Optimum Combining Research Articles

Optimum combining in fractional domain

Fractional domain optimum combining (OC) using fractional Fourier transform has been considered in this article. It has already been established that in an interference-dominated environment, OC is the best among all the diversity techniques used for single-input multiple-output systems. This technique is based on the principle of maximising the signal-to-interference plus noise ratio at the output of the combiner. In this article, a new combiner, which calculates the weights in fractional domain, has been proposed to further enhance the performance of OC in terms of bit error rate (BER). Fractional domain combining gives better signal-to-noise ratio (SNR) at the output of the combiner as compared to time- or frequency-domain combiner due to complete removal of noise. For two receive antennas, the proposed combiner gives an SNR improvement of 7.2 and 2.4 dB as compared to time- and frequency-domain combiners, at a BER of 10−2. It has been concluded that the proposed technique clearly outperforms the existing technique.

Double polarization active Y junctions in the L band, based on Ti:LiNbO_3 lithium niobate waveguides: polarization and contrast performances

Double polarization electro-optic beam combiners based on a Ti:diffusion lithium niobate waveguide have been developed for mid-infrared applications. A monochromatic rejection ratio of up to 33 dB at λ=3.39 μm was obtained, as well as wideband fringes showing low dispersion. In a first part, studying the fringe contrast as a function of waveguide width, we found a compromise among transmission, signal-to-noise ratio, and fringe contrast, depending on the single-mode behavior of the waveguides. We will show that both polarizations are guided, and at least 70% and 90% contrast is achieved, respectively, in TE and TM with a 400 nm wideband light centered at 3.39 μm. After choosing the optimal combiner and designing the electrodes, we studied the electro-optic response of the device, using a monochromatic source and scanning the fringe, by external as well as internal modulation, in order to determine the rejection ratio and the voltage needed to cover half a fringe (V(π)) voltage for both TE and TM polarizations.

Cooperative Multiband Joint Detection With Correlated Spectral Occupancy in Cognitive Radio Networks

In this paper, a frequency-coupled optimum linear energy combiner (OLEC) structure, recently proposed for single user scenarios, is generalized to multiple users and integrated into the spatial-spectral joint detection framework introduced by Quan , to take further advantage of subband occupancy correlation in cooperative wideband spectrum sensing. In particular, the design of the detection thresholds and fusion weights used by a bank of subband multiuser OLECs is formulated as a joint optimization problem, i.e. maximization of aggregate opportunistic throughput under interference constraints (or vice versa). Through numerical experiments with a Markov model of subband occupancy, the proposed scheme is shown to significantly enhance CR network performance in terms of these global metrics.

An Analytical Expression for Performance of Optimum Combining with Multiple Correlated CCIs and Two Antennas

We derive an analytical expression for the average output signal-to-interference-plus-noise ratio (SINR) of optimum combining (OC) for spatially correlated signals from two antennas in the presence of correlated multiple co-channel interferers (CCIs) and Rayleigh fading. First, the moment generating function (MGF) of the output SINR is derived. Then we obtain the probability density function (PDF) by taking the Fourier transform of the characteristic function (c.f.) corresponding to the MGF. Using the derived expression, the average output SINR performance of OC is evaluated as the number of the correlated multiple CCIs increases.

Distributed Relay Selection for MIMO-SDM Cooperative Networks

In this paper, we consider an amplify-and-forward cooperative wireless network in which network nodes use multiple input multiple output (MIMO) spatial division multiplexing (SDM) to communicate with one another. We examine the problem of distributed cooperative relay selection and signal combining at the destination. First, we propose three distributed relay selection algorithms based on the maximum channel gains, the maximum harmonic mean of the channel gains, and the minimum mean squared error (MSE) of the signal estimation. Second, we propose a minimum mean square error (MMSE) signal combining scheme which jointly serves as the optimal signal combiner and interference canceler. It is shown that the MSE selection together with the MMSE combining achieves the maximal diversity gain. We also show that in MIMO-SDM cooperative networks increasing the number of candidate nodes does not help to improve the BER performance as opposed to the cooperative networks where each node is equipped with only single antenna. A practical approach to implementation of the combiner based on the current wireless access network protocols will also be presented.

Optimal and Suboptimal Multi Antenna Spectrum Sensing Techniques with Master Node Cooperation for Cognitive Radio Systems

In this paper, we consider the primary user detection problem in cognitive radio systems by using multi antenna at the cognitive radio receiver. An optimal linear combiner multi antenna based spectrum sensing technique is proposed using the multitaper spectrum estimation method. A suboptimal square law combiner multi antenna based technique, using the multitaper method, is also proposed. The decision statistics’ probability density functions of the proposed techniques are derived theoretically. Probabilities of detection and false alarm formulae are presented using the Neyman Pearson criterion. Both proposed techniques are derived when energy detector is used. Based on our results, we found that the general likelihood ratio detector1 (GLRD1) and the blind GLRD that are proposed in the literature, require signal to noise ratios SNRs=7.5 and 9.6 dB, respectively to achieve a probability of detection of 99.99% at false alarm 1% with additive white Gaussian noise (AWGN) using 4 antennas and 16 samples for sensing. In our proposed optimal and suboptimal techniques, the required SNRs are found as 12 and 7.5 dB, respectively to achieve the same probabilities in the same conditions. Of course, this result gives an indication that even GLRD multi antenna based spectrum sensing techniques are blind in their philosophy, but that comes at the expense of their performance. Simulation results that confirm the theoretical work are also presented. An AWGN and Rayleigh flat fading environments are examined in the results. Finally, a new concept of cooperative spectrum sensing, the master node, is introduced.

Noise correlation in compact diversity receivers

The impact of antenna mutual coupling on signal correlation in multi-antenna receivers has been studied in great detail. By contrast, there has been little work on how mutual coupling affects noise. In this paper we present a noise model for a diversity receiver that includes noise generated by the antennas, front-end amplifiers, and other receiver components. This model shows that noise in a compact diversity receiver may be spatially correlated. Expressions relating noise correlation to properties of the antennas and amplifiers are derived and its impact on the outage probability of an optimal diversity combiner is studied. Examples illustrating the relationship between mutual coupling and noise correlation demonstrate how different noise sources may impact performance in profoundly different ways.

BAN-BAN Interference Rejection With Multiple Antennas at the Receiver

Rejection of interference from a nearby body area network (BAN) becomes significant in BAN applications, where a number of BANs are operating in the near vicinity of each other. Two interference rejection combining (IRC) techniques, optimum combining (OC) and Weiner-Hopf (WH) solution, are applied to the on-body wireless communication channels, and a more robust interference rejection technique, applicable to on-body channels, is proposed and compared to the conventional IRC algorithms. Three on-body channels are investigated by real time measurements of the desired and interference signals in an indoor environment with the antennas mounted on two human subjects walking around each other. The output signal to interference plus noise ratio improvement achieved with each algorithm is presented for the three channels and the dependence of the interference rejection gain on the average desired signal to interference ratio has been shown along with the covariance matrices for each channel. OC gives around 3-5 dB interference rejection gain for belt-wrist and belt-head channels. The WH solution gives the worst performance for all the channels. The proposed algorithm gives a flexible handle on the interference rejection gain and gives better rejection than the two conventional algorithms with proper interval selection.

BER optimal linear combiner for signal detection in symmetric alpha-stable noise: small values of alpha

The maximum likelihood optimal combiner for signal detection in alpha-stable noise is not known in general, except for some special values of the characteristic exponent ?. A linear Rake combiner receiver is simple and easy to realize. The optimal linear Rake receiver, in the sense of minimizing the bit error rate, for the detection of signals contaminated by symmetric alpha stable noise is derived for values of ?, 0 < ? ? 1. Interestingly, for this range of ?, the optimal combiner is found to be a selection combiner which selects the channel (finger) with the largest signal amplitude and suppresses all other channels (fingers). This interesting result is valid over the range 0 < ? ? 1 and allows one to implement effective signal detection without having to know the actual value of the parameter ?. Therefore, the result yields a very simple form of diversity combiner for signal detection in symmetric alpha-stable noise for 0 < ? ? 1. Comparisons with the widely used maximal ratio combining and equal gain combining schemes are made in terms of signal-to-noise ratio advantage defined in the bit error rate sense.

BER optimal linear combiner for signal detection in symmetric alpha-stable noise: small values of alpha

The maximum likelihood optimal combiner for signal detection in alpha-stable noise is not known in general, except for some special values of the characteristic exponent ¿. A linear Rake combiner receiver is simple and easy to realize. The optimal linear Rake receiver, in the sense of minimizing the bit error rate, for the detection of signals contaminated by symmetric alpha stable noise is derived for values of ¿, 0 < ¿ ¿ 1. Interestingly, for this range of ¿, the optimal combiner is found to be a selection combiner which selects the channel (finger) with the largest signal amplitude and suppresses all other channels (fingers). This interesting result is valid over the range 0 < ¿ ¿ 1 and allows one to implement effective signal detection without having to know the actual value of the parameter ¿. Therefore, the result yields a very simple form of diversity combiner for signal detection in symmetric alpha-stable noise for 0 < ¿ ¿ 1. Comparisons with the widely used maximal ratio combining and equal gain combining schemes are made in terms of signal-to-noise ratio advantage defined in the bit error rate sense.

Performance Analysis for RUB-Based Multiuser MIMO Systems With Antenna Diversity Techniques

Random unitary beamforming (RUB) is an attractive low-complexity transmission scheme for multiple-input-multiple-output (MIMO) broadcast channels. In this paper, we study the sum-rate performance of RUB-based multiuser MIMO systems with receive diversity. Two combining techniques, i.e., selection combining (SC) and optimum combining (OC), are employed to reduce feedback load and improve sum-rate performance. With these combining techniques, each user only needs to feed back one beam index and the corresponding output signal-to-interference-plus-noise ratio (SINR). For the SC scheme, we derive the statistics of the output SINR and the exact analytical expression of the sum rate. For the OC scheme, we develop an upper bound of the sum rate in the high-signal-to-noise-ratio (SNR) region. The bound is shown to be tight for the case of a moderate number of users, but the number of users must be at least five times the number of transmit antennas. Selected numerical examples show that the proposed design greatly enhances the sum-rate performance while maintaining low feedback load.

Turbo packet combining strategies for the MIMO-ISI ARQ channel

This paper addresses the issue of efficient turbo packet combining techniques for coded transmission with a Chase-type automatic repeat request (ARQ) protocol operating over a multiple-input--multiple-output (MIMO) channel with intersymbol interference (ISI). First of all, we investigate the outage probability and the outage-based power loss of the MIMO-ISI ARQ channel when optimal maximum a posteriori (MAP) turbo packet combining is used at the receiver. We show that the ARQ delay (i.e., the maximum number of ARQ rounds) does not completely translate into a diversity gain. We then introduce two efficient turbo packet combining algorithms that are inspired by minimum mean square error (MMSE)-based turbo equalization techniques. Both schemes can be viewed as low-complexity versions of the optimal MAP turbo combiner. The first scheme is called signal-level turbo combining and performs packet combining and multiple transmission ISI cancellation jointly at the signal-level. The second scheme, called symbol-level turbo combining, allows ARQ rounds to be separately turbo equalized, while combining is performed at the filter output. We conduct a complexity analysis where we demonstrate that both algorithms have almost the same computational cost as the conventional log-likelihood ratio (LLR)-level combiner. Simulation results show that both proposed techniques outperform LLR-level combining, while for some representative MIMO configurations, signal-level combining has better ISI cancellation capability and achievable diversity order than that of symbol-level combining.

Successive Interference Cancellation for the Uplink of MC-CDMA Systems with Multiple Receive Antennas

Successive interference cancellation(SIC) for the uplink of MC-CDMA mobile communications systems is an effective method to improve performance. We propose a successive interference cancellation(SIC) technique for the uplink of MC-CDMA mobile systems with multiple receive antennas. The destination uses optimum combining(OC) to combine the signals from an OFDM Demodulator with multiple receiving antennas, and applies SIC processing to the combined signals. Achieved interference cancellation order is depends on the signal to interference-plus-noise ratio (SINR) at the output of the optimum combiner. Monte-Carlo simulations are employed to verify the proposed technique.

하향 링크 셀룰러 시스템의 Eigen-Beamforming 전송을 위한 적응적 인접 셀 간섭 완화 방법

MIMO(Multiple-Input Multiple-Output) 시스템에서 EB(Eigen-Beamforming)는 MIMO 채 널의 특이 값 분해(Singular Value Decomposition: SVD)를 통하여 수신기의 유효 신호 대 잡음비(Signal-to-Interference Plus Noise Ratio: SI-NR)를 최대화하는 빔을 형성하는 방법으로써 널리 활용되고 있으나, 인접 셀 간섭 신호의 영향으로 셀 경계에 위치한 단말기의 신호 검출 성능은 급격히 열화되고 전송 효율은 감소하게 된다. 본 논문에서는 EB 전송을 활용하는 경우, 적응적 인접 셀 간섭 완화 방안을 제시하고 그 수신 성능을 평가한다. 특히, EB 전송을 이용하여 기지국예서 전송된 신호를 단말기가 수신할 때, 최대의 유효 신호 대 간섭 잡음비를 얻기 위한 OC(Optimum Combining) 및 MMSE-ISD(Minimum Mean-Squared Error for Intercell Spatial Demultiplexing)를 적응적으로 사용하기 위한 기준을 제시하고 유효 신호 대 간섭 잡음비 및 전송 용량 측면의 수신 성능을 분석한다. 제안하는 적응적 수신 방식은 수신 빔포밍 벡터만을 사용하는 기존의 EB 수신 방식 대비 평균 전송 용량 측면에서 향상된 성능을 보이며, 셀 경계 지역에 단말기가 위치할 경우 최대 2 bps/Hz 성능 개선을 가져온다. EB(Eigen-Beamforming) has widely been applied to MIMO(Multiple-Input Multiple-Output) systems to form beams which maximize the effective signal-to-interference plus noise ratio(SINR) of the receiver using the singular value decomposition(SVD) of the MIMO channel. However, the signal detection performance for the mobile station near the cell boundary is severely degraded and the transmission efficiency decreases due to the influence of the interference signal from the adjacent cells. In this paper, we propose an adaptive interference mitigation method for the EB transmission, and evaluate the reception performance. In particular, a reception strategy which adaptively utilizes optimal combining(OC) and minimum mean-squared error for Intercell spatial demultiplexing(MMSE-lSD) is proposed, and the reception performance is investigated in terms of the effective SINR and system capacity. For the average system capacity, the proposed adaptive reception demonstrates the performance enhancement compared to the conventional EB reception using the receiver beamforming vector, and up to 2 bps/Hz performance gain is achieved for mobile station located at the cell edge.

EM-Based Optimal Maximal Ratio Diversity Combiner for Constant Envelope Signals

An optimal maximal ratio combiner (MRC) based on the expectation-maximization (EM) algorithm is devel- oped for noisy constant envelope signals transmitted over a Rayleigh fading channel. Instead of using a transmitted pilot signal with the data to estimate the combiner gains, the EM algorithm is used to perform this estimation. In the developed MRC, estimation of the transmitted data sequence is performed also by the EM algorithm. Estimation using the EM algo- rithm provides an iterative solution to the maximum likelihood (ML) approach. Therefore, the resulting receiver is opti- mum and does not suffer from the difficulties resulted from direct application of the ML procedure. One of these difficul- ties is the computational complexity which depends exponentially on the data sequence length. Introducing an iterative structure in the developed MRC achieves a linear computational complexity and enables efficient data extraction by the Viterbi algorithm when trellis coding is used.

Analytical Framework for Optimal Combining With Arbitrary-Power Interferers and Thermal Noise

The performance of multiple-input-multiple-output systems with optimum combining (OC) is studied in a Rayleigh fading environment with arbitrary-power cochannel interference and thermal noise. Based on the joint eigenvalue distributions of quadratic functions of complex Gaussian matrices, a closed-form expression for the exact distribution of the output signal-to-interference-plus-noise ratio (SINR) is derived. A closed-form expression for the exact moment-generating function (MGF) of the output SINR of single-input-multiple-output (SIMO) systems is also derived. From the exact MGF, the moments of the output SINR and the symbol error rate of various M-ary modulation schemes are obtained. We verify the accuracy of our analytical results with numerical examples. The new analytical framework provides a simple and accurate way to assess the effects of equal- and unequal-power cochannel interferers and thermal noise on the performance of OC.

An Affine Combination of Two LMS Adaptive Filters—Transient Mean-Square Analysis

This paper studies the statistical behavior of an affine combination of the outputs of two least mean-square (LMS) adaptive filters that simultaneously adapt using the same white Gaussian inputs. The purpose of the combination is to obtain an LMS adaptive filter with fast convergence and small steady-state mean-square deviation (MSD). The linear combination studied is a generalization of the convex combination, in which the combination factor lambda(n) is restricted to the interval (0,1). The viewpoint is taken that each of the two filters produces dependent estimates of the unknown channel. Thus, there exists a sequence of optimal affine combining coefficients which minimizes the mean-square error (MSE). First, the optimal unrealizable affine combiner is studied and provides the best possible performance for this class. Then two new schemes are proposed for practical applications. The mean-square performances are analyzed and validated by Monte Carlo simulations. With proper design, the two practical schemes yield an overall MSD that is usually less than the MSDs of either filter.

Receive Antenna Array Strategies in Fading and Interference: An Outage Probability Comparison

We explore tradeoffs between different reception strategies of multiple receive antennas in fading channels with co-channel interference (CCI). Our tradeoff analysis is based on outage probability. We assume the signal from the desired user at the receive antenna array to be affected by Rice, Nakagami or Rayleigh fading, while CCI signals are assumed to experience Rayleigh fading. We provide closed-form analytical expressions for the outage probability of different diversity schemes, such as maximal ratio combining (MRC) and optimum combining (OC), and also for interference cancellation (IC) based on antenna beamsteering, which steers nulls in the array radiation pattern in the direction of the strongest interferers. Our analysis provides a unified framework for studying outage probability of different multiple-antenna reception strategies, and our closed- form expressions are easily computed, facilitating a performance comparison under a range of operating conditions. Our numerical results show that IC yields significantly better performance than MRC if the system is interference-limited and the number of dominant interferers is lower than the number of receive antennas, or when the output SINR is low. In addition, when the background noise can be neglected, we provide numerical results for MRC and OC when the signals from the desired user at the different receive antennas are arbitrarily distributed.

Exact Performance Analysis of Optimum Combining With Multiple Interferers in Flat Rayleigh Fading

This letter provides a comprehensive overview and extension of recent results on outage probabilities and bit-error rates (BER) for optimal combiners in the presence of multiple interferers and additive noise. Desired signal and interferers are subject to flat Rayleigh fading and all channels are independent. In addition to summarizing previous work, this letter also derives the BER for a wider range of modulations than previously considered. We show that previous approximate results on the equal power interferer case where the number of interferers is less than the number of antenna elements can be made exact in a straightforward way. Finally we extend previous work on the single and double interferer case to the general case of arbitrary numbers of interferers.

Effects of Spatial Correlation on MIMO Adaptive Antenna System With Optimum Combining

In this paper, we investigate the effects of the spatial fading correlation on the performance of a multiple-input multiple-output (MIMO) adaptive antenna system with optimum combining (OC) in the presence of multiple cochannel interferers over a correlated Rayleigh fading channel. Based on the Khatri's distribution functions of quadratic forms in complex Gaussian random matrices, we develop a unified determinant representation of those joint eigenvalue distributions. Taking into account the spatial correlation among the antenna elements at the transmitter or receiver, we derive the closed-form formulas for the probability density function and outage probability of the maximum output signal-to-interference ratio (SIR) in an interference-limited MIMO-OC system. Furthermore, the average output SIR and error probability are also investigated. From numerical examples, we show that a new theoretical approach gives a simple and accurate way to assess the performance of the MIMO-OC system over arbitrarily correlated fading channels