Bit error rate of binary and quaternary DPSK signals with multipledifferential feedback detection

A differentially coherent detection scheme with improved bit error rate (BER) performance is presented for differentially encoded binary and quaternary phase shift keying (PSK) modulation. The improvement is based on using L symbol detectors with delays of 1, 2, . . ., L symbol periods and on feeding back detected PSK symbols. Exact formulas for the bit error probability are derived for the case that correct symbols are fed back. The effect of symbol errors in the feedback path on the BER is determined by computer simulations     

Effect of Noisy Phase Reference on Coherent Detection of Offset-QPSK Signals

Imperfect carrier synchronization causes a performance loss for coherent phase-shift-keyed (PSK) communications. This detection loss is greater for quaternary signaling (QPSK) than for the binary case (BPSK). The use of an offset form of QPSK, also known as double-biphase modulation, is shown to yield a probability of bit error in detection that is equal to the average of the detection performances for BPSK and conventional QPSK. Because of frequency instabilities in communications systems, it is sometimes difficult to obtain carrier synchronization with sufficiently low jitter to preclude significant detection losses. The use of offset QPSK in lieu of conventional QPSK modulation is shown to lower by almost 3 dB the required SNR of the synchronizer phase reference for satisfying a specified value of allowable detection loss.     

Analysis of the error performance of trellis-coded modulations inRayleigh-fading channels

This work presents an exact expression for the pairwise error event probability of trellis-coded modulation (TCM) transmitted over Rayleigh-fading channels. It includes phase shift keying (PSK) and multilevel quadrature amplitude modulation (QAM) codes, as well as coherent and partially coherent (e.g. differential, pilot tone, etc.) detection. Due to the form of the exact pairwise error event probabilities, this calculation technique cannot be used with the transfer function technique to obtain an upper (union) bound on the overall bit error probability. For this reason, the authors estimate the bit error probability by considering only a small number of short error events. Through simulations, they found that the estimation is usually very accurate at high signal-to-noise ratios but not as accurate at lower signal-to-noise ratios. They study several coded modulation schemes this way. Among the results are the fact that TCM provides significant improvement in the error floor when detected differentially, and an asymmetry in the pairwise error event probability for 16 QAM     

Some new twists to problems involving the Gaussian probabilityintegral

Using an alternate form of the Gaussian probability integral discovered a number of years ago, it is shown that the solution to a number of previously considered communication problems can be simplified and, in some cases, made more accurate (i.e. exact rather than bounded). These problems include the evaluation of: (1) the bit-error probability of uncoded phase shift keying (PSK) with Costas loop tracking; (2) word-error probability of antipodal modulation in the presence of fading; (3) bit-error probability of coded M-ary PSK (MPSK) over the memoryless fading channel with given channel-state information; (4) conditional symbol-error probability of MPSK in the presence of carrier synchronization error; and (5) the average error probability for the binary additive white Gaussian noise (AWGN) intersymbol interference channel. Also obtained is a generalization of this new alternate form to the case of a two-dimensional Gaussian probability integral with arbitrary correlation which can be used to evaluate the symbol-error probability of MPSK with I-Q unbalance     

Error probability for coherent and differential PSK over arbitraryRician fading channels with multiple cochannel interferers

This paper discusses the performance of communication systems using binary coherent and differential phase-shift keyed (PSK) modulation, in correlated Rician fading channels with diversity reception. The presence of multiple Rician-faded cochannel users, which may have arbitrary and nonidentical parameters, is modeled exactly. Exact bit error probability (BEP) expressions are derived via the moment generating functions (MGFs) of the relevant decision statistics, which are obtained through coherent detection with maximum ratio combining for coherent PSK modulation, and differential detection with equal gain combining (EGC) for differential modulation. Evaluating the exact expressions requires a complexity that is exponential in the number of interferers. To avoid this potentially time-consuming operation, we derive two low-complexity approximate methods each for coherent and differential modulation formats, which are more accurate than the traditional Gaussian approximation approach. Two new and interesting results of this analysis are: (1) unlike in the case of Rayleigh fading channels, increasing correlation between diversity branches may lead to better performance in Rician fading channels and (2) the phase distribution of the line-of-sight or static fading components of the desired user has a significant influence on the BEP performance in correlated diversity channels     

Detection of decision error caused by the quantum noise in anoptical signal system

In this paper, a signal transmission and decision system in which an event of occurrence of decision error caused by the quantum noise can be detected is presented. The system is, in principle, constituted on the basis of a binary polarization-shift keying (PolSK) signal. Using retransmission technology for the error detection system, the decision error probability can be suppressed to 0. The binary PolSK system uses two polarization channels, and then the system has redundancy on channel efficiency. A more efficient signal system which uses only one polarization channel and is based on the binary phase-shift keying (PSK) signal is presented     

Bounds on the error probability of FSK and PSK receivers due to non-Gaussian noise in fading channels

This paper derives upper and lower bounds on binary error probability as a function of signal-to-noise ratio for several digital data systems operating over a complex Gaussian fading channel. Bounds of varying degrees of tightness are obtained by placing certain physically meaningful constraints on the allowable detected noise probability distributions. Detailed derivations are given for bounds corresponding to constraints on the "crest-factor" of the detected noise and on the ratio of peak noise power to average signal power. The calculations include the effects of diversity corn-billing and are applicable to frequency-shift keying (FSK), binary and quaternary phase-shift keying (PSK) using a pilot tone as reference, and binary and quaternary PSK using the previous signaling element as a phase reference. It is an interesting result of this paper that for moderate noise crest factors the upper and lower bounds can be rather close. In the particular case of nondiversity operation, for example, the lower bound actually becomes approximately equal to the upper bound at SNR's of30dB or greater for noises with a crest factor as high as20dB.     

Reliability Bounds for Coherent Communications with Maximum Likelihood Phase Estimation

This concise paper describes a new technique for upper bounding the performance of coherent binary phase-shift keyed (PSK) systems which derive a phase reference using one-shot maximum likelihood phase estimates. By performance, we mean any positive monotonically increasing function of phase error, such as error probability or power loss. A tight upper bound to the phase error cumulative distribution is shown to consist of the concave support to a previously derived Chernov bound. Performance measures appropriate for binary PSK systems are listed and evaluated with the new bound.     

Analysis of the pairwise error probability of noninterleaved codeson the Rayleigh-fading channel

The majority of previous analytical studies of signal-space coding techniques (includes trellis and block codes) on the Rayleigh-fading channel have assumed ideal interleaving. The effect of finite interleaving on the performance of different coding schemes has been studied only by simulation In this paper we first derive a maximum likelihood (ML) decoder for codewords transmitted over a noninterleaved Rayleigh flat fading channel, followed by an exact expression for the pairwise error event probability of such a decoder. It includes phase shift keying (PSK), quadrature amplitude modulation (QAM) signal sets, trellis coded modulation (TCM) and block coded modulation (BCM) schemes, as well as coherent (ideal channel state information) and partially coherent (e.g., differential, pilot tone, etc.) detection. We derive an exact expression for the pairwise event probability in the case of very slow fading-i.e., the fading experienced by all the symbols of the codeword is highly correlated. We also show that the interleaving depth required to optimize code performance for a particular minimum fading bandwidth can be approximated by the first zero of the fading channel's auto-correlation function     

具有连续相位的8PSK调制

连续相位的QPSK信号具有恒定包络,解决了传统QPSK信号由于相位跳变所带来的包络起伏问题,但其频带利用率没有8PSK高,为提高频带利用率,提出了连续相位8PSK(CP8PSK)调制。本文首先利用差分编码规则来表征8PSK信号一个符号周期的相位变化,进而将其表示为连续相位调制(CPM)的形式,再使用频率脉冲对其相位进行脉冲整形,最终得到具有连续相位的CP8PSK表达式。为了降低系统的整体复杂度,本文还对CP8PSK进行了Laurent分解。根据理论分析CP8PSK信号应当具有恒定包络,而且比连续相位的QPSK调制要有更高的带宽效率和更平滑的频谱,通过MATLAB进行仿真之后,得到的CP8PSK具有恒定包络,且带宽效率在同等情况下要高于整形的交错QPSK(SOQPSK)和8PSK,频谱也更加平滑,抗误码性能与理想8PSK相比损失也不大。      

Symbol Error Probabilities for M-ary CPFSK: Coherent and Noncoherent Detection

Continuous-phase frequency shift keying (CPFSK) is discussed and theoretical predictions for symbol error probabilities are derived, where the memory inherent in the phase continuity is used to improve performance. Previously known results concluded that binary CPFSK can outperform coherently detected PSK at high SNR. New results presented here show thatM-ary CPFSK outperforms more tranditionally usedM-ary modulation systems. Specifically, coherently detected quaternary CPFSK with a five-symbol interval decision can outperform coherent QPSK by 3.5 dB, and octal coherent CPFSK with a three- symbol decision can outperform octal orthogonal signaling by 2.6 dB at high SNR. Results for coherently detected and noncoherently detected CPFSK are derived. These performance improvements are estimates derived from symbol error probability upper bounds. Monte Carlo simulation was performed which then verified the results.     

大规模MIMO系统多用户PSK调制方案的优化

针对超可靠低时延通信短包传输特征,在大规模多输入多输出( Multiple-Input Multiple-Output,MIMO)上行链路系统中,利用较低导频开销来设计相移键控( Phase Shift Keying,PSK)调制方案,并对该方案进行优化兼顾无线链路传输的可靠性.首先,在接收端构建基于最小欧式距离的非相...     

PSK-Type Modulation with Overlapping Baseband Pulses

One of the most interesting challenges in the field of digital radio is to generate and transmit signals which meet the spectral requirements and which have high detection efficiencies. The spectral efficiency of PSK-type modulation with overlapping baseband pulses is known to be better than that with nonoverlapping pulses of the same form; but, to our knowledge, no analysis is presently available to determine their detection efficiency. In this paper a method has been given to evaluate the error probability performance of PSK-type modulation with baseband pulses of finite overlap and mutually independent samples. It is shown that the error probability can be computed with any desired accuracy. For BPSK and for some typical transmit and receive filters and for a transparent channel corrupted by additive Gaussian noise we compare the detection efficiencies when the baseband modulation pulses have zero and nonzero overlap and when the transmitted signal satisfies the same spectral requirement. The nonoverlapping rectangular signaling is shown to be superior to overlapping raised-cosine signaling, but the differential degradation is less than 0.8 dB if the twosided 99-percent bandwidth W99satisfies1.1/T leq W_{99}leq 1.6/T. The analytical results presented here for a binary system can be extended with minor modifications to anyM-ary PSK system,M > 2.     

A Digital Demodulator for PSK Signals

This paper describes a digital demodulator for phase-shift-keyed (PSK) signals in which the phase difference between the received signal and a carrier reference is found by measuring digitally the time interval between the zero crossings of the signal and the reference. In the case of coherent detection the reference is locked to one of theMpossible phases of the signal. The advantage of this demodulator is that bulky low-pass filters and delay lines as well as critical threshold devices can be dispensed with. On the other hand, digital measurement of the phase and the use of a finite-width sampling window lead to degradation of the error performance. This degradation is theoretically analyzed for both coherent and phase-comparison detection. The quantizing error proves to be small enough when the phase difference is coded into a 6-b binary number, and the theoretical results are in good agreement with measurements taken from an experimental phase-comparison demodulator for fourand eight-level PSK signals. The experimental demodulator is also described in the paper.     

Selection diversity for wireless communications in Nakagami-fadingwith arbitrary parameters

By means of analytical and numerical methods, the probability of error and the outage probability of a selection diversity RAKE receiver system employing direct sequence/code division multiple access (DS/CDMA) is derived. A noise-limited propagation environment is modeled as a Nakagami (1960)-fading channel with arbitrary fading parameters and unequal mean power at the receiver. New analytical expressions are derived for the average probability of error and outage probability. Binary detection schemes are considered including binary phase-shift keying (PSK) and frequency-shift keying (FSK). Both coherent and noncoherent detection is considered as well as identical and arbitrary fading. It is shown that the effect of arbitrary fading on system performance is significant and may not be ignored     

Coherent optical CDMA with limited phase excursion

We examine the bit error rate (BER) of the conventional matched-filter detector for an optical code division multiple access (CDMA) system employing coherent homodyne detection. We assume a phase shift keying (PSK) modulation format where the phase is modulated by one of two methods: (1) an external phase modulator or (2) injection locking. Phase excursion is limited to ±0.42 π when using injection locking. We examine the bit error rate performance for both external modulation and modulation of the injection current and find only a moderate penalty (0.55 dB) associated with the limited phase excursion     

Multi-user performance of direct-sequence CDMA using combinedbinary PPM/orthogonal modulation

A new modulation format is proposed for cellular code-division multiple-access (CDMA) communications where binary pulse position modulation (PPM) is embedded in the chip waveform and combined with orthogonal modulation using Walsh/Hadamard codes. Compared to the conventional CDMA using orthogonal codes, this scheme allows reduction in receiver complexity by lowering the modulation level for the second-stage orthogonal modulation. The staggered (half-chip) quadrature direct-sequence signaling is adopted to uniformly distribute the transmit power and allow noncoherent detection at the receiver because carrier phase tracking is not feasible because of the binary PPM, suitable for the reverse link in cellular networks. Statistics of inter-user interferences are characterized, and then derive the symbol error probability for the proposed M-ary modulation format. It is shown that the advantage in view of receiver complexity can be achieved without deteriorating the multi-user performance in terms of the number of users affordable at a specified error rate     

Direct-Sequence Spread Spectrum with DPSK Modulation and Diversity for Indoor Wireless Communications

Direct-sequence spread spectrum with differential phase shift-keying (DPSK) modulation and code-division multiple-access is a promising approach for wireless communications in an indoor environment, which is characterized in this paper by a Rayleigh-fading multipath channel. In this study, we consider two specific channel models having different path-delay distributions and average path power profiles. A star configuration, in which each user exercises average power control in transmitting to a central station, is the basic communication unit, which could be one cell in a cellular hierarchy. We obtain the performance of a single link between a user and its receiver in the central station, and consider two types of diversity, selection diversity and predetection combining to exploit the multipath. A similar system with coherent PSK (CPSK) modulation has been studied previously for one of the channel models considered here. For the same channel model, we show that the irreducible error probability with selection diversity is about half an order of magnitude higher when DPSK is used instead of CPSK. With predetection combining, the performance improves significantly in comparison with selection diversity as the diversity order increases. DPSK modulation with predetection combining is akin to coherent PSK with optimal maximal-ratio combining, but is simpler to implement. The performance with selection diversity for a second channel model, which is based on measurements in an office building, is not significantly different. This indicates that the spreadspectrum approach is rather robust to the path-delay distribution and average path-power profile.     

Bit error probability for coherent M-ary PSK systems

A simple technique for evaluating the bit-error probability of coherent M-ary phase-shift keying (PSK) with any bit-mapping is proposed. Closed-form expressions are given in terms of error functions for half- and quadrant-plane probabilities in the decision space, avoiding the numerical evaluation of complicated integrals that occurs in the direct method. Bit error probability expressions for M-ary PSK with Gray, natural binary, and folded binary bit-mappings are derived     

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