Articles

Signal processing in adaptive arrays using power basics

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The development of the theory of adaptive arrays (AAs) is proposed based on the representation of the inverse covariance matrix (CM) of a noise in the AA channels as a finite power series expansion using the direct CM and by representation of a weight vector of the AA as a finite series expansion of the power vectors. The dimension of the power CM basis is equal to the number of external interference sources is less than the number of AA channels, such polynomials have the same fundamental role as the characteristic polynomials of the CM in an opposite case. Proofs for the existence of the above mentioned polynomials coefficient is presented, and the physical properties of the power vector basis are studied. It is shown that the power vectors are correlated and that there are two stages of AA signal processing.

Methods of defining the vector of adaptive processing in antenna arrays at short sample case

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The efficiency of adaptive spatial signal processing in arrays providing the maximum signal/noise ratio is studied for the case when the number of sample vector is less than the number of elements of the adaptive array (AA) and there is no inverse correlation matrix of a jammer in the AA receiving channels. Three methods for defining the stable solution for the weight vector in the AA, which are based on supplementing a posteriori information on the jammer with a priori data on them, are studied. These methods are almost equally highly efficient, but the latter method requires considerably less calculation. Results of mathematical simulation of the efficiency of the suggested methods are given.

Estimation of parameters of signals received by an antenna array

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Proposition of a method for estimating signal parameters and the weight vector in adaptive antenna arrays (AA) based on the parameters of a minimum polynomial of a sample correlation matrix (CM) of the input process. Being highly efficient, this method allows us to estimate signal parameters with accuracies that are close to the Cramer-Rao limits.

Analysis of weight error loss with a multichannel beamformer processor

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An analysis is presented which delivers the bit error rate (BER) performance achieved by a multiple-channel coherent BPSK receiver subject to noisy multichannel impulse response (MCIR) estimates. The receiver utilities a frequency-dependent beamform processor prior to coherent detection which is subject to weight error owing to imperfect MCIR estimates. It is demonstrated that in the flat static channel at high SNR the fractional increase in BER compared to the perfect MCIR estimation case is equal to [N – 1/2]/LS is the number of antenna elements and LS is the training sequence length. Similar results are derived for the flat Rayleigh-fading case both for total and for zero correlation between the fading at the antenna elements. These results are then extended to consideration of the degradation in receiver sensitivity, termed the weight error loss, which for the Rayleigh-fading channels at high SNR turns out to be independent of both the mean SNR and N, is inversely proportional to LS.

The distribution function of the maximum eigenvalue of a sample correlation matrix of internal noise of antenna-array elements

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The statistical characteristics of internal noise are used to determine the properties of estimates of the number and angular coordinates of external sources of signals received by an antenna array (AA). In the case of a time-limited sample, the correlation matrix (CM) of internal noise of an AA has spectrum of random eigenvalues. In a number of critical problems of detection and estimation of the number of signals it is necessary to know the statistical properties of the maximum signal in order to choose correctly the threshold value and adopt statistical decisions. In this paper, the distribution function of the maximum eigenvalue of the sample CM of internal noise is found explicitly. It is assumed that the exact CM is equal to the identity matrix.

Coherent multichannel reception of binary modulated signals with independent Rician fading

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A novel technique to calculate the BER of a q-branch coherent receiver is described. The assumed system consists of an antipodal binary-modulated transmitted signal, with independent Rician fading on each received branch. The method allows simplification of a (q + 1)-dimensional integral (16), which is readily amenable to numerical evaluation.

Coherent multichannel reception of binary modulated signals with dependent Rician fading

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A novel technique to calculate the BER of a q-branch coherent receiver for an antipodal binary-modulated transmitted signal is described. When the amplitude fading on each branch is Rician and independent, the BER is calculated through simplification of a (q + 1)-dimensional integral down to a one-dimensional integral, which is ready amenable to numerical evaluation. For systems where the Rician fading on the branches is dependent, it is shown that the problem can be transformed to an independent-fading problem using technique of ‘spatial whitening’. The authors apply the results to construct diversity contours for the analysis of dependent Rician-faded channel data.

Comparative performance of cellular communication systems with adaptive modulation and coding and systems with power control

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Authors carry out a comparative analysis of performances of cellular communication system with adaptive modulation and coding (AMC) and a system with power control (PC). It is shown that the performance of an AMC system is higher than the performance of a PC system for an arbitrary probability density function of the signal fading. To achieve identical throughputs of the two systems, the mean transmitted power for PC must be greater than that for AMC. For identical mean transmitted power, the throughput of an AMC system is always greater than that of a PC system. We consider code division multiple-access (CDMA) systems with arbitrary numbers of fading time-taps (paths), having a statistically independent Rayleigh fading of signals from path to path. The influence of self-interference on AMC and PC performance is studied. This self-interference results from the nonideal path separation in the receiver.

Statistical characteristics of the AIC and MDL criteria in the problem of estimating the number of sources of multivariate signals in the case of a short sample

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At present there are many methods for estimating the number of signal sources detected by an antenna array. The most well-known methods are based on the AIC (Akaike Information Criterion) and MDL (Minimum Description Length) criteria. The statistical characteristics of these methods have been analyzed in a large number of papers. However, the results obtained in these papers are valid for unknown internal-noise intensity, and the found theoretical estimates are asymptotic. In the case of short samples, the characteristics of these methods are usually analyzed on the basis of numerical simulations. In this paper we find the AIC and MDL statistical characteristics in the case of a known internal-noise intensity of the antenna array. It is shown that within the framework of such a formulation of the problem, the characteristics of the estimate of the number of multivariate-signal sources obtained by these methods can be calculated analytically on the basis of the formulas derived by the authors of this paper for the distribution of the maximum noise eigenvalue of the sample correlation matrix of Gaussian input signals. Analytical expression for the probability of overvaluation of the number of signal sources are obtained for any size of the sample.

Estimation of channel matrix rank for multielement antenna arrays working in multipath fading environment

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The knowledge of the rank of the multichannel impulse response (MCIR) matrix is necessary for the construction of the optimal space-time signal processing in the received adaptive antenna array in communication systems. A statistical threshold method for the rank MCIR matrix estimate is proposed. This technique uses a priory information about the additive while Gaussian noise (AWGN) in the receive antennas.

Signal processing in wireless communication systems using multielement antenna arrays in Rayleigh fading environment

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The multiple-input-multiple-output (MIMO) communication systems using adaptive beamformer processor (BFP) in receive antenna array and fixed (non adaptive) BFP in transmit antenna array are considered. The transmitter doesn’t have channel knowledge in such systems. Different variant of the adaptive BFP are proposed. The maximum likehood (ML) detector and the simplified algorithms of the independent symbol detection are investigated. In the case of the Rayleigh fading environment the simulation results for the bit error rate (BER) are given.

Adaptive signal processing in antenna arrays with allowance for the rank of the impulse-response matrix of a multipath channel.

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We consider adaptive spatial processing in antenna arrays under conditions of multipath propagation. It is shown that estimation of the elements of the matrix of multichannel impulse response (MCIR) in the receiving channels of antenna arrays is not sufficient for performing such a processing, and we should also determine the MCIR-matrix rank, which is equal to the minimum number of adaptive spatial channels for reception of a multipath signal. We propose a threshold method for estimating the rank of the MCIR matrix on the basis of the statistical properties of maximum-likelihood estimation of the elements of the system. The weight vectors of the beamformer processor ensuring adaptive spatial signal processing are estimated.

Space division multiple access in MIMO systems with parallel data transmission

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We study multiple-input multiple-output (MIMO) cellular communication systems with antenna arrays at both link ends and parallel channels for data transmission. These channels (the so-called eigenchannels) are formed with the help of adaptive transmitting and receiving beamformer processors matched with a random fading environment. To increase the capacity of MIMO systems, we propose a space-division multiple-access (SDMA) method, which does not require estimation of signal-arrival directions and is based on orthogonalization of the parallel channels of all users. We find signal-to-noise ratios at the eigenchannel outputs and the total capacity of a MIMO system in the case of simultaneous servicing of an arbitrary number of users. We present numerical results for the case of Rayleigh fading of signals, which confirm the high effectiveness of the proposed SDMA method.

Crosstalk suppression in parallel spatial channels in MIMO communication systems

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We study the influence of the discreteness of information about the channel state, which is transmitted over the receiver-transmitter return line, on the efficiency of MIMO systems. It is shown that such a discreteness results in energy losses and appearance of crosstalk in parallel eigenchannels of the MIMO system. We propose a method of crosstalk suppression, which ensures a pronounced decrease in the energy losses and restores the nondependence ofeigenchannels with respect to transmitted symbols but leads to the correlation of output internal noise. Expression for a maximum likely estimate of received signals are derived with allowance for the noise correlation. Mathematical simulation results showing the high efficiency of the proposed method are presented for the case of Rayleigh fading of signals.

Reduction of bit error probability during parallel transmission of information in a MIMO system.

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We consider cellular communication systems with antenna arrays at both link ends, in which the data transmission is performed via parallel eigenchannels under conditions of a scattering medium. To reduce the bit error probability, we propose a method of information transmission based on the use of only part of the eigenchannels with maximum signal-to-noise ratios and ensuring a tradeoff of the data-transmission rate against the bit-error probability. Eigenchannels are separated into energy-strong and energy-weak channels with the help of the threshold technique. Two possible versions of using the proposed method under conditions of a random multipath spatial channel are studied. The results of numerical simulation in the case of Rayleigh fading of signals confirm the high efficiency of the proposed method of information transmission.

Weight error loss in MIMO systems with adaptive transmit and receive beamformers

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The effects of non-ideal channel estimation in multiple-input-multiple-output (MIMO) wireless communication systems using the eigenchannel technique for the independent symbol transmission are investigated in this paper. Analytical expression is derived for the Shannon capacity for arbitrary signal-to-noise ratio (SNR), training sequence length (TSL), transmit and receive antenna numbers. The weight error loss (WEL) that quantifies the increase in signal-to-noise ratio (SNR) required to meet a given capacity target due to weight jitter are investigated.

Effectiveness of space-division multiple-access in MIMO communication systems with parallel data transmittion

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We consider multiple-input multiple-output (MIMO) cellular communication systems with antenna array at both link ends and data transmission via parallel eigenchannels matched with a random spatial channel. We analyze the effectiveness of the space-division multiple-access (SDMA) method, which does not require estimation of signal-arrival directions and is based on orthogonalization of the parallel channels of all users. We obtained approximate analytical expressions for the mean ration of the signal power to the noise power and the MIMO system capacity, which are derived for the case of Rayleigh fading of signals. Although the obtained formulas are much simpler than the exact ones, they ensure high accuracy for an arbitrary number of transmitting and receiving antennas and an arbitrary power of transmitter. Our results demonstrate the high effectiveness of the proposed SDMA method.

Gaussian channel model for mobile multipath environment

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A model of an angle-spread source is described, termed the “Gaussian channel model” (GCM). This model is used to represent signals transmitted between a user equipment and a cellular base station. It assumes a Gaussian law of the scatterer occurrence probability, depending upon the scatterer distance from the user. The probability density function of the angle of arrival (AoA) of the multipath components is derived for an arbitrary angle spread. The “wandering” of the “center of gravity” of the scattering source realization is investigated, which in turn is due to the nonergodicity of the angle-scatter process. Numerical results obtained with the help of the sum-difference bearing method show the dependence of the AoA estimation accuracy on the spread-source model.

Gaussian channel model for macrocellular mobile propagation

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A model of an angle-spread source is described, termed the ‘Gaussian Channel Model’ (GCM). This model is used t represent signals transmitted between a User Equipment and a cellular Base Station. The model assumes a Gaussian law of scatterer occurrence probability, depending upon the scatterer distance from the user. Analysis is presented to demonstrate that this model produces a better fit to measured data than some other widely-used scattering models in the literature.

Error probability of the data transmission in MIMO systems with space-division multiple access in Rayleigh fading environment

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We consider multiple-input multiple-output (MIMO) communication systems with adaptive antenna arrays at both ends of the link in which the data transmission is performed via parallel eigenchannels matched to the random spatial channels. The effectiveness of the projection method of space-division multiple access is studied. The method does not require estimation of the arrival directions of signals and is based on orthogonalization of all eigenchannels. Exact analytical expressions are obtained for the bit-error probability during the data transmission via the channel with uncorrelated Rayleigh fading of signals in a MIMO system with an arbitrary number of users and antennas.

Estimation of the mobile phone user position in the cellular communication system in a multipath environment of signal propagation

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We consider the problem of locating a mobile object (user) in the cellular communication system on the basis of the triangulation method and the Gaussian multipath-channel model under urban conditions of signal propagation. The probability density function of the maximum likelihood estimate of Cartesian coordinates of the user is found if two or three base stations arbitrarily located with respect to one another are used. It is shown that the user-locating error depends on the distance between the base stations, mutual location of the user and the base stations, and the variance of the user-bearing estimation error for each station. In this case, using the third base station significantly improves the user-locating accuracy.

On Time-of-Arrival Statistic of Gaussian Channel Model

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A model of an angle-spread source, termed the “Gaussian Channel Model” is considered. The cumulative distribution function of the Time-of-Arrival of the multipath components is derived for an arbitrary angle spread. The simple approximate expressions for the Time-of-Arrival cumulative distribution function and probability density function are proposed. Numerical results obtained with the help of the derived expressions show the good coincidence with the experimental data and other known results.

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