M-ary Differential Phase-shift Keying Research Articles

Self-Coherent Multisymbol Detection of Optical Differential Phase-Shift Keying

This paper treats the recently emerging self-coherent multisymbol decision-feedback-aided detection techniques for optical differential phase-shift keyed (DPSK) transmission based on both an optical preprocessing approach and an electronic postprocessing approach. We present in detail i) the generation of a synthetic low phase-noise effective local oscillator out of the modulated optical data itself, and its estimation theory interpretation; ii) the role of polyphase (interleaved) DPSK in the optical preprocessing approach in easing the decision feedback realization requirements; iii) detection of M-ary DPSK modulation formats for general M, and differential quadrature phase-shift keying in particular; iv) three alternative integrated-optoelectronic receiver implementations for the optical preprocessing approach detailing the structures of the interferometric front-end and the high-speed electronic analog and digital building blocks; and v) the principle, and alternative implementations, of the digital postprocessing approach to self-coherent detection. We finally compare the capabilities of the emerging self-coherent detection and digital coherent detection techniques.

Proposal for Beyond 100-Gb/s Optical Transmission Based on Bit-Interleaved LDPC-Coded Modulation

An iterative bandwidth-efficient coded modulation scheme based on bit-interleaving low-density parity-check (LDPC) codes, and M-ary differential phase-shift keying is proposed. A bit-interleaved LDPC-coded scheme, carrying 3 bits/symbol, provides the coding gain of 8.3 dB at a bit-error rate (BER) of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-7</sup> . The expected coding gain at BER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-12</sup> is 12.8 dB. Possible applications include 100G Ethernet, and high-speed (>100 Gb/s) long-haul transmission

Generalized data-aided multi-symbol phase estimation for improving receiver sensitivity in direct-detection optical m-ary DPSK

We present a generalized framework of data-aided multi-symbol phase estimation (MSPE) for improving the receiver sensitivity of direct-detection optical m-ary differential phase-shift keying (DPSK) through the extraction of a more accurate phase reference. Derivations of the data-aided MSPE algorithms for quaternary DPSK (DQPSK), 8-ary DPSK, m-ary DPSK, and DPSK/ASK are provided. Simulations show that receiver sensitivity improvements of over 2 dB can be obtained with the data-aided MSPE, enabling the performances of direct-detection m-ary DPSK signals to approach those of coherent homodyne-detection without resorting to an optical local oscillator. Performance improvements in nonlinear transmission are briefly discussed, and an electronic nonlinear phase shift compensation scheme is introduced for DPSK/ASK. Also presented is a simple yet universal receiver platform for m-ary DPSK consisting of just one pair of optical I/Q demodulators and a digital signal processing unit.

New performance results for MDPSK with noncoherent diversity in fast Rayleigh fading

The error performance for M-ary differential phase-shift keying (MDPSK) with non-coherent diversity in fast fading was recently tackled, ending up with a very general formula applicable to various operational environments. The only drawback of this formula is its expression with a double integral which, alongside a singularity existing in the integrand, poses considerable burdens in numerical calculation. In this correspondence, by restricting to the case of independent fast Rayleigh fading channels with equal power, we show how to obtain a much simpler solution with only one integral

Theoretical sensitivity of direct-detection multilevel modulation formats for high spectral efficiency optical communications

Sensitivities of several direct-detection multilevel modulation formats, including M-ary differential phase-shift keying (M-DPSK), M-ary differential amplitude-phase-shift keying (M-DAPSK), and M-ary differential polarization-phase-shift keying (M-DPolPSK) are systematically calculated. The theory is based on a unified mathematical framework for direct-detection receivers using optical delay interferometers and balanced detectors. Results quantitatively elucidate the tradeoffs between these direct-detection multilevel modulation formats as well as the classic multilevel modulation format, M-ary amplitude-shift keying (M-ASK). Although the conventional bit error rate estimation method based on the eye Q-factor with Gaussian approximation is not accurate enough for DPSK and DQPSK, it is found to be reasonably accurate for M-DPSK with M>8 and in M-DPolPSK.

"Turbo DPSK" using soft multiple-symbol differential sphere decoding

Coded interleaved differential M-ary phase-shift keying (M-DPSK) with iterative decoding, the so-called "Turbo DPSK," is known as a power-efficient transmission format. Due to the rotational invariance of DPSK, it particularly enables detection without channel state information (CSI). However, the soft-input soft-output (SISO) component decoder for DPSK is the computational bottleneck if performance close to the ideal case of perfect CSI is desired. In this paper, we take a fresh look at SISO decoding without CSI and apply sphere decoding (SD) to reduce complexity. In particular, we devise a maximum a posteriori probability (MAP) multiple-symbol differential sphere decoder (MSDSD) which efficiently solves the high-dimensional search problem inherent to detection without CSI. Together with a soft-output generation device the MAP-MSDSD algorithm forms a new SISO-MSDSD module for iterative decoding. We analyze the extrinsic information transfer (EXIT) characteristic of the novel module, by means of which we are able to design powerful encoder and decoder structures. For, respectively, the additive white Gaussian noise (AWGN) and the continuously time-varying Rayleigh-fading channel without CSI these designs operate within 1.7-1.9 and 2.3-2.5 dB of channel capacity assuming perfect CSI. These figures compare favorably with results available in the literature, especially for reasonably high data rates of 1-2 bit/channel use. Simulation studies of the average and the maximum complexity required by SISO-MSDSD demonstrate the advantageous performance versus complexity tradeoff of our approach.

Power spectra of return-to-zero optical signals

Analytical formulas for the power spectra of return-to-zero (RZ) optical signals generated by Mach-Zehnder (MZ) modulators are derived. Pulse duty cycles of 33%, 50%, and 67%, in conjunction with several modulation techniques, including binary ON-OFF keying (OOK), duobinary OOK, and M-ary differential phase-shift keying (DPSK), phase-shift keying (PSK), and quadrature-amplitude modulation (QAM), are considered. Spectral characteristics and bandwidth requirements of these different schemes are compared

Performance of Noncoherent Maximum-Likelihood Sequence Detection for Differential OFDM Systems With Diversity Reception

For the single-carrier M-ary differential phase-shift keying (MDPSK), the multiple-symbol differential detector, or the noncoherent maximum-likelihood sequence detector (NSD), and its three special cases, namely, the noncoherent one-shot detector, the linearly predictive decision-feedback (DF) detector, and the linearly predictive Viterbi receiver are reviewed based on a hierarchical interpretation. For the multicarrier transmission, the differential orthogonal frequency division multiplexing (OFDM) systems with diversity reception are discussed. It is well known that there are two types of differential OFDM systems, namely, the time domain differential OFDM (TD-OFDM) and the frequency domain differential OFDM (FD-OFDM). In this paper, the NSD and its special cases are incorporated to the differential OFDM systems. Furthermore, we provide a simple closed-form bit-error-rate (BER) expression for the differential OFDM systems utilizing the noncoherent one-shot detector with diversity reception in the time-varying multipath Rayleigh fading channels. Numerical results have revealed that, with multi-antenna diversity reception, the performance of the noncoherent one-shot detector is improved significantly. However, when only one or two receive antennas are available, the implementation of the linearly predictive DF detector or the linearly predictive Viterbi receiver is necessary for achieving better and satisfactory performance.

Multilevel coding in M-ary DPSK/differential QAM high-speed optical transmission with direct detection

A bandwidth- and power-efficient modulation scheme using M-ary differential phase-shift keying (DPSK)/differential quadrature amplitude modulation (DQAM) and low-density parity-check (LDPC) codes as component codes in a multilevel coding (MLC) is proposed for optical transmission systems with direct detection. An MLC scheme with 2 b/s/Hz spectral efficiency based on block-circulant component codes provides the coding gain of 12.3 dB when compared to uncoded 8-DPSK, and 8.3 dB when compared to uncoded 4-DPSK (QDPSK).

Differential transmission for amplify-and-forward Cooperative communications

We propose a differential amplify-and-forward (AF) transmission scheme for a two-user cooperative communications system. By efficiently combining signals from both direct and relay links, the proposed scheme provides superior performance compared to those of direct transmissions with either differential detection or coherent detection. While the exact bit-error-rate (BER) formulation of the proposed scheme is not available currently, we provide, as a performance benchmark, an exact BER formulation and its simple bounds for a case of optimum-combining cooperation system with differential M-ary phase-shift keying (DMPSK) signals. The optimum power allocation is also determined based on the provided BER formulations. We show that the proposed differential cooperative transmission scheme together with the optimum power allocation yields comparable performance to the optimum-combining scheme. Simulation results show that the proposed differential scheme with optimum power allocation yields significant performance improvement over that with an equal power allocation scheme.

An adaptive algorithm for differentially coherent detection in the presence of intersymbol interference

An adaptive equalization method is proposed for use with differentially coherent detection of M-ary differential phase-shift keying (DPSK) signals in the presence of unknown carrier frequency offset. A decision-feedback or a linear equalizer is employed, followed by the differentially coherent detector. The equalizer coefficients are adjusted to minimize the post-detection mean squared error. The error, which is a quadratic function of the equalizer vector, is used to design an adaptive algorithm of stochastic gradient type. The approach differs from those proposed previously, which linearize the post-detection error to enable the use of least mean squares (LMS) or recursive least squares (RLS) adaptive equalizers. The proposed quadratic-error (Q) algorithm has complexity comparable to that of LMS, and equal convergence speed. Simulation results demonstrate performance improvement over methods based on linearized-error (L) algorithm. The main advantages of the technique proposed are its simplicity of implementation and robustness to carrier frequency offset, which is maintained for varying modulation level.

Diversity combining for coherent and differential M-PSK in fading and class-A impulsive noise

In this paper, optimum and suboptimum diversity combining schemes for coherent and differential M-ary phase-shift keying (M-PSK) transmission impaired by general Ricean fading and impulsive Class-A noise are derived and analyzed. The proposed suboptimum coherent combining (SCC) and suboptimum noncoherent combining (SNC) schemes yield similar performance as the corresponding optimum combining schemes but require a lower computational complexity. In addition, the novel SCC and SNC strategies achieve large performance gains over conventional maximum ratio combining (MRC) and equal gain combining (EGC), respectively. For MRC and EGC, respectively, we also provide a performance analysis for coherent and differential M-PSK transmissions over general Ricean fading channels with Class-A noise. Furthermore, tight performance upper bounds for the proposed optimum and suboptimum combining schemes are derived.

Iterative demodulation and decoding of frequency-hopped PSK in partial-band jamming

This paper considers the problem of developing and utilizing side information in a frequency-hopped communication system using phase-shift keying (PSK) and operating in an environment with partial-band jamming. Two aspects of side information are studied. The first deals with estimating the unknown random carrier phase that varies from hop to hop. The second aspect is the detection of jamming signals. We use a serially concatenated convolutional code structure with differential M-ary PSK as the inner code. The iterative receiver uses an expanded trellis in the inner decoder to resolve the phase ambiguity and is augmented by a ratio-threshold test for detecting jammer energy. Performance is compared for different dwell interval lengths and both log-APP and max-log-APP decoding algorithms. This paper also considers the effect of different thresholds on the false alarm and detection probabilities of the ratio-threshold test.

A General SER Formula for an OFDM System With MDPSK in Frequency Domain Over Rayleigh Fading Channels

A closed-form formula for symbol-error rate (SER) of an orthogonal frequency-division multiplexing (OFDM) system with M-ary differential phase-shift keying (MDPSK) in frequency domain over Rayleigh fading channels is obtained. It is found that, by MDPSK in frequency domain, identical SERs can be achieved on all subcarriers. However, both time and frequency dispersion in the channel will introduce error floors. A comparison between OFDM-MDPSK in frequency domain and that in time domain reveals that the former system offers superior SER performance in a fast fading environment, while the latter performs better if the channel is mainly frequency selective. Moreover, the former system has lower implementation complexity.

New exponential bounds and approximations for the computation of error probability in fading channels

We present new exponential bounds for the Gaussian Q function (one- and two-dimensional) and its inverse, and for M-ary phase-shift-keying (MPSK), M-ary differential phase-shift-keying (MDPSK) error probabilities over additive white Gaussian noise channels. More precisely, the new bounds are in the form of the sum of exponential functions that, in the limit, approach the exact value. Then, a quite accurate and simple approximate expression given by the sum of two exponential functions is reported. The results are applied to the general problem of evaluating the average error probability in fading channels. Some examples of applications are also presented for the computation of the pairwise error probability of space-time codes and the average error probability of MPSK and MDPSK in fading channels.

A VLSI Architecture for Novel Decision Feedback Differential Phase Detection with an Accumulator

This paper proposes a novel decision feedback differential phase detection (DF-DPD) for M-ary DPSK. A conventional differential phase detection method for M-ary Differential Phase Shift Keying (DPSK) can simplify the receiver architecture. However, it possesses a poorer bit error rate (BER) performance than coherent detection because of the prior noisy phase sample. Multiple-symbol differential detection methods, such as maximum likelihood differential phase detection, Viterbi-DPD, and DF-DPD using L-1 previous detected symbols, have attempted to improve BER performance. As the detection length, L, increases, the BER performance of the DF-DPD improves but the complexity of the architecture increases dramatically. This paper proposes a simplified DF-DPD architecture replacing the conventional delay and additional architecture with an accumulator. The proposed architecture also improves BER performance by minimizing the current differential phase noise through the accumulation of previous differential phase noise samples. The simulation results show that the BER performance of the proposed architecture approaches that of a coherent detection with differential decoding.

Adaptive innovations-based MLSE receiver for frequency-nonselective Rayleigh fading channels

The performance of an adaptive innovations-based maximum likelihood sequence estimation (MLSE) receiver for differentially encoded M-ary differential phase shift keying (M-DPSK) in frequency-flat Rayleigh fading channels is presented. The proposed receiver can be implemented without the knowledge of the channel statistics, yet reveal a robust demodulation performance against the uncertainties associated with the channel dynamics.

Noncoherent MLSE detection of M-DPSK for DS-CDMA wireless systems

This paper focuses on maximum-likelihood sequence estimation of noncoherent M-ary differential phase-shift keying (M-DPSK) receivers for code division multiple-access (CDMA) systems, which make use of direct-sequence spread-spectrum modulations. A typical frequency-selective Rayleigh environment with multipath diversity at the receiver is considered. In this scenario, the optimum noncoherent decision metric, which requires an estimation of the channel tap weights envelope, is derived. Then, in order not to increase the receiver implementation complexity, a joint channel and data estimation strategy is proposed, which does not require the transmission of a known training sequence (blind estimation). In this case, the decision metric becomes a simple equal gain combining of multiple-symbol square-law detection decision metrics. For this suboptimum noncoherent detector, useful bounds on the bit error probability are provided through a theoretical analysis. Nonconstant and constant multipath intensity profiles are both considered for this purpose. Simulations are also carried out in order to verify the accuracy of the theoretical bounds.

Adaptive noncoherent linear minimum ISI equalization for MDPSK and MDAPSK signals

A novel noncoherent linear equalization scheme is introduced and analyzed. In contrast to previously proposed noncoherent equalization schemes, the proposed scheme is not only applicable for M-ary differential phase-shift keying (MDPSK) but also for M-ary differential amplitude/phase-shift keying (MDAPSK). The novel scheme minimizes the variance of intersymbol interference (ISI) in the equalizer output signal. The optimum equalizer coefficients may be calculated directly from an eigenvalue problem. For an efficient recursive adaptation of the equalizer coefficients, a modified least-mean-square (LMS) and a modified recursive least-squares (RLS) algorithm are proposed. It is shown that the corresponding cost function has no spurious local minima that ensures global convergence of the adaptive algorithms. Simulations confirm the good performance of the proposed noncoherent equalization scheme and its robustness against frequency offset.

Error Probabilities for MRC Diversity Reception of MDPSK in Slow Nakagami Fading

New closed form error probability expressions for M-ary differential-phase-shift-keying (MDPSK) with maximal ratio combining (MRC) diversity reception in Nakagami fading, are derived. These expressions involve easily computable Legendre polynomials and Associated Legendre functions. By setting the fading severity parameter m to unity, the new general error probability formula reduces to the known results for MDPSK systems in slow Rayleigh fading. For binary DPSK, the bit error rate (BER) performance with MRC is compared with known results for selection diversity combining (SDC). It is shown that MRC is more effective than SDC in improving BER performance for the Nakagami channels, as expected. We also discuss the ranges of the fading severity parameter and diversity order, within which the error probability expressions can be computed efficiently.