M-ary CPFSK-DPD with L-diversity maximum ratio combining in Ricianfast-fading channels

We derive a formula for the bit error probability (BEP) of M-ary continuous phase frequency shift keying with differential phase detection and maximum ratio combining diversity in Rician fast-fading channels. We assume that transmitter and receiver filters distort the signal and limit the noise. We compute the BEP as a function of energy-to-noise ratio per bit (E_b/N₀) and other system and channel parameters: Rician factor K=0, 6 dB, 10, ∞; number of diversity channels L=1, 2, 3; Doppler frequency shift f_D T=0, 0.01, 0.02; Butterworth filters in transmitter and receiver of order N_T=3 and N_R=4; optimal sampling time and filter bandwidth. In all cases the BEP is significantly reduced by diversity     

Optimal binary communication with nonequal probabilities

Optimal signal energies are derived for optimal binary digital communication systems with arbitrary signal probabilities and correlation with both coherent and noncoherent detection. The resulting bit-error probability (BEP) is computed and compared with the BEP of the same systems with equal signal energies. One of the conclusions is that for the coherent system with nonnegative correlation, and for the noncoherent system with arbitrary correlation, the optimal signals are on-off keying (OOK), i.e., the signal with probability p/spl les/0.5 has energy E/p, while the second signal has zero energy, where E is the average signal energy. The proposed system is also better than a system with source coding and equiprobable signals.     

Binary PRCPM with differential phase detection and maximal ratiocombining diversity in fading channels

We derive a formula for the bit-error probability (BEP) of binary partial-response continuous-phase modulation (PRCPM) with N-bit differential phase detection (DPD) in a Rician fading channel subject to L-branch maximum ratio combining (MRC) diversity. We compute the BEP for minimum-shift keying (MSK), Gaussian MSK (GMSK), and 2 RC (2-b-duration raised cosine) frequency signals as a function of the energy-to-noise ratio per bit E_b/N₀ and other system and channel parameters [N=1 and 2 and L=1, 2, and 3, Rician factor K=-∞, 0, 6, 10, and ∝ dB, Doppler frequency shift f_DT=0, 0.01, and 0.02, Gaussian premodulation filter bandwidth B_gT=∞, 0.5, 0.25, and the presence or absence of a Doppler frequency tracking loop (DFTL) in the receiver]. In all cases, the BEP is significantly reduced by diversity     

A new spreading scheme for convolutionally coded CDMA communicationin a Rayleigh-fading channel

There has been increased interest in the use of direct-sequence code-division multiple-access (DS/CDMA) for wireless communication systems. We find that the asymptotic bit-error probability (BEP), P_b, of a convolutionally coded code-division multiple-access (CDMA) system in a frequency-selective Rayleigh-fading channel depends on the length of the shortest error event path and the product of symbol distances along that path. Based on this observation, we propose a new spreading scheme that maximizes the length of the shortest error event path. It is shown that the proposed scheme yields an improvement of 1.0-1.3 dB at P_b=10^-5 over the conventional convolutionally coded CDMA system, and even a higher improvement can be achieved as the required BEP is decreased     

Gray Coding for Multilevel Constellations in Gaussian Noise

The problem of finding the optimal labeling (bit-to-symbol mapping) of multilevel coherent phase shift keying (PSK), pulse amplitude modulation (PAM), and quadrature amplitude modulation (QAM) constellations with respect to minimizing the bit-error probability (BEP) over a Gaussian channel is addressed. We show that using the binary reflected Gray code (BRGC) to label the signal constellation results in the lowest possible BEP for high enough signal energy-to-noise ratios and analyze what is "high enough" in this sense. It turns out that the BRGC is optimal for PSK and PAM systems whenever the target BEP is at most a few percent, which covers most systems of practical interest. New and simple closed-form expressions are presented for the BEP of PSK, PAM, and QAM using the BRGC     

Performance analysis of an FFH/BFSK receiver with ratio-statistic combining in a fading channel with multitone interference

The bit-error probability (BEP) is evaluated for a fast frequency-hopping/binary frequency-shift keying spread-spectrum communication system over a frequency-nonselective, slowly fading channel with worst-case band multitone jamming and additive white Gaussian noise. A diversity reception technique with ratio-statistic combining is applied at the receiver. Both square-law and envelope detectors are utilized and analyzed. Based on circularly symmetric signal theory, the paper obtains the closed-form expressions of probability density function and cumulative distribution function of the ratio-statistic output. It is shown from the analytical results, and verified by simulation, that the BEP performance of the ratio-statistic receiver is sensitive to the fading effect on the desired signal, but is insensitive to that on the jamming tones. It is also shown that the envelope detector provides better performance than the square-law detector.     

基于能量检测的UWB数据包联合捕获方法

针对非相干UWB系统的数据包捕获问题,提出了一种联合信号捕获、误码率性能优化与包同步字检测的捕获方案.在信号捕获后发送导频序列实时估计信噪比,并搜索积分窗口长度,以获得最低误码率.给出了数据包捕获模型的合适性能指标,分别采用串行搜索与跳K步搜索策略,结合7位与13位巴克码为包同步字进行数据包捕获,仿真结果表明,三者联合的方案能够在保持一定包捕获性能的同时获得较好的误码率性能.     

Further results in the unified analysis of digital communicationsystems

Stein's (1964) method can be extended to the analysis of the bit error probability (BEP) of quadrature phase shift keying (QPSK), staggered QPSK, and minimum shift keying (MSK) communication systems. The resultant noisy reference BEP waterfall curves are presented. The numerical advantages of this technique and some practical results are discussed. In a parallel manner, the BEP for quadrature amplitude modulation (QAM) communication systems can be analyzed. This technique is numerically more intensive but is used to generate noisy reference BEP waterfall curves for 16-QAM and 64-QAM modulations. Unfortunately, few carrier synchronizers produce a complex Gaussian reference signal, but pragmatically many reference signals can be accurately approximated by a complex Gaussian at moderate to high SNR. Actual BEP performance and the approximate results are compared     

Exact bit-error probability for optimum combining with a Rayleighfading Gaussian cochannel interferer

We derive expressions for the exact bit-error probability (BEP) for the detection of coherent binary phase-shift keying signals of the optimum combiner employing space diversity when both the desired signal and a Gaussian cochannel interferer are subject to flat Rayleigh fading. Two different methods are employed to reach two different, but numerically identical, expressions. With the direct method, the conditional BEP is averaged over the fading of both signal and interference, With the moment generating function based method, expressions are derived from an alternative representation of the Gaussian Q-function     

Performance analysis of single relay selection in rayleigh fading

We provide closed-form expressions for the outage and bit error probability (BEP) of uncoded, threshold-based opportunistic relaying (OR) and selection cooperation (SC), at arbitrary signal to noise ratios (SNRs) and number of available relays, assuming decode-and-forward relays and Rayleigh fading channels. Numerical results demonstrate that SC performs slightly better in terms of outage probability; in terms of BEP, both systems may outperform one another, depending on the SNR threshold that determines the set of relays that participate in the forwarding process.     

Exact closed-form performance analysis of optimum combining with multiple cochannel interferers and Rayleigh fading

A new closed-form expression is derived for the exact bit-error probability (BEP) for optimum combining with binary phase-shift keying. The exact BEP expression is for multiple, equal power, cochannel interferers and multiple reception branches. It is assumed that the aggregate interference and noise is Gaussian and that both the desired signal and interference are subject to Rayleigh fading. The derivation starts by expressing the optimum combining decision statistic as a sum of quadratic forms of Gaussian random variables and it proceeds to average over the fading interference. The new BEP expression has low complexity as it contains only finite sums and products.     

Performance analysis of equalized OFDM systems in Rayleigh fading

Channel estimation is usually needed to compensate for the amplitude and phase distortions associated with a received orthogonal frequency-division multiplexing (OFDM) waveform. This paper presents a systematic approach for analyzing the bit-error probability (BEP) of equalized OFDM signals in Rayleigh fading. Closed-form expressions for BEP performance of various signal constellations [phase-shift keying (PSK), differential phase-shift keying (DPSK), quaternary phase-shift keying (QPSK)] are provided for receivers that use a linear pilot-assisted channel estimate. We also derive the optimal linear channel estimates that yield the minimum BEP and show that some previous known results are special cases of our general formulae. The results obtained here can be applied to evaluate the performance of equalized single-carrier narrowband systems as well.     

Bit-error bounds for trellis-coded MPSK in mixed fading channels

Bit-error probability (BEP) bounds of trellis-coded MPSK systems over two classes of mixed fading channels are studied. These two classes of channels have been proposed as candidate models for mobile satellite communications. The first class consists of slow and frequency-nonselective fading channels whose output field strengths follow a probability law characterized by a convex combination of Rician and Rayleigh/lognormal distributions. For the other class of fading channels, the received signal amplitude has a convex combination of Rician and Rician/lognormal distributions. We analyze performance bounds for trellis codes that belong to the class of either geometrically uniform codes (GUCs) or quasi-regular codes (QRCs). Receivers with either ideal channel state information (CSI) or no CSI at all are considered. We examine asymptotic behaviors of these codes and identify key design parameters. Numerical results are provided to illustrate and compare the BEP performances of various codes and to validate the usefulness of the asymptotic analysis     

Error Performance of DQPSK with EGC Diversity Reception over Fading Channels

This paper derives the average bit error probability (BEP) of differential quaternary phase shift keying (DQPSK) with postdetection equal gain combining (EGC) diversity reception over independent and arbitrarily correlated fading channels. First, using the associated Legendre functions, the average BEP of DQPSK is analyzed over independent Rayleigh, Nakagami-m, and Rician fading channels. Finite-series closed-form expressions for the average BEP of DQPSK over L-branch independent Rayleigh and Nakagami-m fading channels (for integer Lm) are presented. Besides, a finite-series closed-form expression is given for the average BEP of differential binary phase shift keying (DBPSK) with EGC over independent Rician fading channels. Second, an alternative approach is propounded to study the performance of DQPSK over arbitrarily correlated Nakagami-m and Rician fading channels. Relatively simple BEP expressions in terms of a finite sum of a finite-range integral are proposed. Moreover, the penalty in signal to noise ratio (SNR) due to arbitrarily correlated channel fading is also investigated. Finally, the accuracy of the results is verified by computer simulation.     

On convexity of MQAM's and MPAM's bit error probability functions

For MQAM and MPAM with practical values of M and Gray mapping, we provide a rigorous proof that the associated bit error probability (BEP) functions are convex of the signal‐to‐noise ratio per symbol. The proof employs Taylor series expansions of the BEP functions' second derivatives and term‐by‐term comparisons between positive and negative terms. Convexity results are useful for optimizing communication systems as in optimizing adaptive transmission policies. Copyright © 2009 John Wiley & Sons, Ltd.     

On the optimality of bit detection of certain digital modulations

In this paper, we study the optimality of bit detection for coherent M-ary phase-shift keying (PSK) and M-ary quadrature amplitude modulation (QAM), and noncoherent M-ary frequency-shift keying (FSK) signal sets. For M-PSK and M-QAM signal constellations, we employ Gray mapping, consider 8-PSK and 16-QAM signal sets as representative of the general results, and derive the log-likelihood ratio (LLR) for each bit forming the symbol. Using the LLRs, we derive the average bit-error probability (BEP) for the individual bits, and show that the decision regions and the corresponding average BEP for the case of M-PSK coincide with those obtained with the optimal symbol-based detector, whereas, in general, this is not the case for both M-QAM and M-FSK.     

Performance of Differentially Detected DPSK Over Nonselective Rayleigh Fading Channels With Maximal Ratio Combining and Multiple Cochannel Interferers

In this paper, we investigate the performance of differentially detected differential phase-shift keying (DPSK) modulation with postdetection maximal ratio combining, in nonselective Rayleigh fading channels with multiple asynchronous cochannel interferers. The approach is based on an analytical technique we have presented earlier in the literature. Exact bit-error probability (BEP) results for binary DPSK and quaternary DPSK are derived. More specifically, we look into the effects of symbol-timing offsets between the interfering signals and the desired signal on the error performance. Our results show that when all the interfering signals are synchronous with the desired signal, the impairment caused by the cochannel interference to the desired user is maximum. On the other hand, when all the interfering signals are half-symbol-duration-delayed with respect to the desired user, they introduce the minimum impairment. Based on these findings, upper and lower bounds on the BEP are derived in simple closed form. Our explicit BEP results also show that the error probabilities of different transmitted symbols of the desired user are affected differently by the interfering signal     

Optimal 100% Excess Bandwidth Signaling in Cochannel Interference

The problem of transmitter-receiver (T-R) filter design for detection of a binary phase-shift keying signal in asynchronous cochannel interference and Gaussian noise is considered. It is shown that maximum signal-to-interference-plus-noise ratio (SINR) can be achieved only if the T-R filters have a flat spectrum with 100% excess bandwidth. The bit error probability (BEP) performance of a system with the proposed filters is compared to that of a system with conventional root raised-cosine filters both for perfect and imperfect timing recovery cases. It is shown that the proposed filter design is superior to the conventional root raised-cosine filters both in having larger SINR and smaller BEP     

The Tradeoff Between Processing Gains of an Impulse Radio UWB System in the Presence of Timing Jitter

In time hopping impulse radio, N_f pulses of duration T_c are transmitted for each information symbol. This gives rise to two types of processing gains: (i) pulse combining gain, which is a factor Nf, and (ii) pulse spreading gain, which is N_c = T_f/T_c, where T_f is the mean interval between two subsequent pulses. This paper investigates the tradeoff between these two types of processing gains in the presence of timing jitter. First, an additive white Gaussian noise (AWGN) channel is considered, and approximate closed-form expressions for bit error probability (BEP) are derived for impulse radio systems with and without pulse-based polarity randomization. Both symbol-synchronous and chip-synchronous scenarios are considered. The effects of multiple-access interference (MAI) and timing jitter on the selection of optimal system parameters are explained through theoretical analysis. Finally, a multipath scenario is considered, and the tradeoff between processing gains of a synchronous impulse radio system with pulse-based polarity randomization is analyzed. The effects of the timing jitter, MAI, and interframe interference (IFI) are investigated. Simulation studies support the theoretical results.     

Application of best relay selection approach to cooperative DF IDMA systems over Rayleigh/Weibull fading channels

This paper analyzes the performance of cooperative decode‐and‐forward (DF) interleave‐division multiple‐access (IDMA) networks with best relay selection over Rayleigh/Weibull fading environments. In the analysis, approximate outage probability (OP) and bit error probability (BEP) expressions are derived for the considered system. Further, a 2‐hop DF IDMA system is also designed to compare with cooperative one. We propose OP and BEP expression for 2‐hop DF IDMA systems. Numerical results are obtained by changing the number of relays and the value of fading parameter in the proposed expressions. Also, simulations are provided to corroborate the exactness of the derived approximate OP and BEP expressions.