Bit error probabilities MDPSK over the nonselective Rayleigh fadingchannel with diversity reception

Data transmission using M-ary differential phase shift keying (MDPSK) over the nonselective Rayleigh fading channel with diversity reception is considered. While previous studies on error probability mostly assume no fading fluctuation, the author considers, exclusively, the case in which the fading process fluctuates from one symbol interval to the next. Exact bit error probability results for 2, 4, and 8 DPSK as well as tight upper bounds are derived. Some applications of the results are discussed     

On orthogonal signaling over the slow nonselective Rician fadingchannel with unknown specular component

Orthogonal signaling over the slow nonselective Rician fading channel is considered. Previous receiver designs have all assumed the amplitude and phase of the specular component of the received carrier to be known completely, but this assumption is entirely unrealistic. The problem is reformulated with unknown random amplitude and phase of the specular component. The optimum maximum likelihood receiver is obtained for equally likely equal-energy orthogonal signals and is shown to be identical to the quadratic receiver for the purely unknown phase channel and the pure Rayleigh fading channel. The error probability performance is analyzed for a fixed known specular amplitude. When specialized to the binary signaling case this error probability result exhibits a performance that is very close to and asymptotically approaches that of the conventional coherent-specular-component case for high SNR. Thus, knowledge of the specular component phase is not important to the optimum receiver     

Optimal detection of digital data over the nonselective Rayleighfading channel with diversity reception

Based on the criterion of minimum symbol error probability, an analysis is made of symbol-by-symbol detection of a sequence of digital data transmitted using linear suppressed-carrier modulation over L independent diversity channels with AWGN (additive white Gaussian noise) and slow nonselective Rayleigh fading. The optimal receiver is derived, but is found to be difficult to implement in practice because of its exponential growth in complexity as a function of sequence length. Suboptimal decision-feedback approximations are then suggested which are linear and readily implementable and can be integrated as generalized differentially coherent receivers. The exact bit error probabilities of these suboptimal receivers are obtained. Tight upper bounds on these error probabilities are also obtained which show simply how they behave as a function of signal-to-noise ratio and order of diversity. A main conclusion of this work is that optimal data detection on a fading channel should be performed using MMSE (minimum mean squared error) estimates of the quadrature amplitudes of the channel fading processes as a coherent reference     

SNR estimation in Nakagami-m fading with diversity combining and its application to turbo decoding

We propose an online signal-to-noise ratio (SNR) estimation scheme for Nakagami-m (1960) fading channels with L branch equal gain combining (EGC) diversity. We derive the SNR estimate based on the statistical ratio of certain observables over a block of data, and use the SNR estimates in the iterative decoding of turbo codes on Nakagami-m fading channels with L branch EGC diversity. We evaluate the turbo decoder performance using the SNR estimate under various fading and diversity scenarios (m = 0.5, 1, 5 and L = 1, 2, 3) and compare it with the performance using perfect knowledge of the SNR and the fade amplitudes.     

Error rate analysis of MDPSK/CPSK with diversity reception undervery slow Rayleigh fading and cochannel interference

The distribution of the phase noise due to additive white Gaussian noise (AWGN) and cochannel interference (CCI) is analyzed for differential phase detection (DPD) and coherent phase detection (CPD) in a very slow nonfrequency selective Rayleigh fading environment. The effects of modulation timing offset between the desired signal and the CCI and of the overall channel filter response are considered. Simple closed-form expressions are derived for ideal selection diversity reception. The derived phase noise distributions are used for evaluating the bit error rate (BER) performance of 2-16DPSK/CPSK assuming square-root raised cosine Nyquist transmit/receive filters. It is found that the BER performance of CPSK is less sensitive to CCI modulation timing offset than DPSK, and that increasing the filter rolloff factor can improve the BER performance due to CCI. Finally, the accuracy of the BER approximation that uses the symbol error rate is discussed     

Error rates of DPSK systems with MIMO EGC diversity reception over Rayleigh fading channels

This paper analyzes the average bit error probability (BEP) of the differential binary and quaternary phase-shift keying (DBPSK and DQPSK respectively) with multiple-input multiple-output (MIMO) systems employing postdetection equal gain combining (MIMO EGC) diversity reception over Rayleigh fading channels. Finite closed-form expressions for the average BEP of DBPSK and DQPSK are presented. Two approaches are introduced to analyze the error rate of DQPSK. The proposed structure for the differential phase-shift keying (DPSK) with MIMO EGC provides a reduced-complexity and low-cost receiver for MIMO systems compared to the coherent phase-shift keying system (PSK) with MIMO employing maximal ratio combining (MIMO MRC) diversity reception. Finally, a useful procedure for computing the associated Legendre functions of the second kind with half-odd-integer order and arbitrarily degree is presented.     

Iterative channel estimation and decoding for the multipath channels with RAKE reception

We study an improved receiver with iterative channel estimation and decoding for wireless multipath channels with RAKE reception. To keep the complexity low, iterative channel estimation is done on the equivalent channel at the RAKE output. Output after Turbo decoding iteration(s) is processed to yield a better channel estimate.     

On channel estimation and sequence detection of interleaved codedsignals over frequency nonselective Rayleigh fading channels

Due to the receiver complexity introduced by interleaving, the implementation of maximum likelihood (IML) decoding of interleaved coded signals transmitted over frequency nonselective Rayleigh fading channels has been shown to be practically impossible. As an alternative, a two-stage receiver structure has been proposed, where the channel estimation and sequence decoding are done separately. The channel estimation issue in a two-stage receiver is examined in detail in this paper. It is shown that although an optimum (maximum a posteriori (MAP)) channel estimation is not possible in practice, it can be approached asymptotically by joint MAP estimation of the channel and the coded data sequence. The implementation of the joint MAP estimation is shown to be an ML sequence estimator followed by an minimum mean-square error (MMSE) channel estimator. Approximate fill sequence estimation using pilot symbol interpolation is also studied, and through computer simulations, its performance is compared to receivers using hit sequence estimation. The effect of decision delay (DD), prediction order, and pilot insertion rate (PIR) on the reduced complexity ML sequence estimation is investigated as well. Finally, a practical receiver is proposed that makes the best compromise among the error performance, receiver complexity, DD, and power (or bandwidth) expansion due to pilot insertion     

Iterative estimation and decoding for FH-SS with slow Rayleighfading

The performance of turbo codes is investigated in a frequency-hopped spread-spectrum (FH-SS) system with full-band thermal noise and Rayleigh fading. For cases where the data rate exceeds the hopping rate (i.e., there exists multiple bits per hop) and fading side information (SI) does not exist, our approach is to iteratively estimate the fading levels. Simulation is performed for coherent and noncoherent reception, variable number of bits per hop, and cases where fading SI is available or unavailable to the decoder. It is shown that iterative channel estimation performed in conjunction with iterative decoding can improve the overall decoding performance. Finally, the performance of an FH-SS system using standard fading assumptions is compared to the performance of a measured fading channel. Due to flaws in the assumptions, the measured fading channel yields several decibels of performance loss relative to the ideal fading channel     

Further results on the bit error probabilities of MDPSK over thenonselective Rayleigh fading channel with diversity reception

This paper presents a fundamental approach for deriving the bit error probability of BDPSK and QDPSK over the nonselective Rayleigh fading channel for a receiver with an arbitrary IF filter, and for a fading process with an arbitrary Doppler spectrum with arbitrary Doppler bandwidth. The results generalize those published earlier which were restricted to matched filter reception and to a fading process with a small Doppler bandwidth compared to the symbol rate. This allows the error probability to be studied in the presence of varying degrees of ISI due to the bandlimitation of the received signal by the IF filter, and in the presence of fading fluctuations of various rates. The analytical approach presented is simple, and yet powerful in that it can handle the case of diversity reception. This is a great advantage over the alternative approach of using the distribution of the differential phase of the received signal over a symbol interval. The bit error probability results apply to both conventional BDPSK and QDPSK, as well as π/2-2DPSK and π/4-4DPSK, and allow the irreducible bit error probability as well as the SNR at which this irreducible value sets in to be studied as a function of the Doppler bandwidth and IF filter bandwidth. The computed results are applicable to the design of digital cellular mobile communication systems     

Bit-error probabilities of 2 and 4DPSK with nonselective Rayleighfading, diversity reception, and correlated Gaussian interference

A new analytical approach is presented for deriving the bit error probability results for 2 and 4DPSK with differential detection over the nonselective Rayleigh fading channel with diversity reception and with an additional additive, correlated, Gaussian interference process in each diversity channel. The approach differs from that in a previous paper, and is based on a well-known result in the literature. The results are new, and reduce to known results when the correlated interference is absent. They show that the correlated interference behaves like an additional component of the information-bearing signal, and affects the error probabilities of the various transmitted symbols differently, irrespective of its statistical distribution. Its Gaussian statistical distribution is essential only for the analysis of the bit error probability     

Least squares frequency estimation in frequency-selective channelsand its application to transmissions with antenna diversity

A new data-aided frequency estimator for frequency-selective fading channels is introduced. The proposed estimator is developed based on a least squares (LS) error criterion and can estimate frequency offsets without the need for channel information. Statistical analysis indicates that the resulting estimate is unbiased and tends to approach the Cramer-Rao lower bound (CRLB). Simulation shows that the proposed LS method is preferable to existing techniques in mobile communications. The application of the LS estimator to systems with transmitter antenna diversity is also considered. In particular, it is demonstrated that the LS method can be successfully applied to third-generation wireless communication systems     

A robust Viterbi decoder and its application to terrestrial HDTVbroadcasting

The conventional Viterbi (1967) decoder employing the Euclidean distance has been widely used and considered as the optimum one in the sense of maximum likelihood sequence decoding under the hypothesis of additive white Gaussian noise (AWGN). However, what will happen if the noise distributions of actual channels deviate from the assumed AWGN? A robust Viterbi decoder utilizing absolute distance is carefully examined. Analytical and numerical results show that this Viterbi decoder is more advantageous than the conventional Viterbi decoder for actual channels with various kinds of interference, particularly in the presence of impulsive noise. Finally the robust Viterbi decoder is applied to TCM-8VSB terrestrial HDTV broadcasting, achieving 0.5-1.0 dB SNR gains over the conventional Viterbi decoder on contaminated AWGN channels     

An adaptive coherent receiver for MPSK/MDPSK over the nonselective Rayleigh fading channel with unknown characteristics

A coherent symbol-by-symbol (SBS) diversity receiver for m-ary phase-shift keying (MPSK) and differentially encoded MPSK (MDPSK) signals transmitted over a nonselective Rayleigh fading channel is presented. It incorporates a new adaptive filter for channel estimation that does not require any prior knowledge of the fading process model. It estimates the fading gains through decision-feedback and recursive least squares adaptation of the filter coefficients. A novel forgetting-factor adaptation algorithm that enables the filter to react quickly to randomly changing fading statistics caused by shadowing and acceleration/deceleration is introduced. Simulations show that the receiver performs better than that of Adachi's ( IEEE Trans. Veh. Technol. vol. 47 p. 909, 1998), either without shadowing or under slow lognormal shadowing.     

Improved fractional Kalman filter and its application to estimation over lossy networks

This paper presents improvements on the fractional Kalman filter (FKF) based on the infinite dimensional form of a linear discrete fractional order state-space system. Furthermore, taking into account the considerable interest in estimation over networks with packet losses, the application and extension of the improved FKF are included. Some simulation cases are given in order to demonstrate the effectiveness of the proposed algorithms, with significant improvements in terms of estimation and smoothing results.     

QPSK调制方式下瑞利信道发端分集的性能分析及实现

在QPSK调制方式下对瑞利信道的采用Alamouti方法的发端分集和采用MRC方法的收端分集误码性能进行分析比较，并用MATLAB对发端、收端分集技术进行模拟，说明发端分集技术可以取得和收端分集技术相当的性能，并介绍几种简化的发端分集技术。     

A factor graph approach to iterative channel estimation and LDPC decoding over fading channels

This letter provides a comparative study of joint channel estimation and low-density parity-check decoding algorithms for flat Rayleigh fading channels based on the receiver factor graphs. Two approaches for joint channel estimation and decoding are proposed. Intensive simulation studies are carried out to evaluate the receiver sensitivity to the choice of the factor graph. Results show that when channel statistical information is not available at the receiver, a low-pass filtering approach gives a more robust and simpler solution, and it is only 0.5 dB worse than the optimum Wiener filtering. All methods have about 2 dB improvements over the noniterative receivers.     

Joint MF combining and turbo equalization for wireless communications over ISI channels with diversity reception

A new method called joint Matched Filter (MF) combining and turbo equalization is proposed for wireless communications over Inter-Symbol Interference (ISI) channels with diversity reception. This method takes diversity combining and equalization as integrity and need just one turbo equalizer for all diversity branches. Computer simulations prove that our method can take advantage of turbo equalization and diversity reception to combat fading of wireless channels.     

ALOHA with capture over slow and fast fading radio channels withcoding and diversity

The effects of capture on the average system throughput and delay performance of slotted ALOHA were analyzed for slow and fast Rayleigh fading radio channels. A short-range multipoint-to-base station packet radio network is considered. It is shown that larger capture effects and thus improved network performance can be achieved with proper choice of modulation. It is also shown that the use of simple error-correcting codes improves capture. The use of selection diversity also improves the capture effect both for fast and slow fading. It is concluded that the inverse distance variability of the received signal is the main reason for the capture effect. The Rayleigh fading alone yields a very small contribution in terms of throughput; nonetheless, it helps to stabilize the system. Numerical results are presented for a slotted ALOHA system with 50 users. It is found that the maximum average throughput can be increased from about 36% to almost 60% by using channel coding and space diversity     

A new iterative soft-output Viterbi algorithm and its application to the “dicode” channel

We present an iterative soft-output decoding algorithm for serially concatenated coding systems. It has better performance than the conventional noniterative decoding algorithm. When applied together with an outer convolutional code to the dicode channel with partial response (1 — D), we obtain an additional coding gain of about 1 dB at a bit-error rate of 10^-4 after two iterations. This new algorithm can also be applied advantageously to satellite communication and fading channels.