Optimal MSE solution for a decision feedback equalizer

Due to the inherent feedback in a decision feedback equalizer (DFE) the minimum mean square error (MMSE) or Wiener solution is not known exactly. The main difficulty in such analysis is due to the propagation of the decision errors, which occur because of the feedback. Thus in literature, these errors are neglected while designing and/or analyzing the DFEs. Then a closed form expression is obtained for Wiener solution and we refer this as ideal DFE (IDFE). DFE has also been designed using an iterative and computationally efficient alternative called least mean square (LMS) algorithm. However, again due to the feedback involved, the analysis of an LMS-DFE is not known so far. In this paper we theoretically analyze a DFE taking into account the decision errors. We study its performance at steady state. We then study an LMS-DFE and show the proximity of LMS-DFE attractors to that of the optimal DFE Wiener filter (obtained after considering the decision errors) at high signal to noise ratios (SNR). Further, via simulations we demonstrate that, even at moderate SNRs, an LMS-DFE is close to the MSE optimal DFE. Finally, we compare the LMS DFE attractors with IDFE via simulations. We show that an LMS equalizer outperforms the IDFE. In fact, the performance improvement is very significant even at high SNRs (up to 33%), where an IDFE is believed to be closer to the optimal one. Towards the end, we briefly discuss the tracking properties of the LMS-DFE.

Channel Hardening-Exploiting Message Passing (CHEMP) Receiver in Large-Scale MIMO Systems

In this paper, we propose a multiple-input multiple-output (MIMO) receiver algorithm that exploits channel hardening that occurs in large MIMO channels. Channel hardening refers to the phenomenon where the off-diagonal terms of the matrix become increasingly weaker compared to the diagonal terms as the size of the channel gain matrix increases. Specifically, we propose a message passing detection (MPD) algorithm which works with the real-valued matched filtered received vector (whose signal term becomes, where is the transmitted vector), and uses a Gaussian approximation on the off-diagonal terms of the matrix. We also propose a simple estimation scheme which directly obtains an estimate of (instead of an estimate of), which is used as an effective channel estimate in the MPD algorithm. We refer to this receiver as the channel hardening-exploiting message passing (CHEMP) receiver. The proposed CHEMP receiver achieves very good performance in large-scaleMIMO systems (e.g., in systems with 16 to 128 uplink users and 128 base station antennas). For the considered large MIMO settings, the complexity of the proposed MPD algorithm is almost the same as or less than that of the minimum mean square error (MMSE) detection. This is because the MPD algorithm does not need a matrix inversion. It also achieves a significantly better performance compared to MMSE and other message passing detection algorithms using MMSE estimate of. Further, we design optimized irregular low density parity check (LDPC) codes specific to the considered large MIMO channel and the CHEMP receiver through EXIT chart matching. The LDPC codes thus obtained achieve improved coded bit error rate performance compared to off-the-shelf irregular LDPC codes.

Linear Transceiver Design for an Amplify-and-Forward Relay Based on the MBER Criterion

A design methodology based on the Minimum Bit Error Ratio (MBER) framework is proposed for a non-regenerative Multiple-Input Multiple-Output (MIMO) relay-aided system to determine various linear parameters. We consider both the Relay-Destination (RD) as well as the Source-Relay-Destination (SRD) link design based on this MBER framework, including the pre-coder, the Amplify-and-Forward (AF) matrix and the equalizer matrix of our system. It has been shown in the previous literature that MBER based communication systems are capable of reducing the Bit-Error-Ratio (BER) compared to their Linear Minimum Mean Square Error (LMMSE) based counterparts. We design a novel relay-aided system using various signal constellations, ranging from QPSK to the general M-QAM and M-PSK constellations. Finally, we propose its sub-optimal versions for reducing the computational complexity imposed. Our simulation results demonstrate that the proposed scheme indeed achieves a significant BER reduction over the existing LMMSE scheme.

Equivalent differential equations for nonlinear dynamical systems

A technique for obtaining approximate periodic solutions to nonlinear ordinary differential equations is investigated. The approach is based on defining an equivalent differential equation whose exact periodic solution is known. Emphasis is placed on the mathematical justification of the approach. The relationship between the differential equation error and the solution error is investigated, and, under certain conditions, bounds are obtained on the latter. The technique employed is to consider the equation governing the exact solution error as a two point boundary value problem. Among other things, the analysis indicates that if an exact periodic solution to the original system exists, it is always possible to bound the error by selecting an appropriate equivalent system.

Three equivalence criteria for minimizing the differential equation error are compared, namely, minimum mean square error, minimum mean absolute value error, and minimum maximum absolute value error. The problem is analyzed by way of example, and it is concluded that, on the average, the minimum mean square error is the most appropriate criterion to use.

A comparison is made between the use of linear and cubic auxiliary systems for obtaining approximate solutions. In the examples considered, the cubic system provides noticeable improvement over the linear system in describing periodic response.

A comparison of the present approach to some of the more classical techniques is included. It is shown that certain of the standard approaches where a solution form is assumed can yield erroneous qualitative results.

Exploring the use of sensors to measure behavioral interactions: an experimental evaluation of using hand trajectories.

Humans appear to be sensitive to relative small changes in their surroundings. These changes are often initially perceived as irrelevant, but they can cause significant changes in behavior. However, how exactly people's behavior changes is often hard to quantify. A reliable and valid tool is needed in order to address such a question, ideally measuring an important point of interaction, such as the hand. Wearable-body-sensor systems can be used to obtain valuable, behavioral information. These systems are particularly useful for assessing functional interactions that occur between the endpoints of the upper limbs and our surroundings. A new method is explored that consists of computing hand position using a wearable sensor system and validating it against a gold standard reference measurement (optical tracking device). Initial outcomes related well to the gold standard measurements (r = 0.81) showing an acceptable average root mean square error of 0.09 meters. Subsequently, the use of this approach was further investigated by measuring differences in motor behavior, in response to a changing environment. Three subjects were asked to perform a water pouring task with three slightly different containers. Wavelet analysis was introduced to assess how motor consistency was affected by these small environmental changes. Results showed that the behavioral motor adjustments to a variable environment could be assessed by applying wavelet coherence techniques. Applying these procedures in everyday life, combined with correct research methodologies, can assist in quantifying how environmental changes can cause alterations in our motor behavior.

Equalisation with adaptive time lag

In an adaptive equaliser, the time lag is an important parameter that significantly influences the performance. Only with the optimum time lag that corresponds to the best minimum-mean-square-error (MMSE) performance, can there be best use of the available resources. Many designs, however, choose the time lag either based on preassumption of the channel or simply based on average experience. The relation between the MMSE performance and the time lag is investigated using a new interpretation of the MMSE equaliser, and then a novel adaptive time lag algorithm is proposed based on gradient search. The proposed algorithm can converge to the optimum time lag in the mean and is verified by the numerical simulations provided.

Prediction of adipose tissue composition using Raman spectroscopy: average properties and individual fatty acids.

Abstract: Raman spectroscopy has been used for the first time to predict the FA composition of unextracted adipose tissue of pork, beef, lamb, and chicken. It was found that the bulk unsaturation parameters could be predicted successfully [R-2 = 0.97, root mean square error of prediction (RMSEP) = 4.6% of 4 sigma], with cis unsaturation, which accounted for the majority of the unsaturation, giving similar correlations. The combined abundance of all measured PUFA (>= 2 double bonds per chain) was also well predicted with R-2 = 0.97 and RMSEP = 4.0% of 4 sigma. Trans unsaturation was not as well modeled (R-2 = 0.52, RMSEP = 18% of 4 sigma); this reduced prediction ability can be attributed to the low levels of trans FA found in adipose tissue (0.035 times the cis unsaturation level). For the individual FA, the average partial least squares (PLS) regression coefficient of the 18 most abundant FA (relative abundances ranging from 0.1 to 38.6% of the total FA content) was R-2 = 0.73; the average RMSEP = 11.9% of 4 sigma. Regression coefficients and prediction errors for the five most abundant FA were all better than the average value (in some cases as low as RMSEP = 4.7% of 4 sigma). Cross-correlation between the abundances of the minor FA and more abundant acids could be determined by principal component analysis methods, and the resulting groups of correlated compounds were also well-predicted using PLS. The accuracy of the prediction of individual FA was at least as good as other spectroscopic methods, and the extremely straightforward sampling method meant that very rapid analysis of samples at ambient temperature was easily achieved. This work shows that Raman profiling of hundreds of samples per day is easily achievable with an automated sampling system.

Reduced-complexity iterative equalization for severe time-dispersive MIMO channels

In this paper, a reduced-complexity soft-interference-cancellation minimum mean-square-error.(SIC-MMSE) iterative equalization method for severe time-dispersive multiple-input-multiple-output (MIMO) channels is proposed. To mitigate the severe time dispersiveness of the channel, a single carrier with cyclic prefix is employed, and the equalization is per-formed in the frequency domain. This simplifies the challenging problem of equalization in MIMO channels due to both the intersymbol interference (ISI) and the coantenna interference (CAI). The proposed iterative algorithm works in two stages. The first stage estimates the transmitted frequency-domain symbols using a low-complexity SIC-MMSE equalizer. The second stage converts the estimated frequency-domain symbols in the time domain and finds their means and variances to incorporate in the SIC-MMSE equalizer in the next iteration. Simulation results show the bit-/symbol-error-rate performance of the SIC-MMSE equalizer, with and without coding, for various modulation schemes.

Improved Linear Transmit Processing for Single-User and Multi-User MIMO Communications Systems

In this paper, we propose a novel linear transmit precoding strategy for multiple-input, multiple-output (MIMO) systems employing improper signal constellations. In particular, improved zero-forcing (ZF) and minimum mean square error (MMSE) precoders are derived based on modified cost functions, and are shown to achieve a superior performance without loss of spectrum efficiency compared to the conventional linear and nonlinear precoders. The superiority of the proposed precoders over the conventional solutions are verified by both simulation and analytical results. The novel approach to precoding design is also applied to the case of an imperfect channel estimate with a known error covariance as well as to the multi-user scenario where precoding based on the nullspace of channel transmission matrix is employed to decouple multi-user channels. In both cases, the improved precoding schemes yield significant performance gain compared to the conventional counterparts.

Turbo channel estimation and equalisation for a superposition-based cooperative system

This study investigates the superposition-based cooperative transmission system. In this system, a key point is for the relay node to detect data transmitted from the source node. This issued was less considered in the existing literature as the channel is usually assumed to be flat fading and a priori known. In practice, however, the channel is not only a priori unknown but subject to frequency selective fading. Channel estimation is thus necessary. Of particular interest is the channel estimation at the relay node which imposes extra requirement for the system resources. The authors propose a novel turbo least-square channel estimator by exploring the superposition structure of the transmission data. The proposed channel estimator not only requires no pilot symbols but also has significantly better performance than the classic approach. The soft-in-soft-out minimum mean square error (MMSE) equaliser is also re-derived to match the superimposed data structure. Finally computer simulation results are shown to verify the proposed algorithm.

Approaching near-capacity on a multi-antenna channel using successive decoding and interference cancellation receivers

In this paper, we address the problem of designing multirate codes for a multiple-input and multiple-output (MIMO) system by restricting the receiver to be a successive decoding and interference cancellation type, when each of the antennas is encoded independently. Furthermore, it is assumed that the receiver knows the instantaneous fading channel states but the transmitter does not have access to them. It is well known that, in theory, minimum-mean-square error (MMSE) based successive decoding of multiple access (in multi-user communications) and MIMO channels achieves the total channel capacity. However, for this scheme to perform optimally, the optimal rates of each antenna (per-antenna rates) must be known at the transmitter. We show that the optimal per-antenna rates at the transmitter can be estimated using only the statistical characteristics of the MIMO channel in time-varying Rayleigh MIMO channel environments. Based on the results, multirate codes are designed using punctured turbo codes for a horizontal coded MIMO system. Simulation results show performances within about one to two dBs of MIMO channel capacity.

Joint complex diversity coding and channel coding over space, time and frequency

This study provides a general diversity analysis for joint complex diversity coding (CDC) and channel coding-based space-time-frequency codeing is provided. The mapping designs from channel coding to CDC are crucial for efficient exploitation of the diversity potential. This study provides and proves a sufficient condition of full diversity construction with joint three-dimensional CDC and channel coding, bit-interleaved coded complex diversity coding and symbol-interleaved coded complex diversity coding. Both non-iterative and iterative detections of joint channel code and CDC transmission are investigated. The proposed minimum mean-square error-based iterative soft decoding achieves the performance of the soft sphere decoding with reduced complexity.

The feasibility of using near infrared and Raman spectroscopic techniques to detect fraudulent adulteration of chili powders with Sudan dye

Chili powder is a globally traded commodity which has been found to be adulterated with Sudan dyes from 2003 onwards. In this study, chili powders were adulterated with varying quantities of Sudan I dye (0.1-5%) and spectra were generated using near infrared reflectance spectroscopy (NIRS) and Raman
spectroscopy (on a spectrometer with a sample compartment modified as part of the study). Chemometrics were applied to the spectral data to produce quantitative and qualitative calibration models and prediction statistics. For the quantitative models coefficients of determination (R2) were found to be
0.891-0.994 depending on which spectral data (NIRS/Raman) was processed, the mathematical algorithm used and the data pre-processing applied. The corresponding values for the root mean square error of calibration (RMSEC) and root mean square error of prediction (RMSEP) were found to be 0.208-0.851%
and 0.141-0.831% respectively, once again depending on the spectral data and the chemometric treatment applied to the data. Indications are that the NIR spectroscopy based models are superior to the models produced from Raman spectral data based on a comparison of the values of the chemometric
parameters. The limit of detection (LOD) based on analysis of 20 blank chili powders against each calibration model gave 0.25% and 0.88% for the NIR and Raman data, respectively. In addition, adopting a qualitative approach with the spectral data and applying PCA or PLS-DA, it was possible to discriminate
between adulterated chili powders from non-adulterated chili powders.

The use of handheld near-infrared reflectance spectroscopy (NIRS) for the proximate analysis of poultry feed and to detect melamine adulteration of soya bean meal

The use of handheld near infrared (NIR) instrumentation, as a tool for rapid analysis, has the potential to be used widely in the animal feed sector. A comparison was made between handheld NIR and benchtop instruments in terms of proximate analysis of poultry feed using off-the-shelf calibration models and including statistical analysis. Additionally, melamine adulterated soya bean products were used to develop qualitative and quantitative calibration models from the NIRS spectral data with excellent calibration models and prediction statistics obtained. With regards to the quantitative approach, the coefficients of determination (R2) were found to be 0.94-0.99 with the corresponding values for the root mean square error of calibration and prediction were found to be 0.081-0.215 % and 0.095-0.288 % respectively. In addition, cross validation was used to further validate the models with the root mean square error of cross validation found to be 0.101-0.212 %. Furthermore, by adopting a qualitative approach with the spectral data and applying Principal Component Analysis, it was possible to discriminate between adulterated and pure samples.

MIMO cooperative communication network design with relay selection and CSI feedback

In this paper, we investigate an amplify-and-forward (AF) multiple-input multiple-output - spatial division multiplexing (MIMO-SDM) cooperative wireless networks, where each network node is equipped with multiple antennas. In order to deal with the problems of signal combining at the destination and cooperative relay selection, we propose an improved minimum mean square error (MMSE) signal combining scheme for signal recovery at the destination. Additionally, we propose two distributed relay selection algorithms based on the minimum mean squared error (MSE) of the signal estimation for the cases where channel state information (CSI) from the source to the destination is available and unavailable at the candidate nodes. Simulation results demonstrate that the proposed combiner together with the proposed relay selection algorithms achieve higher diversity gain than previous approaches in both flat and frequency-selective fading channels.