility that HC algorithm is used to estimate the spreading sequence is analysed according to the fitness function. Lastly, simulation results show that the novel method is capable of retrieving the spreading sequences with approximate performance to previous methods, whereas the computational complexity is much lower than previous methods.

At the transmitter of a Direct Sequence Spread Spectrum (DSSS) communication system, data bits are spread using a spreading sequence. To demodulate the transmitted data bits, the received signal should be de-spread using the same spreading sequence. However, there are many non-cooperative communication systems, where a receiver does not have the information on the spreading sequence. In such systems, to demodulate the transmitted data bits across a wide area, it is necessary to blindly estimate the spreading sequence at low Signal-to-Noise Ratio (SNR). Furthermore, for real-time processing, the computational complexity for the blind estimation should be minimized. In this paper, a novel algorithm is proposed to blindly estimate a spreading sequence and data bits based on turbo processing for both synchronous and asynchronous cases. The proposed algorithm can significantly improve the error rates of estimated data bits and the chips in the spreading sequence compared to an Eigen-Value Decomposition (EVD) based algorithm. Furthermore, compared to the EVD-based algorithm, the proposed algorithm drastically reduces the number of required multiplications.

The problem of blind detection in a synchronous CDMA system when there is no knowledge of the users' spreading sequences is considered. An EM-based algorithm which exploits the finite alphabet property of the digital communications source is proposed. Simulations show that this approach, which makes use of knowledge of the subspace spanned by the signaling multiplex, achieves the Cramer-Rao lower bound. The issues of subspace estimation and timing acquisition are also considered.

We propose the random Manchester codes (RMC) to improve the bit error probability (BEP) performance in both synchronous and asynchronous fiber-optic code-division multiple-access (CDMA) systems. The spreading sequences used in the synchronous and asynchronous systems are modified prime sequence codes and optical orthogonal codes (OOCs), respectively. Thermal noise, shot noise, and avalanche photodiode (APD) bulk and surface leakage currents are taken into consideration in the BEP analyzes. The results show that the proposed systems can support a larger number of simultaneous users than other systems with similar system complexity under the same bit-error probability constraint.

CDMA systems commonly use aperiodic spreading codes to distribute a signal spectrum uniformly over the channel bandwidth and differentiate neighboring cell sites. CDMA receivers often suffer from interference due to multipath fading. Blind signal estimation schemes cannot be used because they require periodic spreading sequences. RAKE receivers are often used, but they cannot fully exploit the rich structure of CDMA signals to minimize interference. This paper presents an iterative technique to estimate multipath parameters which can serve as a preprocessing step in a receiver to increase signal-to-interference ratio. We investigate the performance of the proposed method using computer simulations. Preliminary simulation results show an average of 10 dB gain on channel parameter estimation.

Differential coding allows signal demodulation without carrier phase estimation, and thus is commonly used to cope with phase ambiguity and residual carriers. In a wireless scenario where the system transfer function is FIR due to multipath reflections, channel estimation and equalization is usually required. Inspired by the work by Tong (1995) on blind sequence estimation, we propose a vector differential coding scheme that allows instantaneous signal detection at the receiver without knowledge of the channel. The new technique can be regarded as a generalization of the standard differential coding method for removing convolutional ambiguities.

In this paper, Welch's lower bound on the total squared correlation (TSC) for a set of vectors is extended to a set of band-limited waveforms. First, a continuous-time equivalent of total squared correlation (CTE-TSC) is derived by examining the definition of the TSC for a set of vectors in multiple access communication system. The multiple-access system is assumed to employ these vectors as spreading sequences and matched filters as receivers. Then, a lower bound on the CTE-TSC is derived using a frequency domain approach. It is shown that the lower bound on the CTE-TSC has the same form as the Welch's lower bound except that the dimensionality of the vectors is replaced by the average degrees of freedom of the vectorized Fourier transform of the band-limited waveforms. Unlike the dimensionality of a vector, this average degrees of freedom of a band-limited signal used as a transmit waveform for a linear modulation is not restricted only to positive integers. Interestingly, it turns out that the set of waveforms that achieves the lower bound on the CTE-TSC is also the set of the optimum transmit waveforms for overloaded multiple access communication system employing linear minimum mean-squared error (LMMSE) receivers. This extends to continuous cases the discrete counterpart that the Welch bound equality sequences are optimal sequences for overloaded synchronous code-division multiple-access system employing LMMSE receivers

It is well known that jointly optimal multiuser detection for code division multiplex access (CDMA) systems has complexity which grows exponentially with the number of users. Recently, several authors [S. Ulukus and R. D. Yates, April 1998], [C. Sankaran and A. Ephremides, Sept. 1998], [C. Schlegel and A. Grant, 2000] have reported that, for certain special sets of spreading sequences, optimal multiuser detection in synchronous CDMA systems can be performed with computational complexity which is polynomial in the number of users. In this paper, we show that the existing polynomial complexity (PC) algorithms of [S. Ulukus and R. D. Yates, April 1998], [C. Sankaran and A. Ephremides, Sept. 1998], [C. Schlegel and A. Grant, 2000] lead to efficient algorithms for a wider class of spreading sequences than initially proposed. We identify these sequences and prove the existence of optimal polynomial-complexity algorithms for detecting synchronous CDMA signals using these sequences. We also give constructions of sets of binary antipodal spreading sequences for which optimal polynomial-complexity algorithms exist and show that for any sequence length N, we can construct at least N such sequences.

This dissertation is concerned with the task of efficiently and accurately tracking the singular values and left singular vectors of a rapidly changing dominant column space of a matrix, in which a column of the matrix is replaced each time step. As part of this task, the dimension of this dominant subspace is determined automatically for each time step. Two methods for determining the singular values and left singular vectors of this dominant columnspace are presented. The first method, which is an exact method, will update all of the singular values and left singular vectors using the rank-two secular function. The derivation of this function, and its properties, are original contributions of this dissertation. This method requires a single O(n3) matrix product to rotate the singular vectors using direct multiplication, and all other computation is O(n2). The second method, the Improved Fast Adaptive Subspace Tracking (IFAST) method, will give accurate approximations of the r largest singular values and corresponding left singular vectors in O( nr2) time. An accuracy analysis of the approximation error of the second method, using the rank-two secular function from the first method, is presented. The block Hankel matrix structure is presented, which can give improved SNR for exponential signals in sensor arrays, at the expense of beam-width. The two rank determination methods of Shah and Tufts, where one is for time-series (Hankel) data and the other is for unstructured sensor array data, are combined into a single general method which works with unstructured, Hankel, and block Hankel matrices. An efficient way to calculate the thresholds used by this method is presented, allowing use in real-time applications.

We consider the singular vectors of any m × n submatrix of a rectangular M × N Gaussian matrix and study their asymptotic overlaps with those of the full matrix, in the macroscopic regime where N / M , m / M as well as n / N converge to fixed ratios. Our method makes use of the dynamics of the singular vectors and of specific resolvents when the matrix coefficients follow Brownian trajectories. We obtain explicit forms for the limiting rescaled mean squared overlaps for right and left singular vectors in the bulk of both spectra, for any initial matrix A . When it is null, this corresponds to the Marchenko–Pastur setup for covariance matrices, and our formulas simplify into Cauchy-like functions.

The aim of a correspondence analysis is the graphical representation of the categories of variables in one frame of reference. This visualization is possible due to the decomposition of the basic matrix with the use of Singular Value Decomposition (SVD). There are three matrices used in the process of decomposition: right singular vectors, left singular vectors, and a singular value diagonal matrix. The aim of this paper is to compare four different approaches and algorithms of SVD methods used in a correspondence analysis. In the literature, four approaches are known to singular value decomposition, defined by: R.A. Fisher (1940), M.J. Greenacre (1984), E.B. Anderson (1991), and J.D. Jobson (1992). Those computational procedures will be presented and compared in this paper. Also, methods of determining the coordinates of the category column and line matrix, as well as the values of inertia will be defined for these approaches. A key problem is to compare the well-known approaches, since in the literature only one approach ‒ proposed by Greenacre ‒ is used for singular value decomposition. The reason of the superiority of this algorithm over the others may be the simplicity and ease of the mathematical calculations. Greenacre’s algorithm is also used in R statistical software, making its availability and popularity growing, however, other algorithms are worth presenting and focusing on.

The compressed beamforming weights feedback is used in the precoded MIMO-OFDM system, e.g., IEEE 802.11n/ac WLAN, to reduce the amount of feedback information. The precoded sub-system at the receiver of this system needs to perform singular value decomposition (SVD) on the estimated channel matrices at all sub-carriers. The computed angles of the right singular vectors are to be feedback to the transmitter. Also the computed singular values and left singular vectors are to be used for designing the optimal detector. Under the exemplary scenario of four antennas at the access point and two antennas at the station, our designed architectures for the precoding sub-system can provide SVD throughput rates 16.8 and 50.4 M matrices/sec for the uplink and downlink transmissions, respectively.

The FORTRAN codes in this Chapter address the question of computing distinct singular values and corresponding left and right singular vectors of real rectangular matrices, using a single-vector Lanczos procedure. For a given real rectangular ℓ × n matrix A, these codes compute nonnegative scalars σ and corresponding real vectors x ≠ 0 and y ≠ 0 such that EquationSource$$ % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qacaWGbbGaamiEaiabg2da9iabeo8aZjaadMhaieaacaWFGaGaamyy % aiaad6gacaWGKbGaa8hiaiaadgeapaWaaWbaaSqabeaapeGaamivaa % aakiaadMhacqGH9aqpcqaHdpWCcaWG4bGaaiOlaaaa!4716! $$Ax = \sigma y and {A^T}y = \sigma x.$$$$ ((6.1.1)) Every real rectangular ℓxn matrix, where ℓ ≥ n, has a singular value decomposition, EquationSource$$ % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qacaWGbbGaeyypa0Jaamywaiabfo6atjaadIfapaWaaWbaaSqabeaa % peGaamivaaaaieaak8aacaWFGaGaam4DaiaadMgacaWG0bGaamiAai % aa-bcapeGaamiwaiabg2da9iaadIfapaWaaWbaaSqabeaapeGaamiv % aaaak8aacaWGybGaeyypa0JaamysaiaacYcacaWFGaGaamywamaaCa % aaleqabaGaamivaaaakiaadMfacqGH9aqpcaWGjbGaa8hiaiaa-fga % caWFUbGaa8hzaiaa-bcacqqHJoWucaWF9aWaamWaaeaafaqabeGaba % aabaGaeu4Odm1aaSbaaSqaaiaadMeaaeqaaaGcbaGaaGimaaaaaiaa % wUfacaGLDbaaaaa!59A3! $$A = Y\Sigma {X^T} with X = {X^T}X = I, {Y^T}Y = I and \Sigma = \left[ {\matrix {{\Sigma _I}} \\ 0 \\ \endmatrix } \right]$$$$ ((6.1.2)) where Σ is ℓ × n and = diag {σ1,..., σn} with σi, 1 ≤ i ≤ n, the singular values of A. X is a n × n orthogonal matrix, Y is a ℓ × ℓ orthogonal matrix, and the columns of X and of Y are respectively, right and left singular vectors of A. There are many applications for this type of decomposition. Singular values and vectors are discussed in detail for example in Stewart [1973].KeywordsError EstimateSingular VectorMain ProgramVector ComputationReal Symmetric MatrixThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The problem of simultaneous column and row subset selection is addressed in this paper. The column space and row space of a matrix are spanned by its left and right singular vectors, respectively. However, the singular vectors are not within actual columns/rows of the matrix. In this paper, an iterative approach is proposed to capture the most structural information of columns/rows via selecting a subset of actual columns/rows. This algorithm is referred to as two-way spectrum pursuit (TWSP) which provides us with an efficient solution for the CUR matrix decomposition. TWSP is applicable in a wide range of applications since it enjoys a linear complexity w.r.t. number of original columns/rows. We demonstrated the application of TWSP for joint channel and sensor selection in cognitive radio networks and efficient supervised data reduction.

Iterative computation of the smallest singular value and the corresponding singular vectors of a matrix