Nonlinear frequency domain MMSE turbo equalization using probabilistic data association

Much effort has been devoted to the design of wireless communication systems for high data rate applications. MC-CDMA (multi-carrier code division multiple access) is able to transmit at high data rate because it converts to slow data rate at serial to parallel converter. We introduce the MC-CDMA system based on non-linear MMSE (minimum mean square error). The purpose of this paper is to design MC-CDMA with non-linear adaptive filter (called n-equalizer), which has the ability to alleviate problems, associated with various noise components. The Monte-Carlo simulation method is used to show the performance of the system suggested here.

The well-known probabilistic data association (PDA) filter handles the uncertainty in measurement origins inherent in tracking-in-clutter problems by using a probabilistically weighted sum of all measurements in the gate. In fact, the measurements in the gate may or may not include the one originated from the target. As such, two hypothetical models can be set up, corresponding to the events that the target measurements is and is not in the gate, respectively. This paper present an approach that integrates the PDA filter with the multiple-order method in a coherent manner based on the use of the above two hypothetical models. It is shown theoretically that the standard PDA filter is a special case of the first-order Generalized Pseudo Bayesian algorithm in the proposed formulation using a particular set of model transition probabilities. It is then proposed to adopt the superior interacting multiple-model architecture in this new formulation to improve the performance. The new algorithm is capable of achieving better performance by tuning the transition probabilities at a computational complexity comparable to that of the PDA filter. Simulation results are provided.

In minimum mean squared error (MMSE) based turbo equalization, the decoder's extrinsic information is used as the MMSE equalizer's prior information. In order to improve the performance, the combined prior information which consists of the whole decoder's extrinsic information and the partial decoder's full information in the last iteration, is used by the MMSE equalizer. Meanwhile, the MMSE equalizer is lead by matched filter as a preprocessor to reduce the complexity. The extrinsic information transfer (EXIT) chart analysis and simulation results show that the performance of the proposed scheme is much better than that of the conventional turbo equalizer.

This paper examines the performance of linear and nonlinear minimum mean-square error (MMSE) receivers when coupled with a second-order phase tracking subsystem in time-varying frequency-selective fading channels. Two detection techniques based on MMSE equalization with and without decision-feedback (DF) are presented and compared. Results indicate that the proposed receiver algorithms are immune to the near-far problem and shown to offer an increase in capacity relative to the conventional matched-filter (MF) receiver. Furthermore, by adding extra taps in the forward section both structures can perform implicit time diversity by combining the received powers of all paths to improve the receiver performance. Finally it is demonstrated that the phase tracking subsystem is able to track the phase of fast varying fading channels when the stand-alone MMSE structures cannot work.

Filtered multitone (FMT) modulation divides the communication band into several subbands to shorten the span of symbols affected by multipath in underwater acoustic (UWA) communications. However, there is still intersymbol interference (ISI) in each subband of FMT modulation degrading communication performance. Therefore, ISI suppression techniques must be applied to FMT modulation UWA communications. The suppression performance of traditional adaptive equalization methods often exploited in FMT modulation UWA communications is limited when the effect of ISI spans tens of symbols or large constellation sizes are used. Turbo equalization consisting of adaptive equalization and channel decoding can improve equalization performance through information exchanging and iterative processes. To overcome the shortcoming of traditional minimum mean square error (MMSE) equalization and effectively suppress the ISI with relatively low computation complexity, an FMT modulation UWA communication using low-complexity channel-estimation-based (CE-based) MMSE turbo equalization is proposed in this paper. In the proposed method, turbo equalization is first exploited to suppress the ISI in FMT modulation UWA communications, and the equalizer coefficients of turbo equalization are adjusted using the low-complexity CE-based MMSE algorithm. The proposed method is analyzed in theory and verified by simulation analysis and real data collected in the experiment carried out in a pool with multipath propagation. The results demonstrate that the proposed method can achieve better communication performance with a higher bit rate than the FMT modulation UWA communication using traditional MMSE adaptive equalization.

In orthogonal frequency-division multiplexing (OFDM) systems, it is generally assumed that the channel response is static in an OFDM symbol period. However, the assumption does not hold in high-mobility environments. As a result, intercarrier interference (ICI) is induced and the system performance is degraded. A simple remedy for this problem is the application of the zero-forcing (ZF) and minimum mean square error (MMSE) equalizers. Unfortunately, the direct ZF method requires the inversion of an NxN ICI matrix, where N is the number of subcarriers. When N is large, the computational complexity can become prohibitively high. As for the direct MMSE method, in addition to an NxN matrix inverse, it requires an extra NxN matrix multiplication, making the required computational complexity higher compared to the direct ZF method. In this dissertation, we first propose a low-complexity ZF method to solve the problem in single-input-single-output (SISO) OFDM systems. The main idea is to explore the special structure inherent in the ICI matrix and to apply Newton's iteration for matrix inversion. With our formulation, fast Fourier transforms (FFTs) can be used in the iterative process, reducing the complexity from O(N^3) to O(Nlog_2 N) . Also, the required number of the iteration is typically one or two. We also analyze the convergence behavior of the proposed method and derive the theoretical output signal-to-interference-noise-ratio (SINR). For the MMSE method, we first reformulate the MMSE solution in a way that the extra matrix multiplication can be avoided. Similar to the ZF method, we then exploit the structure of the ICI matrix and apply Newton's iteration to reduce the complexity of the matrix inversion. For a multiple-input-multiple-output (MIMO) OFDM system, the required complexity of the ZF and MMSE methods becomes more intractable. We then manage to extend the proposed ZF and MMSE methods for SISO-OFDM systems to MIMO-OFDM systems. It turns out that the computational complexity can be reduced even more significantly. Simulation results show that the performance of the proposed methods is almost as good as that of the direct ZF and MMSE methods, while the required computational complexity is reduced dramatically. Finally, we explore the application of the proposed methods in mobility-induced ICI mitigation for OFDM multiple access (OFDMA) systems, and in carrier frequency offset (CFO) induced ICI mitigation for OFDMA uplink systems. As that in OFDM systems, the proposed methods can reduce the required computational complexity, effectively.

Object-Oriented Environment for Assessing Tracking Algorithms

We investigate linear and nonlinear minimum mean-square error (MMSE) multiuser detectors for high data rate wireless code-division multiple access (CDMA) networks. The reverse link spacetime detectors comprise an antenna array followed by a feedforward filter (FFF) which processes parallel chip matched filter (CMF) output samples and a feedback filter (FBF) which processes detected symbols of all in-sector users. We explore adaptation issues, calculate outage probabilities, and isolate the effects of antenna, diversity, and interference suppression gains for Rayleigh and Ricean multipath fading channels with varying timing control.

This paper presents some experimental results on both the channel estimation based minimum mean square error Turbo equalizer (CE MMSE-TEQ) and the direct-adaptation turbo equalizer (DA-TEQ) in single-input single-output (SISO) underwater acoustic (UWA) channels. For CE MMSE-TEQ, we compare the soft-decision feedback Turbo equalizer (SDFE), the bidirectional soft-decision feedback Turbo equalizer (Bi-SDFE) and the classic linear Minimum Mean Square Error (MMSE) Turbo equalizer in terms of bit error rate (BER) performance. For DA-TEQ, the recently proposed soft-decision direct-adaptation TEQ (Soft DA-TEQ) is evaluated with the same set of experimental data. Both QPSK and multilevel modulations (8PSK and 16QAM) have been tested with the symbol rate of 9.77 ksymbols/s. Experimental results show that the CE-TEQs are more robust in SISO underwater acoustic transmission under harsh channel conditions. Especially, with low pilot overheads, the recently proposed Bi-SDFE achieved low BER performance in all cases.

Square-root formulations have not been developed for state-of-the-art tracking algorithms. The only exception is the square-root implementation of the PDAF by R. Kenefic (1990). It is shown that there is a substantially better implementation of the square-root probabilistic data association filter (PDAF) than Kenefic's algorithm in terms of both numerical robustness and computational efficiency. On the average, the proposed algorithm requires half the number of computations required by Kenefic's algorithm for square-root PDAF. The same approach is extended to develop computationally efficient square-root algorithms for the interesting multiple model (IMM) and IMM probabilistic data association (IMMPDA) filters. >

A single-sensor, single-target mixture reduction (MR) data association algorithm is extended for use in multisensor, multitarget tracking situations. MR is extended for tracking an arbitrary number of targets using an arbitrary number of sensors under the assumption that the sensor measurement errors are independent across sensors. Like the single-sensor, single-target MR algorithm, which gives better performance than the probabilistic data association (PDA) filter, the multisensor, multitarget MR extensions give similar improvements in performance compared to the joint PDA (JPDA) and multisensor JPDA (MSJPDA) algorithms. Further, in the formulations for the multisensor and multitarget MR algorithms, the equations for the calculation of the data association probabilities have been put in the same form as for the JPDA, thus allowing previously developed fast JPDA computational techniques to be applicable. N the problem of tracking targets in random clutter, the optimal Bayesian solution leads to Gaussian mixture distributions that consist of an exponentially increasing number of components.1 In practice, the number of components in each mixture is kept in check by approximating it with fewer components. The nearest neighbor (NN) approximation reduces each target's mixture to its largest component.13 The joint probabilistic data association (JPDA) approximation merges the components of each target's mixture into a single Gaussian component.1'4 However, when there are several significant, well-spaced components in the original mixture, important information may be lost by using the NN or JPDA methods. A more flexible approximation method for single-sensor, single-target tracking, known as mixture reduction (MR), has been proposed by Salmond.5 This MR algorithm preserves the mean and covariance of the original mixture of components, successively merging components until the number of components is reduced to some userspecified limit. In this paper, we first review Salmond's MR algorithm for single-sensor tracking of a single target in clutter. We then derive extensions to Salmond's MR algorithm for use in tracking multiple targets and when there are measurements available from multiple sensors. Just as the single-sensor, single-target MR algorithm gives better performance5 than the probabilistic data association (PDA) filter, the multisensor, multitarget MR extensions are shown to give similar improvements in performance as compared to the JPDA and multisensor JPDA (MSJPDA)6 algorithms. Extension of the MR algorithm for tracking of multiple targets is necessary for use in realistic tracking scenarios where there are usually many targets that need to be tracked. Moreover, many current tracking systems have been designed with multiple sensors, thus requiring the further extension to a multisensor algorithm. The paper is organized as follows. In Sec. II, the target dynamics and measurement equations are defined. We review the singlesensor, single-target MR algorithm5 in Sec. Ill, and we extend the algorithm to the multitarget and multisensor cases in Sec. IV and V, respectively. In Sec. VI, simulation results evaluating the performances of the MR extensions are presented. Finally, concluding remarks are given in Sec. VII.

A methodology for the use of the multirate sampling technique in the measurement acquisition process of a probabilistic data association (PDA) filter is presented. The proposed filter, called the multirate sample probabilistic data association (MSPDA) filter, increases the computational efficiency of the tracking system without compromising the accuracy of the tracking algorithm. The use of multirate sampling enhances the utilization of the central processor, since the time spent in acquiring and processing certain measurements relevant to the components of a state vector is considerably saved. The performance of the MSPDA filter is compared with that of the traditional PDA tracker and other presently used filters. It is shown that the computational saving is about 25% while the degradation in accuracy is only to the extent of 5% of the MSE of the corresponding state vector component. >

Turbo equalization schemes based on minimum mean square error (MMSE) criteria available in the literature for multiple-input multiple-output (MIMO) systems are computationally expensive, as they require a relatively large matrix inversion. In this paper, we propose a low complexity turbo equalization (TE) scheme with successive interference cancellation for orthogonal frequency division multiplexing (OFDM) based MIMO receiver systems (TE-SIC-MIMO). TE-SIC-MIMO leverages on the soft feedback symbol estimate to selectively remove the intercarrier interference (ICI) and co-antenna interference (CAI) from the received data, thus turning the system matrix into an easily invertible form. Extrinsic Information Transfer (EXIT) chart analysis supplemented with numerical simulation results shows that TE-SIC-MIMO performance under static and rapidly time varying multipath conditions is mostly on par with MMSE turbo equalization scheme available in the literature, that is based on a sub-matrix of the system matrix at signal-to-noise ratios (SNR) of practical interest. However, the computation complexity of TE-SIC-MIMO turns out to be much lesser than the TE scheme considered.

If N is standard Gaussian, the minimum mean square error (MMSE) of estimating a random variable X based on √( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">snr</i> ) <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> + <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> vanishes at least as fast as 1/ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">snr</i> as <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">snr</i> → ∞. We define the MMSE dimension of X as the limit as <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">snr</i> → ∞ of the product of snr and the MMSE. MMSE dimension is also shown to be the asymptotic ratio of nonlinear MMSE to linear MMSE. For discrete, absolutely continuous or mixed distribution we show that MMSE dimension equals Rényi's information dimension. However, for a class of self-similar singular X (e.g., Cantor dis tribution), we show that the product of snr and MMSE oscillates around information dimension periodically in snr (dB). We also show that these results extend considerably beyond Gaussian noise under various technical conditions.

Underwater acoustic channels usually suffer from the extended multipath propagation which causes inter symbol interference (ISI). At the receiving end, serious ISI would result in the decrease of the reliability of underwater acoustic communication systems. In this paper, Turbo equalization is applied to increase the reliability of communication systems. The realization of the channel equalizer in Turbo equalization is the linear minimum mean-square error (MMSE) estimate. To avoid performance loss, Turbo equalization and factor graph are combined together which provides a full-window method. Moreover, a modified extrinsic information feedback mechanism of turbo equalization is proposed. The reliability of communication systems is further enhanced by using this mechanism. Simulation results show that the proposed algorithm performs well with low complexity. This demonstrates the potential of the suggested algorithm in practice.