Differential Phase-shift Keying Systems Research Articles

Performances of DPSK and FSK CDMA systems with complex signature sequences

This paper investigates the performance of direct?sequence code?division multiple?access (CDMA) communication systems in Gaussian noise channels using binary and M?ary noncoherent signaling schemes with complex signature sequences. Differential?phase?shift?keyed (DPSK) signaling with differentially coherent demodulation and frequency?shift?keyed (FSK) signaling with noncoherent demodulation are considered. Upper and lower bounds are presented for the probability of bit error (p.b.e.) of binary DPSK and binary FSK systems when the number of users is small. Simulation and Gaussian approximation are used to obtained the p.b.e. when the number of users is large. Two types of complex sequences (FZC and 4?phase sequences) and one type of binary sequences (Gold sequences) are used for evaluating numerical results. Results show that complex sequences outperform binary sequence when the number of users is small. However, as the number of users gets large, all sequences have similar performances. These suggest that complex sequences should be used when the number of users is small, but binary sequences should be used when the number of users is large, as binary sequences are easier to generate.

Compensating frequency drift in DPSK systems via baseband signal processing

A new baseband signal processing method for compensating frequency shift in differential phase-shift keying (DPSK) systems is introduced. This method consists of a signal processor for the initial acquisition of frequency shift and a simple adaptive equalizer for tracking. The former is based on the observation that the effect of frequency shift can be eliminated by using boundary values of the received baseband signal between symbol periods. The latter is a single tap equalizer employing the least mean-square (LMS) adaptation algorithm. Computer simulation results demonstrate that the proposed frequency shift compensation technique outperforms existing methods, and works well for a wide range of frequency shift.

Optically implemented DPSK and CPFSK systems: effect of post-detection filtering

Results for the sensitivity of preamplifier differential phase-shift keying (DPSK) and continuous phase-shift keying (CPFSK) systems with electronic post-detection filtering are presented based on a rigorous model which is outlined. It takes into account amplifier and laser phase noise. The best sensitivities for a 10/sup -9/ error probability are 20 (DPSK) and 36 (CPFSK) received photons. It is found that the CPFSK system can tolerate significant phase noise by increasing the modulation index and the bandpass filter bandwidth. A linewidth of 5 times the bit-rate causes 4.3 dB penalty using polarization control and for a modulation index of 51. DPSK systems cannot tolerate linewidths larger than about 1% of the bit-rate.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Reduction of AM-induced penalty in DPSK receivers by sum-square demodulation

A DPSK (differential phase shift keying) demodulator which is insensitive to the amplitude modulation induced by semiconductor optical amplifier phase modulators is proposed. The demodulator consists of only two additional power dividers/combiners, compared to a traditional DPSK demodulator. Analysis shows that the receiver penalty caused by amplitude modulation can be reduced from 2-4 dB to zero. The demodulator is demonstrated in a 2.5-Gb/s DPSK system experiment using an optical amplifier as phase modulator. >

Chromatic dispersion limitations for FSK and DPSK systems with direct detection receivers

Chromatic dispersion limitations for frequency-shift keying (FSK) and differential phase-shift keying (DPSK) systems using narrow-linewidth lasers and direct-detection receivers are discussed. The limitations are found to depend strongly on the receiver configuration. The receiver must include an optical frequency discriminator, such as a Mach-Zehnder interferometer, and either a balanced photodetector pair or a single photodetector at the interferometer output. For transmission at 1550 nm over 1310-nm optimized single-mode fiber, the distance for 1-dB eye closure penalty at 10 Gb/s ranges from 20 to 70 km, depending on the modulation format and the receiver configuration. >

The effect of crosstalk and phase noise in multichannel coherent optical DPSK systems with tight IF filtering

Results for two-channel differential-phase-shift-keying (DPSK) systems using finite integrator and raised cosine response IF filters are presented. The sensitivity of an optical receiver in a two-channel DPSK system is studied. The results are compared with previous work in the limit of no phase noise and it is shown that the agreement is good. The penalty due to crosstalk for different linewidths and filter shapes is computed, and it is shown that the minimum channel spacing is a few bit rates for an ideal integrator IF filter and is larger for an IF filter with a raised cosine impulse response. The penalty is increased somewhat by phase noise. >

Bit error rate performance of pi /4-DQPSK in a frequency-selective fast Rayleigh fading channel

The bit error rate (BER) performance of pi /4-differential quadrature phase shift keying (DQPSK) modems in cellular mobile communication systems is derived and analyzed. The system is modeled as a frequency-selective fast Rayleigh fading channel corrupted by additive white Gaussian noise (AWGN) and co-channel interference (CCI). The probability density function of the phase difference between two consecutive symbols of M-ary differential phase shift keying (DPSK) signals is first derived. In M-ary DPSK systems, the information is completely contained in this phase difference. For pi /4-DQPSK, the BER is derived in a closed form and calculated directly. Numerical results show that for the 24 kBd (48 kb/s) pi /4-DQPSK operated at a carrier frequency of 850 MHz and C/I >

Optical heterodyne image-rejection receiver for high-density optical frequency division multiplexing system

An optical heterodyne image-rejection receiver (IRR) for high-density optical frequency division multiplexing (OFDM) systems is described. The IRR was realized using balanced receivers, which showed more than 18-dB suppression over the 1.5-3.0-GHz IF region. Measured crosstalk penalties in a two-channel 560 Mb/s differential phase-shift keyed (DPSK) heterodyne optical communication system were realized for the first time. The crosstalk penalties in an OFDM system are estimated theoretically with and without the IRR. The required channel spacing and number of channels that can be accommodated in the 10-nm tuning range of the local laser are presented. A particular configuration of the IRR, its operation, and its performance limitations are discussed. The experimental results for image-rejection reception in a two-channel 560-Mb/s DPSK system are also given. Crosstalk penalties are estimated experimentally and compared to the theoretical calculation. Since the conventional configurations of the IRR are very sensitive to the polarization fluctuation of the transmitted signals, polarization-insensitive IRRs are proposed and their features are considered.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Influence of laser phase on 400-Mbit/s coherent optical DPSK system

The influence of laser phase noise on a 400-Mb/s optical DPSK (differential phase-shift keying) system is experimentally investigated with linewidths ranging from 1.2 MHz to 8 MHz. This range corresponds to linewidth to bit rate ratios epsilon of 0.33-2%. The system performance with these nonzero linewidths is evaluated against a negligible linewidth performance baseline. The sensitivity degradation at a bit error rate of 10/sup -9/ increases from 1.8 to 7 dB as epsilon is increased from 0.33-1%. When epsilon is increased beyond 1%, bit error rate floors higher than 10/sup -9/ develop. These findings agree well with the existing theories and allow the generalization of these results to other bit rates, as well as establishing practical criteria for lasers to be used in DPSK systems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Offset DPSK with differential phase detector in satellite mobile channel with narrow-band receiver filter

An expression is derived for the error probability of M-ary offset differential phase-shift keying (DPSK) with the differential phase detector and narrowband receiver filter in the satellite mobile (Rician) channel, which includes as special cases the Gaussian and land mobile (Rayleigh) channels. The error probability is computed as a function of various system parameters for M=2, 4, and 8 symbols and third-order Butterworth receiver filter. Both symmetric and conventional DPSK systems are considered. The optimal normalized bandwidth is close to 1.0. Symmetric and conventional DPSK differ significantly in error probability only for M=2 and in the lower range filter bandwidth. In most cases, symmetric DPSK outperforms conventional DPSK. This was particularly noted when the time delay between the specular and diffused signal components was taken into account.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Spread spectrum mobile radio, 1977-1982

In 1977, Cooper and Nettleton proposed a spread spectrum mobile radio system using frequency-hopping multiple access, Hadamard coding for error correction, and differential phase shift keyed (DPSK) modulation, and they claimed higher spectral efficiency than frequency-division (FD) FM systems. Subsequent analyses showed that the DPSK system has a spectral efficiency of 8.4 percent as compared to the efficiency of unity for a FD-FM system with 30-kHz channel spacings. Goodman et al. suggested an alternative modulation scheme in 1980, using multilevel frequency shift keying (MFSK), and a 30 percent efficiency was obtained. The research results in spread spectrum mobile radio are summarized, and the areas requiring further investigation before a commercial system can be implemented are identified.

Correction to 'Error Performance of Differentially Coherent Detection of Binary DPSK Data Transmission on the Hard-Limiting satellite Channel'

The error performance of differentially coherent detection of a binary differential phase-shift keying (DPSK) system operating over a hard-limiting satellite channel is derived. The main objective is to show the extent of error rate degradation of a DPSK system when a power imbalance exists between the two symbol pulses that are used in a bit decision interval. Consideration is also given to the DPSK error rate performance for the special case of {\em uncorrelated} uplink and {\em correlated} downlink noises at the sampling instants in adjacent time slots. Error probabilities are given as functions of uplink signal-to-noise ratio (SNR) and downlink SNR with different levels of SNR imbalance and different downlink SNR and uplink SNR as parameters, respectively. Our numerical results show that 1) as long as the symbols are equiprobable, the error probability is not dependent upon the downlink noise correlation, regardless of whether there is a power imbalance; 2) error performance is definitely affected by the power imbalance for all cases of symbol distributions; and 3) the error probability does depend upon downlink noise correlation for all levels of power imbalance if the symbol probabilities are not equal.

Error performance of differentially coherent detection of binary DPSK data transmission on the hard-limiting satellite channel

The error performance of differentially coherent detection of a binary differential phase-shift keying (DPSK) system operating over a hard-limiting satellite channel is derived. The main objective is to show the extent of error rate degradation of a DPSK system when a power imbalance exists between the two symbol pulses that are used in a bit decision interval. Consideration is also given to the DPSK error rate performance for the special case of {\em uncorrelated} uplink and {\em correlated} downlink noises at the sampling instants in adjacent time slots. Error probabilities are given as functions of uplink signal-to-noise ratio (SNR) and downlink SNR with different levels of SNR imbalance and different downlink SNR and uplink SNR as parameters, respectively. Our numerical results show that 1) as long as the symbols are equiprobable, the error probability is not dependent upon the downlink noise correlation, regardless of whether there is a power imbalance; 2) error performance is definitely affected by the power imbalance for all cases of symbol distributions; and 3) the error probability does depend upon downlink noise correlation for all levels of power imbalance if the symbol probabilities are not equal.

Hard-limited versus linear combining for frequency-hopping multiple-access systems in a Rayleigh fading environment

In comparing two proposed frequency-hopping mobile radio systems for digitized speech, Goodman et al. have observed that the system employing multiple frequency-shift keying (MFSK) can accommodate many more users than the one with differential phase-shift keying (DPSK). Besides the difference in modulation methods, the MFSK system uses hard-limited combining while the DPSK one uses linear combining. Upper bounds are obtained on the probability of error for DPSK systems with hard-limited combining and linear combining. These bounds suggest that the DPSK system with hard limiters can support about twice as many users as the original one.

Analysis of an underwater DPSK telemetry experiment

An experimental DPSK (differential phase shift keyed) system was used to transmit messages in Dabob Bay, Washington. The 75-kHz carrier was modulated by a 48-bit binary encoded block message. A bit error rate of less than 1% was achieved with a projector-to-hydrophone range of 1000 yards with a signal-to-noise ratio around 12 dB. Results of a lab simulation and theoretical considerations indicated that a 1% rate should occur at a signal-to-noise ratio around 6 dB. Possible causes for this discrepancy, along with effects due to Doppler and multipath, will be discussed. [Work supported by U. S. Naval Torpedo Station.]

Analysis of the fundamental error statistics in DPSK systems using a Markov chain model (Corresp.)

Finite-state Markov chain models are proposed to represent the process of the occurrence of errors in differential phase-shift-keying (DPSK) systems and also in coherent phase-shift-keying (CPSK) systems with differential coding-and-decoding schemes. A simple and general formula is derived for the probability P(m,n) of the occurrence of m errors in a sequence of n digits which is the fundamental error statistic required to evaluate random-error-correcting codes applied to these channels.

On the Binary DPSK Communication Systems in Correlated Gaussian Noise

Using the recently developed probability density function we obtain "directly" the error rate expressions for the binary differential phase-shift keyed (DPSK) systems when the noise values at the sampling instants in adjacent time slots are statistically dependent. Two cases are considered: One corresponding to equal SNR at each of the two sampling instants, and the other to unequal SNR's. The consideration of the former case, together with the assumption of unequal a priori symbol probabilities P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> and P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> results in an error rate expression <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P_{E} =1/2[1 + (P_{0} - P_{1})\rho] \exp (-h^{2})</tex> where ρ is the noise correlation coefficient, and h <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> is the SNR. This expression shows clearly why P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</inf> is independent of noise correlation when the source symbols are equi-probable provided intersymbol interference is assumed absent. We then obtain the error probability expression in terms of unequal SNR's (at the two sampling instants) and the correlation coefficient ρ. Since intersymbol interference in a binary DPSK system gives rise to unequal SNR's, this expression provides a useful formula for estimating the system performance under such circumstances.

Unified Analysis of a Class of Digital Systems in Additive Noise and Interference

A unified approach is presented for evaluation of the error probabilities of a class of digital communications systems in additive noise and interference. This class of systems includes coherent systems such as M -ary amplitude-shift keying (ASK), M -ary phase-shift keying (PSK), and M -ary amplitude-and-phase keying (APK); it also includes differential coherent systems such as binary differential PSK (DPSK). The noise is not necessarily Gaussian. The interference can be intersymbol interference, co-channel interference, adjacent-channel interference, any of their linear combinations, or intermodulation prodducts at the output of some nonlinear device. This approach essentially expands the characteristic function of the interferences into a power series so that the desired error probability can be evaluated as the sum of terms representing perturbations around the error probability due to additive noise alone. Bounds on three kinds of truncation errors, which are simple and applicable to all aforementioned digital systems, are obtained. As a result, any desired accuracy in the evaluation of the error probabilities can be achieved with this approach. In the special case in which the noise is Gaussian, explicit bounds on truncation errors are also obtained. Examples are given to illustrate how the unified analysis can be applied to evaluate the error probabilities of various digital systems. More specifically, the combined effects of Gaussian noise, intersymbol interference, and co-channel interference on the error performance of M -ary coherent PSK and APK (MCPSK and MCAPK) systems are computed. The probability of error of a binary DPSK (BDPSK) system in the presence of Gaussian noise and intersymbol interference is analyzed. The intermodulation products at the output of a hardlimiter are also determined.

Error Probabilities Due to Impulsive Noise in Linear and Hard-Limited DPSK Systems

A method previously presented by the authors for the evaluation of error probabilities in digital systems when impulsive noise is the main cause of incorrect decisions is here applied to differential phase-shift keying (DPSK) modems. Specifically, the receiver impulsive characteristic, which is proportional to the error rate, is evaluated for binary DPSK systems both in the linear and hard-limited modes of operation. Two encoding systems are considered, in-phase encoding and quadrature encoding, and it is shown that they yield essentially the same performance, at least when the binary symbols are equally likely. The results are compared with the performance of phase-shift keying (PSK) and it is found that, in the presence of impulsive noise, DPSK systems have, for the same SNR, an error rate which is nearly twice the error rate obtained for PSK. However, the dependence of error rate on SNR is generally a slowly decreasing function so that a considerable improvement in SNR is required to improve performance.

Performance Characteristics of Adaptive/Self-Synchronizing PSK Receivers Under Common Power and Bandwidth Conditions

An analytical and numerical investigation of the performance characteristics of partially coherent system techniques which consist of 1) the squaring-tracking loop, 2) the pilot-tone tracking loop, and 3) the differential phase-shift keying (DPSK) technique is discussed. Performance characteristics (error probabilities) are obtained under a unified receiving systems framework, with commonality expressed in terms of the receiver data and reference acquisition channel bandwidths and equal total transmitted power conditions. The modulation addressed is binary phase-shift keying (PSK), operating over a Gaussian noise channel with nonstationary phase characteristics. System performance is expressed analytically, computed numerically, and illustrated graphically with the following conclusions. The squaring-tracking loop technique provides the best performance and closely approximates coherent PSK performance when reference smoothing over several bauds is employed. The performance of the squaringtracking loop system and the DPSK system are comparable within a decibel for tracking loop averaging over 1 baud. Performance of the pilot-tone system depends critically upon the tracking loop bandwidth and the power allocation between pilot carrier and information sidebands. In no case considered does the pilot-tone system outperform the squaring-tracking loop system. On the basis of minimum error rate, the systems can be ranked as follows: 1) the squaring-tracking loop system, 2) DPSK, and 3) the pilottone system. At large signal-to-noise ratios, pilot-tone systems can outperform DPSK.