Weighted Linear Least Square Localization Algorithms for Received Signal Strength

We generalize the multiuser (CDMA spread spectrum) communication systems to the fading environments. We first extend Verdu's (1986) conventional optimum receiver to Rayleigh-fading environments and then evaluate its performance. Having no knowledge of the received power at the receiving end, we therefore need an estimator to efficiently estimate the received signal strength of each user in fading environments. A linear minimum mean square error (LMMSE) unbiased estimator is proposed to attain this goal. By using the minimum mean square error (MMSE) Bayesian estimation, we further propose the LMMSE bit estimator for efficient demodulation. Its performance is close to the optimum multiuser receiver but with a much simpler polynomial complexity. To further reduce the complexity, we extend the LMMSE estimator to the sequential LMMSE estimator. In sequential estimation, we do not need to implement the matched filter banks and to perform the matrix inversion when estimating. In addition, it converges after approximately 2k iterations, where k is the number of users. With this fast convergence property and the simple structure, the sequential LMMSE estimator provides an attractive alternative to the implementation of a multiuser system.

Path loss prediction models are essential tools in radio network planning for cellular transmission as they are used for received signal strength estimation, link budget design and analysis, cell size estimation, and interference optimization.This paper presents empirical path loss models developed for WCDMA microcells operating at 2100MHz on live radio Globacom Node Bs in the urban, suburban, and rural areas in Rivers state.The performance of COST 231 Hata model, Stanford University Interim, and Electronic Communication committee 33 were compared with measured field data.COST 231 Hata model gave a better prediction but with high RMSE and SD which are outside the acceptable value for a good radio signal propagation.COST 231 Hata model was for adjustment based on Linear Least Square Algorithm (LLSA).After adjustment and simulations, the adjusted COST 231 Hata model gave better predictions with minimum MSE and SD that are within the acceptable values.The adjusted COST 231 Hata can accurately be used for predicting the radio characteristic of Rivers State.

For wireless sensor networks, received signal strength (RSS) and proximity (also known as connectivity) measurements have been proposed as simple and inexpensive means to estimate range between devices and sensor location. While RSS measurements are recognized to suffer from errors due to the random nature of the fading channel, proximity measurements, ie., knowing only whether or not two devices are in communication range, are often discussed without considering that they are affected by the same fading channel. Proximity measurements are actually just a binary quantization of RSS measurements. We use the Cramér-Rao bound (CRB) to compare the minimal attainable variances of unbiased sensor location estimators for the cases of RSS and proximity measurements. For completeness, we also present the CRB for sensor localization with systems using K-level quantized RSS (QRSS) measurements, of which proximity measurements are the special case: K=2. Examples are presented for the case of one unknown-location sensor, and for the case of a 5 by 5 grid of sensors. These examples show that lower bounds for standard deviation in proximity-based systems are, as a rule of thumb, about 50% higher than the bounds for RSS-based systems. Furthermore, results are presented which show how many bits of quantization are necessary for a QRSS-based system to nearly achieve the bounds of an unquantized RSS system.

Visible light communication (VLC) has been proposed as a promising way for next generation wireless communication networks to mitigate the scarcity of the radio frequency (RF) spectrum, and has consequently attracted much attention. This paper introduces a single-input single-output (SISO) VLC system under the joint effects of statistical random channel and signal-dependent shot noise (SDSN). Moreover, it estimates the channel of the considered system using maximum likelihood (ML), least square (LS), linear minimum mean square error (LMMSE), maximum posteriori probability (MAP) and minimum mean square error (MMSE) estimators. Furthermore, a Bayesian Cramér-Rao lower bound (BCRLB) is derived for the proposed system and it is compared to the mean square error (MSE) of the proposed estimators. The problem of unknown SDSN factor, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\zeta ^{2}$</tex-math></inline-formula> , at the receiver side is discussed and two solutions are investigated. The receiver of a VLC system under SDSN and random channel gain <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$h$</tex-math></inline-formula> is designed and its BER is studied. Finally, Monte Carlo simulation results of the proposed estimators, which show the dramatic effect of the SDSN on the considered system, are provided. In particular, the presence of noise variance, as well as the SDSN factor, causes an increase in the MSE of the system, while increasing the power reinforces the system performance.

With the increasing rate of wireless devices and high bandwidth operations, wireless networking and communications are becoming over crowded. To cope with such crowded and messy situation, massive MIMO is designed to work with hundreds of low-cost serving antennas at a time as well as improve the spectral efficiency at the same time. Time Division Duplexing (TDD) has been used for gaining beamforming which is a major part of massive MIMO, to gain its best improvement to transmit and receive pilot sequences. All the benefits are only possible if the channel state information or channel estimation is gained properly. Least Square (LS), Minimum Mean Square Error (MMSE) and Linear Minimum Mean Square Error (LMMSE) are the estimators commonly used for estimating channel matrices. We have optimized these methods using genetic algorithm to minimize the mean squared error and finding the best channel matrix from existing algorithms with less computational complexity. Our simulation result has shown that the use of Genetic Algorithm (GA) worked well on existing algorithms in a Rayleigh slow fading channel and existence of Additive White Gaussian Noise. We found that the GA optimized LS is better than existing algorithms. GA provides optimal result in some few iterations in terms of Mean Square Error (MSE) with respect to SNRand computational complexity.

For large-scale multiple-input multiple-output (MIMO) systems, linear minimum mean square error (MMSE) method is one of the most near-optimal ways for signal detection. However, MMSE involves matrix inversion which is of high complexity for computation. In this paper, a Lanczos-based method is proposed to solve the problem by transferring the matrix inversion computation into an iteration process of solving a linear equation. The simulation result proves that the BER of Lanczos-based method outperforms the recently proposed Neumann series approximation algorithm with the same SNR. At the same time, the Lanczos-based method could reduce the computational complexity from O(K3) to O(K2), where K is the number of users. Then the convergence speed is analysed by Kaniel-Paige-Saad theory. Finally, the result shows that the performance of Lanczos-based method achieves the classical MMSE exact matrix inversion methods with only a small number of iterations.

In this paper, we propose a set of joint transmit diversity selection (TDS) and relay selection (RS) algorithms based on discrete iterative stochastic optimization for the uplink of cooperative multiple-input-multiple-output (MIMO) systems. Decode-and-forward (DF) and amplify-and-forward (AF) multirelay systems with linear minimum mean square error (MSE), successive interference cancelation, and adaptive reception are considered. The problems of TDS and RS are expressed as MSE and mutual information (MI) joint discrete optimization problems and solved using iterative discrete stochastic algorithms. Such an approach circumvents the need for exhaustive searching and results in a range of procedures with low complexity and increased speed of convergence that can track the optimal selection over an estimated channel. The proposed schemes are analyzed in terms of their complexity, convergence, and diversity benefits and are shown to be both stable and computationally efficient. Their performance is then evaluated via MSE, MI, and bit error rate comparisons and shown to outperform conventional cooperative transmission and, in the majority of scenarios, match that of the optimal exhaustive solution.

The paper focuses on the performance analysis of the timing acquisition scheme based on received signal strength (RSS) measurements for ultra-wideband (UWB) communication systems. To our knowledge, few paper discusses the performance of the timing acquisition scheme based on RSS measurements for UWB in details. The timing acquisition scheme based on RSS measurements has many advantages, such as low cost, high speed and robustness. However, low transmission power limitation and complicated indoor multipath propagation environments make it difficult to measure accurate RSS at the receiver and affect the accuracy of the time delay offset estimation for the local template signals. In addition, the time variation of the indoor channel state can form a multiple-to-one mapping relation between the RSS measurements and the distance, which largely limits the method application. In the paper, we analyze the accuracy of time delay offset estimation for this method by deriving the Cramer-Rao lower bound (CRLB). The number results show that the accuracy of the timing acquisition method based on RSS measurements suffers from both the UWB signal transmission speed and the varying distance between the transmitter and receiver. It is noted that though the accuracy of the method can hardly fulfil the fine timing acquisition requirement for UWB systems, it will largely reduce the coarse timing acquisition time and improve the performance for UWB timing acquisition systems if combined with other timing acquisition ones

This paper presents a new design method for delay-tolerant linear dispersion codes (DT-LDCs) for asynchronous cooperative communication networks. We consider a system that is equipped with linear minimum mean square error (MMSE) receiver. Based on the DT-LDC framework, we propose a new design method to yield DT-LDCs that approach near-optimal capacity as well as minimum average MSE. The proposed design employs stochastic gradient algorithm to guarantee the local optimum. Moreover, it is improved by using simulated annealing type optimization to approach the global optimum. Simulation results confirm the performance of the newly-proposed delay-tolerant LDCs.

In non-destructive testing (NDT), it is desirable to have as much information as possible about the size, orientation, and shape of a defect. But due to the reflections in numerous dispersive acoustic modes and the mode conversion that occurs at the defects, the resulting images become very difficult to interpret. This paper designs time reversal (TR) based Bayesian estimators with the goal of compensating the effects of multi-modal propagation. We present a linear acoustic model for imaging the defects and use TR to reconstruct the image using a linear Minimum Mean Square Error (MMSE) beamformer. The simulation results show that the TR based MMSE beamformer is successful to achieve a significantly higher accuracy in localizing the scatterers as compared to its conventional counterpart.

Massive multiple‐input multiple‐output (M‐MIMO) is one of the cutting edge technologies that provides significant improvement in throughput, coverage and spectral efficiency. The challenge with M‐MIMO systems is to extract individual signals from the composite signal, thus making optimal detectors prohibitively complex. Recently, approximate message passing (AMP) and its variant detectors have gained substantial importance due to their decreased complexity and improved performance. However, AMP algorithm does not always converge. Non‐linear detectors like vertical Bell‐Labs layered space‐iime improve the bit error rate (BER) but with high complexity, whereas, linear minimum mean square error (MMSE) detector offers low complexity while compromising on BER performance. Neumann series based MMSE detectors further reduce MMSE computational complexity, however, the BER performance remains the same. In this work, the authors propose a hybrid Neumann series based MMSE detector which decomposes the detected signal into its constituent components and apply a neighbourhood selection algorithm on the obtained components thus improving the overall performance. Another contribution of this work is derivation of an off‐set value for optimised neighbourhood set selection that enables more accurate detection while further reducing computational complexity. Simulation results confirm that the proposed scheme outperforms aforementioned algorithms in terms of BER performance and computational complexity in a continuously changing Rayleigh channel.

In this letter, we introduce an analytical expression to the coded bit error rate (BER) of a MIMO system with a linear minimum mean square error (MMSE) receiver. We derive the moment generating function (MGF) of the SINR for arbitrary antenna configurations from the cumulative density function of SINR.We show that the moment generating function of the SINR at the MMSE detector output can be used to estimate the BER performance of a coded MIMO system. The analysis is simple and gives an accurate BER estimation at a high SNR. Based on the analytical and simulated results, the diversity order is dependent on the antenna configuration and the free distance of the convolutional code. Finally, we compare the analytical expression with simulated results for validation.

Sum rates for multi-user MIMO vector perturbation precoding with regularization

Node localization is employed in many wireless networks as it can be used to improve routing and enhance security. In this paper, we propose a new algorithm based on decision tree classification and K-means clustering which are well known techniques in data mining. Several performance measures are used to compare the K-means localization algorithm with those using linear least squares (LLS) and weighted linear least squares based on singular value decomposition (WLS-SVD). It is shown that the proposed algorithm performs better than the LLS and WLS-SVD algorithms even when the geometric anchor distribution about an unlocalized node is poor.

Linear precoding plays an important role in the spatial multiplexing multiple-input multiple-output (MIMO)-orthogonal frequency-division multiplexing (OFDM) systems which are considered one of the primary candidates for the physical-layer techniques in the next-generation wireless communication systems. It requires the channel state information (CSI) at the transmitter to adapt the transmitted signal to the channel conditions. In most communication systems, the CSI is estimated at the receiver and fed back to the transmitter. However, the error performance in a precoded MIMO-OFDM system is significantly degraded due to the long feedback delay that causes the outdated CSI at the transmitter. In this paper, a novel approach using multi-block linear channel prediction is proposed to combat the feedback delay in a limited feedback precoded spatial multiplexing MIMO-OFDM system. The time-varying channel is modeled by autoregressive (AR) process, whose coefficients are obtained by linear minimum mean square error (MMSE) method. To increase prediction range, block-based channel samples are used to establish the AR model, and multiple blocks are employed to iteratively predict the CSI. Simulation results show that the performance degradation caused by large feedback delay can well be mitigated.