Distribution of instantaneous frequency for signal plus noise

A concise formula is derived for the probability distribution of the instantaneous frequency of an arbitrary bandpass signal plus Gaussian noise. The results are presented in terms of Marcum'sQ-functions, with well-known properties. The results are applicable in the performance analysis ofn-ary FM and PM data transmission systems. Illustrative examples of the application of the formula are worked out for binary FSK.     

Decision-Directed Automatic Gain Control for MAPSK Systems

An automatic gain control (AGC) loop is presented for use withM-ary amplitude- and phase-shift keying (MAPSK) systems. The gain control amplifier is regulated by an error signal formed by the difference between the estimated amplitude level and the received amplitude level. The AGC performance is thus independent of the short-term average received signal energy. AGC loop analysis and simulation is presented forM-ary amplitude-shift keying (MASK) and quadrature amplitude-shift keying (QASK). The AGC is shown to have a negligible degradation on the symbol probability of error for most practical cases. A generalized AGC for an arbitrary MAPSK system is also presented.     

M-ary FSK Performance for Coherent Optical Communication Systems Using Semiconductor Lasers

This paper describes the design and performance of anMary frequency shift keyed (FSK) signaling and demodulation scheme for an optical communication system using semiconductor lasers and heterodyne detection. Frequency or phase noise in semiconductor lasers causes spectral spreading, producing a nonzero linewidth laser signal. This degrades communication performance when compared to a system using an ideal laser with zero linewidth. We present estimates of the bit error rate (BER) performance ofM-ary frequency shift keying (FSK) with noncoherent demodulation in the presence of white Gaussian frequency noise and additive channel noise. This is typical of an optical system using semiconductor lasers and heterodyne detection. Estimates use the union-Chernoff bound with a simplified channel model to predict the effects of frequency noise. Two effects of frequency noise are identified: signal attenuation or suppression, and crosstalk. These cause an offset in the BER curve from the BER in the absence of frequency noise, and an error rate floor, respectively. The error rate floor is lower than previously predicted. When performance is not crosstalk limited,M-ary FSK is found to perform better than binary FSK with the same system bandwidth constraints, as would be predicted if ideal lasers are used. Theoretical results are compared with Monte Carlo simulations of the system.     

Error Analysis for Noncoherent M-ary Orthogonal Communication Systems in the Presence of Arbitrary Gaussian Interference

A general error analysis for the noncoherentM-ary orthogonal keyed receiver in the presence of arbitrary Gaussian interference is presented. Relations to well-known formulas which apply to the broadband white Gaussian noise environment are given. Numerical results for various special interference situations are presented, and the impact of unequal values of the noise power in the different receiver channels on the error performance is discussed.     

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.     

A Spectral Analysis of M-ary Direct Sequence Spread-Spectrum Multiple Access Communication Systems

This paper presents the power spectrum of the transmitted signal in a synchronous spread-spectrum communication system in which the users' information symbol sequences are encoded intoM-ary channel symbol sequences. Furthermore, when maximal-length shift register sequences are used as the spreading code sequences of the system, the average power spectrum over all possible sets of the allowable simultaneous users is presented. It is shown that distribution of the spectrum is influenced considerably by the spreading code and the channel symbol sequences.     

User-Capacity Maximization in Synchronous CDMA Subject to RMS-Bandlimited Signature Waveforms

Maximum Throughput of FHSS Multiple-Access Networks Using MFSK Modulation Kwonhue Choi and Kyungwhoon Cheun Optimum values for the modulation order$M$, code rate$r$, and the number of frequency-hop slots$q$maximizing the network throughput are obtained based on simulations for frequency-hopped spread-spectrum multiple-access networks, where$L Q$-ary Reed–Solomon (RS) code symbols are transmitted per hop, and each$Q$-ary RS code symbol is transmitted using$log_M Q$$M$-ary frequency-shift keying modulated signals. Network throughput is evaluated under additive white Gaussian noise and Rayleigh fading channels. For the case when the received RS symbol is not interfered by multiple-access interference (MAI), a closed-form expression for the symbol-error probability is derived, and for the case when the symbol is interfered by MAI, simulated symbol-error probabilities are used. It is shown that the optimum$M$is four or eight, irrespective of the channel environment and the number of users. The optimum code rate is determined primarily based on the channel environment, and does not show much dependence on$M$or$Q$. It is also shown that for the case of synchronous hopping under Rayleigh fading at high signal-to-noise ratios, the difference in instantaneous power among the interfering users significantly improves the performance, compared with the case when there is no fading. We also consider the case when the receiver erases the symbols that are interfered and compare the performance to the case of the hard-decisions receiver.     

Continuous Phase Modulation--Part II: Partial Response Signaling

An analysis of constant envelope digital partial response continuous Phase modulation (CPM) systems is reported. Coherent detection is assumed and the channel is Gaussian. The receiver observes the received signal over more than one symbol interval to make use of the correlative properties of the transmitted signal. The Systems areM-ary, and baseband pulse shaping over several symbol intervals is considered. An optimum receiver based on the Viterbi algorithm is presented. Constant envelope digital modulation schemes with excellent spectral tail properties are given. The spectra have extremely low sidelobes. It is concluded that partial response CPM systems have spectrum compaction properties. Furthermore, at equal or even smaller bandwidth than minimum shift keying (MSK), a considerable gain in transmitter power can be obtained. This gain increases withM. Receiver and transmitter configurations are presented.     

Error-Correcting Codes Against the Worst-Case Partial-Band Jammer

This paper provides performance analyses of a broad spectrum of error-correcting codes in an antijam communication system under worst-case partial-band noise jamming conditions. These analyses demonstrate the coding advantages available for systems operating with and without frequency diversity. Utilizing both the exact approach (where possible) and upper-bounding approaches (Chernoff and union bounds), the decoded bit error rates for typical error-correcting codes (binary andM-ary, block and convolutional) have been obtained, and these codes have been compared according to theE_{b}/N_{0}required to achieve a bit error rate of 10^-5. The best performance is achieved with the use ofM-ary signaling and optimum diversity withM-ary codes, such as Reed-Solomon block codes, dual-kconvolutional codes, convolutional orthogonal codes, or concatenated codes.     

An Error Probability Formula for M-ary DPSK in Fast Rician Fading and Gaussian Noise

A formula for the symbol error probability is derived which applies to differential detection ofM-ary phase-shift keying (MDPSK) in fast Rician fading and white Gaussiau noise. This formula is an extension of a result already known for MDPSK in Gaussian noise interference.     

Performance of Reed-Solomon Coded Frequency-Hop Spread-Spectrum Communications in Partial-Band Interference

This paper is concerned with the performance of a Communications system which utilizes frequency-hop spread spectrum, diversity transmission, Reed-Solomon coding, and parallel error-correction and erasure-correction decoding. Both binary signaling andM-ary orthogonal signaling are considered. The goals are twofold. First, it is desirable to provide good performance in partial-band Gaussian noise interference by use of coding and diversity with an efficient error-correction algorithm. Second, it is necessary to totally neutralize narrow-band interference (regardless of the power level or statistical distribution of the interference) in order to have an effective spread-spectrum system. Through an analysis of the effects of partial-band interference on a frequency-hop spread-spectrum system with diversity, it is shown that the use of ReedSolomon coding with a parallel errors and erasures decoding algorithm accomplishes these goals. The paper also investigates the accuracy of the Chernoff bound as an approximation to the true performance of a frequency-hop spreadspectrum communication system with diversity; side information,M-ary orthogonal signaling, and Reed-Solomon coding. The performance results presented in the paper are based on analysis and computer evaluation. Approximate results based on the Chernoff bound are also given. It is shown that the Chernoff bound forM-ary orthogonal signaling gives a very poor approximation for many cases of interest. This is largely due to the looseness of the union bound.     

Performance of Non-coherent MFSK with Selection and Switched Diversity Over Hoyt Fading Channel

A closed-form expression of cumulative distribution function (CDF) of the instantaneous signal to noise ratio (SNR) in Hoyt fading channel is derived. This CDF and associated formulas are then used to find out the error probability of non-coherent M-ary frequency shift keying with multichannel reception. Simple finite-range integral expression for the symbol error probability (SEP) with selection diversity is found through CDF method. Next, closed-form expressions of moment generating functions (MGF) are presented for the switched diversity case and SEP values are calculated using the derived MGFs. Some other performance parameters like, outage probability and average SNR with switched diversity, are provided. In addition, analytic frameworks are presented for calculation of optimum switching thresholds that ensure minimum outage probability or minimum SEP. The analysis is quite general in the sense that it covers switch and stay combining and Rayleigh fading as special cases.     

Transmission Characteristics of an M-ary Coherent PSK Signal Via a Cascade of N Bandpass Hard Limiters

This paper provides a general analysis of the transmission characteristics of a coherent PSK signal, where anM-ary coherent signal is transmitted via a repeater system composed of a cascade ofNbandpass hard limiters. The probability density function of a composite phase of the signal and noise over the system is newly derived to obtain an error probability. In addition, the comparison with the repeater system composed of a cascade ofNlinear amplifiers is made to clarify the features of the transmission characteristics. It is found that the probability density function of the composite phase over the system is symmetric about each input carrier-to-noise power ratio (CNR), and it reduces to some well-known results. It is also shown that for a reasonably large input CNR in each stage, the presence of the bandpass hard limiter (BPHL) provides some improvement, but that for small input CNR it causes degradation in performance.     

The structure of least-mean-square linear estimators for synchronousM-ary signals (Corresp.)

Several authors have shown that the structure of the least-mean-square linear estimator of the sequence of random amplitudes in a synchronous pulse-amplitude-modulated signal that suffers intersymbol interference and additive noise is a matched filter whose output is periodically sampled and passed through a transversal filter (tapped delay line). It is our purpose in this paper to generalize this result to synchronousm-ary signals (e.g., FSK, PSK, PPM signals). We prove that the structure of the least-mean-square linear estimator of the sequence of random parameters in a synchronousm-ary signal, which suffers intersymbol interference and additive noise, is a parallel connection ofmmatched filters followed by tapped delay lines. A similar structure is derived for the continuous waveform estimator of a synchronousm-ary signal. Finally, we present a structure for estimation-decision detection of synchronousm-ary signals, which is based on least-mean-suare linear estimates of aposterioriprobabilities.     

On Nonuniform Windowing M-ary FSK Data in a DFT-Based Detector

Nonuniform amplitude windowingM-ary frequency shiftkeying (FSK) data prior to demodulation reduces the crosstalk normally caused by Doppler and oscillator drift. A major disadvantage of such nonuniform windowing is the loss in signal detectability as a result of the mismatch between the nonuniform windowed signal and the uniform windowed detectors. This paper is concerned with the tradeoff of nonuniform windowing to combat frequency offset degradation and signal detectability losses caused by the use of such windows in a DFT (discrete Fourier transform)-based detector of noncoherentM-ary FSK. What is shown here is that if a frequency control system can maintain frequency to within a certain deviation (which depends on error rate and nonuniform window), nonuniform windowing is not warranted; on the other hand, if the frequency deviation becomes too large, nonuniform windowing is advised. A technique is developed that will determine this crossover deviation.     

PePerformance of Coherent M-ary PSK Systems in an Impulsive and Gaussian Noise Environment

The general probability of error expressions of coherentM-ary PSK (M = 2, 4, 8, 16) systems in the presence of both impulsive and Gaussian noise are derived. This work is an extension of our paper related to BPSK and DPSK systems in a complex interference environment [1]. The presented impulsive and Gaussian channel disturbance is a first-order approximation to operational multichannel satellite and terrestrial microwave systems in which, in addition to front-end Gaussian noise, out-of-band intermodulation noise may be present. Our analysis contains an extension of the method developed by Bello and Esposito [2], [3], to include the Gaussian as well as the impulsive noise environment. The numerical results show that a well defined threshold region exists, above which the effect of the impulsive noise on the system performance is predominant.     

Maximum likelihood synchronization for OFDM using a pilot symbol:analysis

A performance analysis of algorithms for maximum likelihood estimation of channel parameters for orthogonal frequency-division multiplexing packet detection and synchronization is presented. The detection and synchronization algorithms, which are based on the use of a pilot symbol, are described in Coulson (2001). The performance analyses concentrate on operation in additive white Gaussian noise channels, and the accuracy of these analyses are demonstrated using experimental and simulation data. Methods to extend these analyses to frequency flat multipath fading channels are presented     

Impact of large Doppler on error performance of FH/MFSK with RS orBCH coding in Rayleigh and Rician fading

The degradation of performance caused by Doppler shift to frequency hopped (FH)/M-ary frequency shift keying (MFSK) Reed-Solomon (RS) coded signal over a Rayleigh and Rician channel is analyzed. The receiver employs a digital processing scheme, consisting of an analog-to-digital (A/D) converter followed by quadrature decomposition and complex-valued envelope discrete Fourier transformation (DFT). Predecoder symbol error probability and post-decoder word error probability are presented as a function of Doppler shift, channel randomness parameter, and the symbol energy-to-noise ratio. The noise is assumed to be white and Gaussian distributed. Results show that for a typical symbol error rate of 10^-3, the margin for 8-ary uncoded transmission must be increased by 8 dB to account for Doppler in a Rician fading channel     

Analytical performance evaluation of the OFDM systems in the presence of jointly fifth order nonlinearity and phase noise

This paper presents an exact theoretical analysis of the performance degradation in an orthogonal frequency division multiplexing (OFDM) system when the signal including phase noise is passed through a nonlinear circuit such as high power amplifier (HPA). This circuit is modeled as a fifth order memory-less nonlinear polynomial model (5th order MLNPM). The nonlinear model is derived from important electrical parameters such as gain, 1-dB compression and 3rd order intercept point. Theoretical analysis shows that the detected data symbol at the receiver consists of attenuated version of the original transmitted data symbol, common phase error (CPE), inter-sub-carrier interference (ICI), third and fifth order intermodulation (IM) components. The analytical expressions for intermodulation noise term are derived using combinatorial methods. By use of the derived expressions, a closed-form output signal to noise ratio (SNR), degradation factor (DF) and probability of error can be evaluated theoretically. For verifying the accuracy of our analysis, comparisons between the theoretical and simulated results with electrical parameter of an actual and applicable HPA are presented. The comparisons show that bit error rate (BER) of analytical results is closely match with simulation results for OFDM system using M-QAM modulation.     

Delay-and-multiply clock regeneration in APD-based direct-detectionoptical OOK communication systems

A clock recovery scheme for direct-detection optical on-off keying (OOK) communication systems with nonreturn-to-zero pulse shaping is proposed and investigated. In the suggested model, the optical field is detected with the aid of an avalanche photodiode (APD) photodetector, which is followed by a clock regeneration subsystem. The proposed clock recovery subsystem consists of a delay-and-multiply nonlinearity followed by a conventional phase-locked loop (PLL), tuned to the slot frequency of the desired optical OOK signal. Performance of the proposed system is obtained in terms of the signal-to-noise ratio (SNR_L) of the linearized PLL device (or, equivalently, the inverse of phase, or timing, error variance) when background noise and receiver thermal noise are present. Numerical results are presented in order to explain the influence of noise processes on the performance of the proposed clock recovery subsystem. The performance of this system is also compared to that of an early-late gate and square-law symbol synchronizers