Performance analysis of Spectrum Sensing based on Distributed Satellite Clusters

The effect of imperfect timing is analyzed in equal gain combining (EGC) and maximal ratio combining (MRC) techniques over Rayleigh and Nakagami-m fading channels with binary phase-shift keying modulation. In the case of EGC, the bit-error probability is derived, while in the case of MRC, error rate bounds are presented. Theoretical results are justified by computer simulation. Numerical results demonstrate that both EGC and MRC are fairly sensitive to timing errors, and comparatively, MRC is more sensitive.

This paper presents an analysis of maximum ratio combining (MRC) receiver of quaternary phase-shift keying (QPSK) signals transmitted over a Weibull fading channel. We determine the influence of imperfect cophasing and branches unbalance on bit error rate dependence on average signal-to-noise ratio. The performance dependence on diversity order and fading severity is also observed. Keywords — Cophasing, Diversity systems, Error probability, Fading. I. INTRODUCTION N order to reduce the influence of multipath fading on signal detection, it is possible to use spatially separated receiver antennas at the reception and to combine the signals from different branches of the receiver in a certain manner. The optimal combining technique is maximum ratio combining (MRC). This combining technique involves cophasing of the useful signal in all branches, multiplication of the received signal in each branch by the estimated envelope of that particular signal and summing of the received signals from all antennas (1). By cophasing, all the random phase fluctuations of the signal that emerged during the transmission are eliminated. For this process it is necessary to estimate the phase of the received signal. This phase estimation can be performed from the modulated or unmodulated received signal carrier. In previous papers concerning this matter the assumptions of the ideal phase estimation of the incoming signal were mainly used (2), (3). Only in (4) and (5) the influence of the imperfect phase estimation was examined and that was in the case of the equal gain combining (EGC) in the receiver. In paper (4), the influence of the phase error on the error probability in the case of digital binary (BPSK) and quaternary phase-shift keying (QPSK) signal detection was observed. This error probability was calculated applying the Gram-Charlier expansion. The analysis is performed under the assumption of the uncorrelated Rayleigh fading at receiving antennas. In paper (5) closed-form expressions for outage probability and error probability during the BPSK and QPSK signal detection over the Nakagami-m fading channel were obtained. Dual branch EGC technique was applied. In both papers the analysis of the system was done under the assumption that the branches of the receiver are balanced. However, as it is well-known (6), it is very rare to meet in practice the identical propagation paths in each branch. Also, the electrical components in different branches of the receiver are not ideal. Thus, it is also of interest to consider the influence of the branch unbalance in the receiver on system performances. In this paper an analysis of QPSK signal reception is presented. The signal is transmitted over the Weibull fading channel and MRC technique is applied in the receiver, while the receiving branches are assumed unbalanced. The phase estimation is performed from the unmodulated carrier and is not ideal. The difference between the phase of the incoming signal and the estimated phase for that signal is a statistical process and it follows the Tikhonov distribution (4), (5), (7). It is shown in which measure the imperfect phase estimation affects the bit-error rate (BER).

ABSTRACTIn this paper, the performance analysis of wireless communication system over shadowed-Rice (SR) composite fading channel has been investigated and analysed. The unified analytical expressions of the average symbol error probability (ASEP) for several coherent and non-coherent modulation schemes separately with different constellation sizes are derived for composite fading channel under two different fade mitigation methods, with maximal ratio combining (MRC) microdiversity (Method 1) and MRC applied over the composite fading channel (Method 2). Furthermore, an asymptotic analysis is carried out and a closed-form expression of the ASEP with Method 2 is presented. Analytical expressions of the corresponding average probability of energy detection (PD) are formulated for both the methods. Finally, the derived PD expression is utilised to analyse the performance of cooperative system assuming erroneous feedback channel. Analysis of optimisation of detection threshold as well as number of cognitive users to minimise the total error rate is also carried out. The closed-form expressions are validated by comparing them with exact numerical results and Monte Carlo simulation.

The bit error rate (BER) performance for quadrature amplitude modulation (QAM) with different diversity combining scheme is derived for Rayleigh fading channel using Log-likelihood ratio (LLR). Three combining techniques, maximal ratio combiner (MMC), selection combining (SC), and Equal Gain Combiner (EGC) are considered for the BER analysis in this paper. The average BER performance of QAM symbol through a flat fading channel is derived from the individual bits forming the QAM symbol with MRC, SC, and EGC space diversity. The analytical and simulation of BER performance of the QAM symbol through the fading channel with MMC, SC, and EGC combiner is compared. The both analytical and simulation result shows that the probability of bit error decreases with the order of diversity for all the cases of MRC, SC, and EGC. It is also seen from the results that MRC provides better BER performance than the other two combiners (SC and EGC) for the same environment of the fading channel.

We propose a novel optical wireless (OW) system based on a power adaptive multibeam spot-diffusing transmitter serving multiple seven-segment maximum ratio combining (MRC) angle diversity receivers. A feedback link is assumed between the transceivers so that each receiver conveys to the multibeam transmitter the new beams transmit power weights to be used to achieve the best signal quality at a given receiver location. Two cases involving three and five receivers are considered. Four different configurations for the placement of the three-receiver case in the room are also examined. The system's performance in each case is evaluated in terms of signal-to-noise ratio (SNR) and is compared with the single receiver scenario with and without power adaptation. In the presence of one receiver, the transmit spot powers can be adjusted for optimum performance at that receiver location. For multiple receivers, there is conflict, and we propose spot power adaptation based on the average requirements (power distribution in spots), i.e., transmit equal gain combining (EGC) of spot power or MRC of transmit spot powers. The results show that the three receivers benefit most from an adaptive transmitter when each is placed at a corner of the room. In this case, an SNR increase of as much as 2.6 dB is achieved for all three receivers at the corners by both MRC and EGC. Moreover, when all receivers are placed away from the line of diffusing spots, our proposed MRC collaborative approach is 1 dB better than the noncollaborative system. This gain reduces the difference from the upper bound set by the single receiver adaptation, which is 3 dB. For a mobile transmitter, MRC also significantly improved the SNR for the farthest receivers at the opposite end from the transmitter located near one room corner.

The accurate performance evaluation of differential amplitude and phase-shift keying (DAPSK) with postdetection equal gain combining (EGC) over generalized fading channels is of great theoretical interest and practical importance. In this paper, by using a decision variable-based moment generating function approach, exact error probability results for DAPSK over generalized Rician and Nakagami fading channels are derived, taking into account the effects of all the system and fading channel parameters. Several maximum likelihood (ML)-based detectors that do not require channel state information (CSI) are proposed for generalized Rician fading channels, and an exact bit error probability (BEP) union bound for the ML detection is derived. Assuming CSI, a performance upper bound for DAPSK with EGC is also presented. Simulation and numerical results show when both detectors have no CSI, the conventional DAPSK detector may perform closely to (though worse than) the ML detector. However, the EGC receiver with CSI performs substantially better than the ML detector without CSI, and very closely to the coherent APSK detector.

Several diversity combining techniques are employed in a direct-sequence code-division multiple access (DS/CDMA) cellular system. The diversity receptions are combined using maximal ratio combining (MRC), equal gain combining (EGG), second-order selection combining (SC2) and a simplified version of MRC (SVM) that is simply a compromise between MRC and EGG. When the path loss exponent r=4, our results indicate that only MRC can significantly improve the system performance with a capacity gain of about 160% as compared to conventional detection with perfect power control. The other techniques investigated cannot improve the cellular CD/CDMA performance. However, when r is reduced to 2, all combining methods studied can enhance the cellular capacity dramatically. These diversity techniques are found to be effective in combating the problem associated with imperfect power control in cellular DS/CDMA.

In this paper, we consider Single Input Multiple Output (SIMO) systems with Maximum Ratio Combining(MRC) and Equal Gain Combining (EGC). We assume spatially independent and timely correlated Rayleigh flat fading channels, modeled by AR2 processes. We consider a frame of N+2 symbols, where Channel State Information at Receiver (CSIR) is available in the beginning for two consecutive symbols, also called as partial CSIR. Using this CSIR, we predict CSIR for the remaining N symbols and detect them. For this partially coherent systems, we have derived closed-form expressions of BER for BPSK constellation. We have also presented simulation results and verified our analytical expressions. We have shown the effects of frame size N, time varying condition of channel by doppler frequency ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> on BER. We have compared performance of the SIMO systems with SISO system and shown significant improvement in BER over SISO systems.

A Monte Carlo simulation was conducted to assess the performance of Multi-Carrier Code Division Multiple Access (MC-CDMA) in a sectored cell, in an indoor environment. In each sector, terminal schedule packet transmission using slotted p-persistent Inhibit Sense Multiple Access, while the packets themselves are transmitted using MC-CDMA. The simulated bit error rate performance of MC-CDMA with combining strategies maximal ratio combining (MRC) and equal gain combining (EGC) used in the frequency domain are presented. A comparison is made between analytically determined bit error probability for a single user in an additive white Gaussian noise channel using binary phase shift keying (BPSK), and simulated bit error rate for a single user using MC-CDMA with MRC and EGC. The determination of the number of sectors in a cell is also given. MC-CDMA with diversity combining outperforms BPSK in a non-fading AWGN channel. Further, as the user-number increases, EGC performs better than MRC if these combining strategies are used with MC-CDMA. Finally, the results show the basis for determining the number of sectors in a cell. When using slotted p-persistent ISMA, it is envisaged that only a single user will transmit at a time in a sector.

Multi-carrier code division multiple access (MC-CDMA) scheme with base station antenna arrays has the potential of being an appropriate candidate for the next generation mobile and wireless personal communication systems due to its high system capacity. In this paper, the reverse link performance of a MC-CDMA system along with base station antenna arrays employing three combining schemes: equal gain combining (EGC), maximal ratio combining (MRC) and minimum mean square error combining (MMSEC) in Rayleigh fading channel environments is analyzed and compared. Simulation results and analysis results are also presented and compared. It is shown that MRC can improve system performance significantly over EGC in the given channel while MMSEC just gives a little performance improvement over MRC.

In space diversity combining, conventional methods such as maximal ratio combining (MRC), equal gain combining (EGC) and selection combining (SC) are commonly used to improve the output signal-to-noise ratio (SNR) provided that the channel is perfectly estimated at the receiver. However, in practice, channel estimation is often imperfect and this indeed deteriorates the system performance. In this paper, diversity combining techniques based on two evolutionary algorithms, namely genetic algorithm (GA) and particle swarm optimization (PSO) are proposed and compared. Numerical results indicate that the proposed methods outperform the conventional MRC, EGC and SC methods when the channel estimation is imperfect while it shows similar performance as that of MRC when the channel is perfectly estimated.

In this paper we propose an M-ary biorthogonal pulse shape modulation (BPSM) scheme for an impulse radio ultra wideband (IR-UWB) system transmitting over lognormal fading channels. Our proposed modulation scheme enables different transmission rates for a fixed number of orthogonal pulses M/2, while the symbol period T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> is constant. In our scheme information bits are mapped into N pulses (N symbols), using M/2 orthogonal pulses and their negates. The N generated pulses are superimposed to form one pulse that will be transmitted over the channel. The transmission rate provided by this scheme is N(log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> M/N)/T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> , which is significantly higher than (log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> M/N)/T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> provided by the conventional biorthogonal signaling. The RAKE receiver demodulates the N symbols. For the proposed modulation scheme we derive closed form expressions for symbol error probability, for both maximum ratio combining (MRC) and equal gain combining (EGC)-RAKE receivers, using Wilkinson's method. Furthermore, we numerically evaluate performances of the proposed transceiver, assuming perfect and imperfect channel estimation at the receiver, and compare them with our analytical expressions.

This chapter is attempted to provide a survey of the advanced concepts and related issues involved in Multiple Input Multiple Output (MIMO) systems. MIMO system technology has been considered as a really significant foundation on which to build the next and future generations of wireless networks. The chapter addresses advanced MIMO techniques such as polarization diversity and antenna selection. We gradually provide an overview of the MIMO features from basic to more advanced topics. The first sections of this chapter start by introducing the key aspects of theMIMO theory. TheMIMO systemmodel is first presented in a genericway. Then, we proceed to describe diversity schemes used in MIMO systems. MIMO technology could exploit several diversity techniques beyond the spatial diversity. These techniques essentially cover frequency diversity, time diversity and polarization diversity. We further provide the reader with a geometrically based models for MIMO systems. The virtue of this channel modeling is to adopt realisticmethods for modeling the spatio-temporal channel statistics from a physical wave-propagation viewpoint. Two classes for MIMO channel modeling will be described. These models involve the Geometry-based Stochastic ChannelModels (GSCM) and the Stochastic channel models. Besides the listedMIMO channel models already described, we derive and discuss capacity formulas for transmission over MIMO systems. The achieved MIMO capacities highlight the potential of spatial diversity for improving the spectral efficiency of MIMO channels. When Channel State Information (CSI) is available at both ends of the transmission link, the MIMO system capacity is optimally derived by using adaptive power allocation based on water-filling technique. The chapter continues by examining the combining techniques for multiple antenna systems. Combining techniques are motivated for MIMO systems since they enable the signal to noise ratio (SNR) maximization at the combiner output. The fundamental combing techniques are the Maximal Ratio Combining (MRC), the Selection Combining (SC) and the Equal Gain Combining(EGC). Once the combining techniques are analyzed, the reader is introduced to the beamforming processing as an optimal strategy for combining. The use of multiple antennas significantly improves the channel spectral efficiency. Nevertheless, this induces higher system complexity of the communication system and the communication system performance is effected due to correlation between antennas that need to be deployed at the same terminal. As such, the antenna selection algorithm for MIMO systems is presented. To elaborate on this point, we introduce Space time coding techniques for MIMO systems and we evaluate by simulation the performance of the communication system. Next, we emphasis on multi polarization techniques for MIMO systems. As a background, we presume that the reader has a thorough understanding of antenna theory. We recall the basic antenna theory and concepts that are used throughout the rest of the chapter. We rigorously introduce the 3D channel model over the Non-Line of Sight (NLOS) propagation channel for MIMO system with polarized antennas. We treat the depolarization phenomena and we study its effect on MIMO system capacity. The last section of the chapter provides a scenario for collaborative sensor nodes performing distributed MIMO system model which is devoted to sensor node localization in Wireless Sensor Networks. The localization algorithm is based on beamforming processing and was tested by simulation. Our chapter provides the reader by simulation examples for almost all the topics that have been treated for MIMO system development and key issues affecting achieved performance.

On the performance of digital systems in α-[formula omitted] fading and non-Gaussian noise channels

A new postdetection maximal ratio combining (MRC) and weighted maximal ratio combining (WMRC) diversity receivers for (N, M) differential amplitude phase shift keying (DAPSK) signal are proposed. In the MRC receiver, decision at each branch is made by the minimum distance criterion. The performance of the MRC receiver is analyzed in terms of the union bound for the bit error probability. The WMRC receiver assigns weighting factors to the decision variable at each diversity branch according to the relative distance from the optimum decision boundary. From the results, performance of the WMRC is found to be better than that of the MRC and equal gain combining (EGC) receiver on both the Rayleigh and Rician fading channel. It is also found that the performance improvement of the WMRC over the MRC increases as the number of the diversity branches increases.