An improved Gaussian approximation was presented in [3,4], and it was shown that this approximation provides an accurate result for the probability of bit error in asynchronous DS/CDMA, using a random sequence in an AWGN channel. In this section, we extend the work in [3] and evaluate the probability of bit error for asynchronous DS/CDMA in **multipath** **Rayleigh** **fading** channel, using the improved Gaussian approximation. Following the approach in [3], let T c = 1 (T b = N), b 1 0 = 1, and P = 2. Then

The last three to four decades has witnessed giant strides in the development of digital communication systems, motivated by the information revolution and convergence of computer communication, mobile communication and internet. The tremendous acceleration towards the convergence of communication and internet is bringing the advancement of digital communication to its extreme capacity. A performance comparison of **Rayleigh** **fading** channels in M-PAM and Rectangular QAM schemes is provided and the scheme which produces the lowest Bit Error Rate (BER) is computed in this paper. The most efficient modulation technique is evaluated in terms of the production of the lowest Bit Error Rate and such a type of scheme can be implemented to obtain a versatile digital communication system.

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Three wavelet packets from three different families are used for this simulation namely Daubechies wavelet packets with order 6, db6, Symmlets wavelet packets with order 6 (sym6), and Coiflets wavelet packets with order 2, (coif2). These families are chosen because they are orthogonal and have compact support (i.e., fast de- caying time, which results in good localization in both time and frequency). The filter length is taken to be L = 12. Figure 11 shows BER versus SNR for these three wavelet families for CWPM system for N = 128 over selective **Rayleigh** **fading** channel with Doppler spread factor f d T s = 0.015. From this figure, it’s shown that

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catenation and discovered that independent diversity scheme performs better in a **multipath** **Rayleigh** **fading** channel than channel coding but in the case a Rician channel, channel-coding technique outperforms diversity mitigation technique. The concatenation of spatial diversity and channel coding combines the diversity gain of orthogonal space-time block codes (OSTBC) and the coding gain of trellis-coded modulation (TCM) for performance improvement as seen from the results of the simulation. One advantage of this con- catenation over OFDM is the use of M-PSKTCM, which combines coding, and modulation to provide a large gain and make efficient use of bandwidth. The proposed concatenation produced a gain of 5dB over OFDM-BPSK, which takes an SNR, of 22dB to obtain a bit error rate of 10-4 that was attained with a lesser value of 17dB with this concatenation. Similarly, the concatenated space-time block coding requires more than 18dB to give a FER of 10 -2 , which takes a minimum of 17.6dB to achieve here. The spatial diversity gain offered by OSTBC and the coding gain offered by TCM makes the combination an excellent **fading** mitigation scheme refer to results of this study.

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I N MANY communication scenarios, a receiver has to per- form both frequency and timing synchronization in a large frequency and timing uncertainty. The synchronization problem becomes especially difficult if the propagation channel is multi- path and **fading**. In mobile channels, **multipath** components ex- perience different Doppler offsets; however, if the mobile speed and the carrier frequency are relatively low, the frequency offset is mainly due to the difference between carriers of the receiver and transmitter, and the assumption of equal frequency offsets for all **multipath** components can be accepted. Under such an assumption one approach to solve the synchronization problem is to estimate and compensate for the frequency offset, and then perform the timing synchronization (or equalization). This work is devoted to the first stage: frequency estimation in **multipath** **Rayleigh**-**fading** channels with an unknown sparse impulse re- sponse. Specifically, we consider a maximum likelihood (ML) data-aided frequency estimation [1].

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Fig. 7 shows, the BER performance of LOWPM system which takes QAM4 mapping in **multipath** **Rayleigh** **fading** channel is good and is slightly worse only than that in Gauss white noise channel, which shows the ability to anti-**multipath** **fading** of LOWPM system. But when there is Doppler frequency shift existing in **multipath** **Rayleigh** **fading** channel, the performance of system deteriorates and bit error rate has been in a high state. In mobile communication, the mobile station are mostly in the moving state so that Doppler frequency shift is inevitable. Therefore, the

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There exists a large number of distribution schemes to describe the statistics of mobile radio signal. A key as- sumption in the theoretical explanation of the **Rayleigh**, Rician, Nakagami and Weibull distribution was that the statistics of the channel do not change over the small (local) area under consideration. However, to describe the long-term signal variations lognormal distribution is being used [1]. These distributions are helpful in precise designing of wireless systems to make the systems more robust to noise.

To investigates the ideal position and number of the pilot symbol, we examine ideal preparing arrangements in OFDM frameworks and we break down the number of pilot symbols required to satisfy the sampling theorem. Symmetrical Frequency Division Multiplexing (OFDM) has turned into a well-known regulation technique in rapid remote correspondences. By parceling a wideband **fading** channel into level narrowband channels, OFDM can relieve the hindering impacts of **multipath** **fading** utilizing a basic one-tap equalizer [12,13]. There is a developing need to rapidly transmit data remotely and precisely. OFDM is a reasonable possibility for high information rate transmission with forward error correction (FEC) techniques over remote channels. In this task the framework throughput of a working OFDM framework has been improved by including turbo coding. The utilization of turbo coding and power distribution in OFDM is valuable to the ideal execution at higher information rates Reenactment is to be done over added substance white Gaussian clamor (AWGN) and imprudent commotion (which is delivered in broadband transmission) channels. In this paper Bit Error Rate execution of OFDM, QPSK, and 16-QAM System over **Rayleigh** blurring channel is investigated. OFDM is a symmetrical recurrence division multiplexing to diminish the between image obstruction issue. The evening out calculation is a Normalized LMMSE equalizer. At long last, reenactments of OFDM sign are conveyed with **Rayleigh** blurred sign to comprehend the impact of channel blurring and to get the ideal estimation of Bit Error Rate (BER) and Signal to commotion proportion (SNR) [14,15].

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In low signal-to-noise ratio (SNR) the secondary user cannot sense primary user due to an obstacle or fade effect, therefore hidden primary user problem must be alleviated. In [7], to reduce the **multipath** and shadowing effects of the wireless channels, diversity reception (i.e. multiple antennas) techniques provide promising solutions as to improve BER performances. In [8] diversity reception has long been familiar as a great communication receiver technique for alleviating the harmful effects of channel **fading** and co- channel interference. Diversity means the providing of two or more independent **fading** paths from transmitter to receiver. These independent signals are combined in a special way to increase the overall SNR. Diverse methods can be categorized in accordance with the type of combining used at the receiver, namely, equal gain combining (EGC), maximal-ratio combining (MRC) and selection diversity combining (SDC). In this paper we derive the average probability of detection over **Rayleigh** **fading** channels in simplest form. A new technique of signal detecting is proposed. The proposed scheme has minimum hardware used.

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We undertake high SNR analysis by finding the diversity-multiplexing gain trade-off of three further wireless systems with **fading**. This is a recent method for measuring the relationship between rate and reliability. Using techniques from existing works we find the optimal diversity-multiplexing gain trade-off for an (M × N ) multiple antenna system with R single antenna relays. This uses a two-stage protocol in which the source first transmits to relays, then the relays multiply their received signal by a unitary matrix, before forwarding the result to the multiple-antenna receiver. The optimal trade-off is found to be equal to that of a multiple-input multiple-output (MIMO) link with R transmit and min { M, N } receive antennas.

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The beamformer uses an M-element uniform linear array (ULA) antenna m 3 , 4 , 5 , 8 to gather signals from the mobile stations. After receiving the signal at the antenna elements, a beamforming algorithm is applied which enhances the desired signal with respect to interfering signals. The channel estimator is used to generate per symbol period, delays and phases that correspond to four most significant transmission paths in the **multipath** channel from the mobile station to the base station. The Rake combiner takes in the delays and weights estimated by the channel estimator and use the maximal ratio combining method to generate the receiver outputs.

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• The effect of scheduling and multiuser diversity reduces with the channels correlation, although the rate reduction is ignorable in low correlation conditions (Figures 1 and 2). There is an interesting intuition behind this point; In a system with a number of users experiencing independent **fading** conditions it is more likely that, at any time instant, one of the users experi- ences good channel quality. Therefore, the data trans- mission efficiency can be improved by always communicating the best users (multiuser diversity). However, if the channels are not independent, the probability that one of the users has good channel qual- ity while the others experience bad channels, and cor- respondingly the effect of multiuser diversity, decreases. Therefore, it is expected that for users close to each other, for instance the users in a single cell, e.g., [25-28]], the practical gain due to multiuser diversity would be less than the one theoretically obtained under independent channels assumptions. Note that the con- clusion is valid for any number of users. Also, it is interesting to mention that, although channels correla- tion reduces the forward channel data transmission

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Spectrum sensing is one of the main research issues under wireless communication for dynamic spectrum sharing .there are many spectrum sensing algorithm proposed in literature each of them has its own advantages and disadvantages. Among the algorithms emery detector based spectrum sensing is less complex and adapted in wireless standard. The issues in the energy detector is the poor performance in **fading** environment and correct threshold selection for the given environment. Here in this paper a location based threshold selection in the **Rayleigh** **fading** environment is used for the analysis and the probability of detection, probability of false alarms are calculated for the performance evolution. Here a cooperative spectrum sensing is carried out by taking various like indoor environment and relay network of the case amplify and forward .the energy of received signal is usually function of distant from the transmitter, so under location based threshold selection more threshold value is used if the sensing node is near to primary transmitter or less value is used if it is far away from the transmitter .under this work it is assumed that all the node in the network is assumed that they are all known the location of them and the primary user

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Abstract - There are various kinds of channel used in wireless communication. This Paper shows a performance analysis on the basis of different **fading** channels. This is the comparative analysis with different kinds of modulation techniques. communication. The effects of noise on **fading** and property of the channel were tested. Here we have also measured the Bit Error Rate with respect to different modulation techniques and compare the rate in different channels. The results show that the BER performance is improved dramatically in low SNR than in high SNR. This is reasonable since at low SNR, white Gaussian noise dominate the BER which can be improved by enhancing SNR while in high SNR, phase estimation error dominate the BER error which cannot be improved by simply enhancing SNR. Next we have tested, analyzed and compared the performance of the channels. The more accurate model is **Rayleigh** model which can be considered for developing **multipath** **fading** channel model.

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Abstract. In this paper, we first analyze the performance of GMSK against partial-band interference in short-wave and slow-frequency hopping. Numerical simulation results show that when the value is different, the BER of the BER varies with the SIR. When is small, the BER of SFH/GMSK is smaller than that of SFH/MFSK under the same conditions. When is large, the BER of SFH/GMSK is smaller than that of SFH/BFSK, but larger than the BER of SFH/4FSK. Then we analyze the anti-**multipath** interference performance of GMSK in short-wave slow frequency hopping, and choose **Rayleigh** **fading** channel and Rice **fading** channel for simulation. The flat **fading** and frequency selective **fading** are used in **Rayleigh** **fading** channel respectively. The simulation results show that in **Rayleigh** multi-path **fading** channel, SFH/GMSK anti-**multipath** **fading** performance is better than SFH/MFSK; in Rician channel, the larger the K value is, the smaller the error rate is. Finally, three kinds of diversity combining methods are added to a frequency-selective **fading** SFH/GMSK short-wave channel system. The simulation results show that compared with the bit error rate of **multipath** channels, by combining multipaths the system performance of bit error rate can get 2dB improvement.

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In this perspective, this paper studies the capacity of **Rayleigh**-**fading** correlated spectrum sharing networks. Assuming perfect CSI available at the secondary user transmitter and receiver, the channel performance is investigated under different primary user outage prob- ability and instantaneous or average received interfer- ence power constraints. The channel capacity is obtained under both adaptive and nonadaptive second- ary user power allocation conditions. The results show that there is considerable potential for data transmission of unlicensed users with limited degradation of the licensed users data transmission efficiency. Also, while the effect of **fading** channels dependencies is ignorable at low correlation values, the channel capacity is signifi- cantly affected as the channels correlation increases. 2 Channel model

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Many works (in the Summary of Related works table) have studied the performance of HetNet with **Rayleigh** **fading**, as it is easier to analyze the **fading** distribution. Realistically, mounting macro BS on high elevation for wide coverage, LOS and NLOS signals can be exploited, thus Ricean channel is realized. While the small cell BSs have small coverage, hence generate strong scattering signals outside the coverage range. Then from the ideas in [1,21], this work develops a HetNet model and analytically characterizes the SIR with Ricean and **Rayleigh** **fading** distributions. That is, we evaluate the SIR with the convolution of the desired signal (from macro BS) with Ricean distribution and interfering signals (from femto BSs) with **Rayleigh** distribution. And, massive MIMO is considered for modeling the **fading** channels, this is a novel contribution in this work. We study the SIR distribution by analyzing the geometry users, Ricean **fading** distribution and transmit power allocation. Further, we propose transmit power control technique for the downlink beamforming coordination.

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In mobile communication systems, multiuser detection is also known under the names of cochannel interference sup- pression, multiuser demodulation, or interference cancella- tion, and requires rather complicated high-precision power control. The design of multiuser detectors has been mo- tivated by the channel environment encountered in many CDMA applications, for channels with **fading**, **multipath**, or noncoherent modulation have been considered [1, 2]. In par- ticular, recent focus has been on the blind (or non-data- aided) multiuser detectors such as SIC [3], PIC [4], and DFD [5], these require no training data sequence, but only knowledge of the desired user signature sequence and its tim- ing [6]. The main motivation of employing a blind mul- tiuser detector in CDMA is to recover the original sequence from the received signal that is corrupted by noise and MAI, without the help of training sequences and a priori knowl- edge of the channel. Prior work by Ristaniemi and Jout- sensalo [7] leads to the proposal of two types of receivers, RAKE-ICA and MMSE-ICA, in a **Rayleigh** **fading** channel using the modified FastICA algorithm [8]. However, the es- timation of eigenvectors and eigenvalues becomes an addi- tional burden for the proposed RAKE-ICA. Also, the MMSE- ICA which required training sequences causes an increase in

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This paper compares and analyzes the performance of the most accepted **Rayleigh** **fading** channel simulators, and it is a continuation of our previous work [11] with substantial novel contributions. Some important outcomes of [11] are reported here, to be further studied and discussed. We will use three quantitative measures to investigate the accuracy of different **Rayleigh** **fading** generators in terms of both first- and second-order statistics. In [11], the quality of the second-order time-averaged autocorrelation function (ACF) is investigated using the power margin quality measures [12]. For the non-ergodic stochastic simulation models, this statistic varies from one simulation trial to another and a look into the convergence of these models is highly recommended which is missing in [11]. The convergence of two of the most successful stochastic SOS-based models is checked here using the variance of time-averaged ACF. In addition, the first-order statistic probability density function (PDF) of the envelope is assessed with a more convenient measure than used in previous studies [11], [13]. Moreover, the complexity of the different models is tested based on the time of execution. Compared to [11], the method with which the time of execution was computed has been refined for more accurate results.

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Since the MIMO fulfilled the present day technology needs, it has become very popular these days. Communication in wireless channels always comes in pair with the **multipath** **fading**. **Multipath** is the arrival of the multiple copies of the transmitted signal at the receiver through different angles and/or differing time delays and/or differing frequencies. MIMO offers significant increase in the data through put and link range without additional bandwidth or transmit power. Space diversity techniques have become very popular since last decade. This space diversity has provided increased efficiency of the communication systems by decoupling users through channel aware signal processing techniques. The adaptive equalization techniques have further helped to compensate the time dispersion in the channel. Much research has been done on the various processing techniques. Due to the simplicity the linear equalization techniques have attracted a lot of the researchers for communication signal processing. Two key equalization techniques include: MMSE (Minimum mean square error) and ZF (Zero forcing) techniques [2]. Though they are not optimum in performance they satisfy other criterions such as reduced mean square error (MMSE) and also interference eliminated (ZF). So far, a rich literature is available over the performance of ZF and MMSE for micro diversity systems, where there is a communication between co-located diversity antenna at the base station and the distributed users [3],[4],[7]. But not much research has been done on macro diversity systems where both transmit and receive antennas are widely separated. They occur naturally in network MIMO systems [9], [10] and collaborative MIMO systems [11, p.69] and [12].

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