Using Log likelihood relation for BER analysis of QAM in space diversity

Bit-error rate investigation of satellite-to-ground downlink optical communication employing spatial diversity and modulation techniques

An enhanced transmission is presented in a multiple‐input‐multiple‐output (MIMO) dense‐wavelength division multiplexed (DWDM) free‐space‐optical (FSO) communication link using diversity coding techniques under the effect of turbulent weather phenomenon. The findings show good performance with an (8 channels × 2.5 Gbps data rate/channel) 20 Gbps 1500 m transmission distance. The bit‐error‐rate (BER), outage probability (OP), and signal‐to‐noise ratio (SNR) of the diversity combining techniques using maximum‐ratio combining (MRC), selection combining (SC), and equal‐gain combining (EGC) technique are evaluated in this work. The obtained results illustrate that Alamouti, space‐time coding (STC), space‐time block coding (STBC), space‐time trellis code (STTC), orthogonal STBC (O‐STBC), and quasi‐orthogonal STBC ( QO‐STBC ) on the minimum mean‐square‐error, and MRC are worth implementing on the DWDM‐FSO wireless communication systems. The mitigation of atmospheric turbulence is achieved using MIMO diversity combining techniques coding. The simulation results for diversity coding techniques using QO‐STBC/STTC and SC/MRC in the MIMO‐DWDM FSO communication system can improve BER performance, OP, and SNR. The MRC exhibits the lowest OP and BER when compared with the SC and EGC. The numerical results demonstrate that the FSO communication link using DWDM QO‐STBC/STTC improves the power penalty at both BER values under varying atmospheric turbulence conditions for ST, MT, and WT, in comparison to FSO systems without DWDM QO‐STBC/STTC diversity coding techniques.

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.

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.

There has been an increasing interest in digital transmission in the field of mobile radio. In a mobile communication system, because of multipath propagation, the communication channel is modeled as a Rayleigh fading channel. One of the most efficient techniques to reduce the fading effect and improve the system performance is space diversity reception. The average bit error rate (BER) performance of TC M-ary PSK with 2 branch selection combining (SC) and maximal ratio combining (MRC) diversity systems on a correlated Rayleigh fading channel is analysed, and some numerical results are shown. Although the correlation between branch causes signal-to-noise (SNR) loss (relative to the uncorrelated fading case) for SC and MRC diversities, the diversity can lead one to achieve the diversity gain compared to a system without diversity. It is found that the diversity gain of TC 8PSK with SC and MRC diversities is decreased with increasing the fading correlation parameter /spl xi//sup 2/, the diversity gain of TC 8PSK with MRC diversity is larger than TC 8PSK with SC diversity.

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

The effects of multipath fading and additive white Gaussian noise (AWGN) on the bit error rate (BER) performance of direct-sequence code-division multiple-access (DS-CDMA) systems is studied in this paper. The expression for the conditional BER, conditioned on a given level of fading is derived and then the unconditional BER is evaluated. The BER performance results of the system are evaluated in a fading channel for different magnitude of fading. The proposed approach is also extended to estimate the BER performance of the CDMA system having multiple receiving antennas. The effectiveness of the selection method and maximal ratio combining (MRC) method as diversity combining schemes are investigated and compared. To enhance the system performance channel coding is also applied to the system.

In this paper, we analyze the error probability performance of maximal ratio combining (MRC), equal gain combining (EGC), and selection combining (SC) diversity schemes with coherent BPSK signaling on Rayleigh fading channels with Gaussian channel estimation errors. We first show that, with weighting errors, the conditional probability of error is not an explicit function of the signal-to-noise ratio (SNR) at the output of the diversity combiner. We then show that averaging the conditional probability of error with the density function of the SNR at the output of the combiner yields a lower bound on the exact probability of error, independent of the underlying diversity combining scheme. Later, we derive the exact probability of error for MRC, EGC, and SC diversity schemes and show that the exact probability of error with weighting errors is very similar to the case of perfect channel estimation, but with the average SNR per diversity branch, /spl gamma/_, for the case of perfect channel estimation, replaced by the effective SNR, /spl gamma/_/sub /spl rho//, due to weighting errors, which is a function of both /spl gamma/_ and /spl rho/, the magnitude of the normalized cross correlation between the actual and the estimated channel gains. Finally, we show that, as /spl rho/ /spl rarr/ 0, the average probability of error approaches 0.5, irrespective of the order of diversity and the diversity combining rule.

This paper analyzes the bit error rate (BER) for quadrature amplitude modulation (QAM) with L-fold maximal ratio combining (MRC) space diversity in Rayleigh fading channel. The formula is obtained by averaging the bit error probability of M-ary QAM in an additive white Gaussian noise channel over a chi-square distribution with 2L degrees of freedom. This formula overcomes the limitations of the earlier work, which has been limited only to deriving a BER for QAM with two branch MRC space diversity. The BER performance of quadrature phase shift keying with MRC diversity is obtained from the derived formula by setting M=4.

In this paper, a new signal detection scheme for overloaded multiple-input multiple output (MIMO) systems is proposed. In MIMO signal detection with belief propagation (BP), a factor graph consists of many loops that arise high complexity and cause performance degradation due to outliers. Various schemes have been proposed to overcome these issues. In BP with maximal ratio combining (MRC) and minimum mean square error (MMSE) pre-cancellation, a conventional scheme applies MRC on received signals in advance to obtain diversity gain to improve bit error rate (BER) performance as compared with BP using only MMSE pre-cancellation. To achieve further performance improvement, BP using a combined channel matrix is proposed in this paper. In the proposed scheme, the number of observation nodes is increased by combining a part of an original channel matrix to the channel matrix with MRC and MMSE pre-cancellation to enhance diversity gain. Numerical results obtained through computer simulation show that the BER performance of the proposed scheme is superior to that of BP or BP with MRC and MMSE pre-cancellation. The proposed scheme improves BER performance by about 3.1 dB at a BER of 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> as compared with the BP withMRC and MMSE pre-cancellation. The computational complexity of the proposed scheme increases as the number of rows of the additional channel submatrix. It is in the same order of magnitude as that of the original BP based MIMO detection scheme.

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).

In this paper, we investigate the performance of a free space optical link using Alamouti type Space Time Block Code (STBC) over weak atmospheric turbulence-induced fading channels. An analytical approach is presented to evaluate the bit error rate (BER) performance of a direct detection on-off keying (OOK) free space optical link over a weak atmospheric turbulent condition considering Alamouti type space time block code (STBC) and maximal ratio combining (MRC) at the receiver. The results are evaluated numerically and also by simulation. Results show that there is significant improvement in BER performance at a given BER due to coding and diversity combining at the receiver. The amount of improvement for (M × L ) STBC is of the order of 18 dB, 10 dB and 5 dB for laser source, M=2 and number of photodetector, L= 1, 2 and 4 respectively.

A general expression for the bit-error rate (BER) performance of quadrature amplitude modulation (QAM), have been presented in this paper, considering arbitrary branch Maximal Ratio Combining (MRC) Receiver, over two-wave diffuse power (TWDP) Fading Channels. Analysis of the impact caused by the fading parameters Δ and K, on the performance of the M branch-MRC receiver, have been done for different QAM constellations. Numerical evaluation of the expressions and finally the verification of the results using Monte Carlo Simulation have been done.

Multi-carrier code division multiple access (MC-CDMA)has been considered as a strong candidate for next generation wireless communication system due to its excellent performance in multi-path fading channel and simple receiver structure. However, like all the multi-carrier transmission technologies such as OFDM, the inter-carrier interference (ICI) produced by the frequency offset between the transmitter and receiver local oscillators or by Doppler shift due to high mobility causes significant BER (bit error rate) performance degradation in MC-CDMA system. Many ICI cancellation methods such as windowing and frequency domain coding have been proposed in the literature to cancel ICI and improve the BER performance for multi-carrier transmission technologies. However, existing ICI cancellation methods do not cancel ICI entirely and the BER performance after ICI cancellation is still much worse than the BER performance of original system without ICI. Moreover, popular ICI cancellation methods like ICI self-cancellation reduce ICI at the price of lowering the transmission rate and reducing the bandwidth efficiency. Other frequency-domain coding methods do not reduce the data rate, but produce less reduction in ICI as well. In this paper, we propose a novel ICI cancellation scheme that can eliminate the ICI entirely and offer a MC-CDMA mobile system with the same BER performance of a MC-CDMA system without ICI. More importantly, the proposed ICI cancellation scheme (namely Total ICI Cancellation) does not lower the transmission rate or reduce the bandwidth efficiency. Specifically, by exploiting frequency offset quantization, the proposed scheme takes advantage of the orthogonality of the ICI matrix and offers perfect ICI cancellation and significant BER improvement at linearly growing cost. Simulation results in AWGN channel and multi-path fading channel confirm the excellent performance of the proposed Total ICI Cancellation scheme in the presence of frequency offset or time variations in the channel, outperforming existing ICI cancellation methods.

In this paper, we propose a weighting factor (WF) estimation method for peak power reduction (PPR) based on adaptive flipping of parity carriers in a turbo-coded orthogonal frequency-division multiplexing (OFDM) system. In this PPR scheme, the peak-to-average power ratio of a turbo-coded OFDM signal is reduced with adaptive flipping of the phase of the parity carriers corresponding to the WFs. At the receiver, the WFs are estimated at a turbo decoder by exploiting the redundancy of an error-correcting code using no extra side information. The proposed WF estimation method is based on an iterative decoding of the turbo code, i.e., the turbo decoder provides not only error correction capability but the WF estimation function as well. When the proposed WF estimation method is used for the system using a turbo code with constraint length <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> = 4 and a code rate of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> = 1/2, the instantaneous power of the OFDM signal at the complementary cumulative distribution function of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> can be reduced by about 2.1 dB through the application of the PPR scheme. When the bit error rate (BER) performance is evaluated as a function of the peak signal-to-noise power ratio (PSNR), the proposed method achieves better BER performance than the case without the PPR in an attenuated 12-path Rayleigh fading condition. The improvements in BER performance as a function of PSNR are about 1.1, 2.0, and 2.1 dB at BER = 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> for turbo-coded OFDM signals using QPSK, 16-state quadrature amplitude modulation (QAM), and 64-state QAM schemes, respectively.