Coherent Quadrature Phase Shift Keying Research Articles

INTREPID program: technology and architecture for next-generation, energy-efficient, hyper-scale data centers [Invited

The INTREPID program is developing power-efficient coherent optics for package-level integration with future switch integrated circuits as a path to realizing higher-radix switches for flatter networks. The link architecture is underpinned by coherent quadrature phase-shift keying (QPSK) polarization-multiplex transceivers at 200 Gb/s per λ , further enhanced with wavelength division multiplexing (WDM) to enable energy-efficient 800 or 1600 Gb/s inter-switch fiber connections. The technology is compatible with conventional three-level data center designs as well as a two-level data center design introduced here, which includes an added layer of passive, arrayed waveguide grating routers (AWGRs) or WDM circuit switches to further improve the cost, energy efficiency, and latency of the network.

Photonic Vector Signal Generation Based on OEO and Optical Coherent QPSK Modulation

A novel scheme for photonic vector signal generation based on a self-starting optoelectronic oscillator (OEO) and optical coherent quadrature phase-shift keying (QPSK) modulation is proposed and experimentally demonstrated. The optical output sidebands of the OEO are employed for optical heterodyne mixing, where one first-order sideband is modulated by QPSK baseband data using a dual-parallel Mach–Zehnder modulator, followed by coherent detection so as to directly generate frequency-doubled K-band vector signals. In the experiment, a 19.9 GHz QPSK modulated vector signal with a bit rate of 100 Mb/s is generated when the OEO operates at 9.95 GHz. The generated signal is back demodulated with error vector magnitude (EVM) less than 7%.

On the Average Achievable Rate of QPSK and DQPSK OFDM Over Rapidly Fading Channels

Motivated by recent experimental observations, where differentially coherent detection outperforms coherent detection on certain underwater acoustic channels, we revisit the performance of these two methods with respect to the achievable rate in orthogonal frequency-division multiplexing systems. Our comparison is based on a class of time-varying channels, where coherent quadrature phase shift keying (QPSK) detection requires channel estimation through a set of designated pilot symbols, while differentially coherent QPSK (DQPSK) enjoys an almost pilot-free detection. We show that given the cost of pilot overhead and channel estimation errors, the average rate achievable with DQPSK can be higher than that of QPSK. We use analytical results to identify channels for which this is the case, and expand the results to larger constellation sizes such as 8PSK, 16PSK, and 16QAM. In addition to acoustic channels, wireless radio channels with unusually long delay spread or high Doppler spread, such as those found in unmanned aerial systems and high-speed trains, may also benefit from using differentially coherent detection. In general, differentially coherent detection is favored in rapidly time-varying channels which require large pilot overhead and/or whose bit error rate performance is dominated by channel estimation errors. Our analysis includes the results for array receivers and soft detectors, showing that the favorable parameter range for differentially coherent detection expands significantly in both cases.

Average BER of coherent optical QPSK systems with phase errors over M turbulence channels

The average bit-error-rate (BER) performance is studied for a coherent free-space optical communication system employing differentially encoded quadrature phase-shift keying (QPSK) with the Mth-power phase estimation method. A closed-form expression, considering the combined effects of the Malaga (M) turbulence fading, pointing errors, and phase estimation errors, is derived in terms of Meijer’s G function. Numerical and Monte Carlo simulation results are presented to verify the derived expression.

Performance evaluation of sum‐of‐cisoids Rice/Rayleigh fading channel simulators with respect to the bit error probability

AbstractSum‐of‐cisoids (SOC) processes provide an important framework for the modeling and simulation of multipath fading channels. In this paper, we analyze the performance of SOC Rice/Rayleigh narrowband fading channel simulators with respect to the bit error probability (BEP) of quadrature phase shift keying (QPSK) and differential phase shift keying (DPSK) systems with both coherent and noncoherent demodulation. For the BEP of coherent QPSK and DPSK, exact analytical expressions are derived, which provide insight into the influence of the number of propagation paths and the path gains on the system performance. It will be shown that at least 10 multipath components are required to guarantee that the absolute value of the relative error of the BEP is less than 5%. Regarding the BEP of noncoherent DPSK, we show analytically and by simulations that the system performance reacts very sensitively to the model error caused by an imperfect computation of the channel simulator's Doppler frequencies. Our study is not only important for the performance evaluation of SOC‐based channel simulators but also for the performance evaluation of QPSK and DPSK systems in the presence of a limited number of scatterers. Especially for a small number of propagation paths with unbalanced path gains, where the central limit theorem does not apply, the derived analytical expressions for the BEP reveal their full importance.

Parity Check Encoded QPSK for Rate Adaptation in Coherent DSP-Based Receivers

An ultrashort rate-1/2 parity check (PC) code is used to switch the net data rate of a coherent quadrature phase shift keying (QPSK) transmission system to the equivalent of a binary phase shift keying (BPSK) system. Simulation results of PC encoded-QPSK show an improvement in receiver sensitivity of 0.8 dB over BPSK at the soft-FEC threshold of BER = 2×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> . In addition, the code allows establishing an absolute phase reference at the receiver; i.e., differential coding is not required.

Improved two-stage equalization for coherent Pol-Mux QPSK and 16-QAM systems

We report a two-stage blind frequency domain equalization method for long-haul coherent polarization-multiplexed (pol-mux) systems using quadrature phase shift keying (QPSK) and 16-quadrature amplitude modulation (16-QAM). In the first stage, blind CD parameter prediction is conducted prior to a CD equalizer. This supports flexible path switching in optical networks. In the second stage, a frequency-domain multi-modulus algorithm (MMA) equalizer is used to cope with the residual fiber impairments and perform polarization de-multiplexing. Compared with the conventional constant modulus algorithm (CMA), MMA shows advantages including better steady state performance and a faster convergence rate. Furthermore, all the estimation and equalization algorithms are implemented in the frequency domain which potentially provides the least complexity for the pol-mux optical coherent systems. The proposed algorithm is experimentally demonstrated with an 800-km 10 Gbaud coherent optical pol-mux system. For QPSK signal, the proposed method achieves error-free transmission and shows superior convergence speed against CMA, and for 16-QAM signals, the proposed MMA outperforms CMA with more than 1-dB improvement in Q-value.

Performance Comparison of Electronic PMD Equalizers for Coherent PDM QPSK Systems

Polarization division multiplexed (PDM) quadrature phase-shift keying (QPSK) coherent optical systems employ blind adaptive linear electronic equalizers for polarization-mode dispersion (PMD) compensation. In this paper, we compute the performance of various adaptive, fractionally spaced, feed-forward electronic equalizers, using the outage probability as a criterion. A parallel programming implementation of the multicanonical Monte Carlo method is developed, which automatically performs concurrent loop computation on multicore processors, for the estimation of the tails of the outage probability distribution. The constant modulus algorithm (CMA), the decision-directed least mean squares (DD-LMS), and their combination are applied for the adaptation of electronic equalizer filter coefficients. In the exclusive presence of PMD, we demonstrate that half-symbol-period-spaced CMA-based adaptive electronic equalizers perform slightly better than their DD-LMS counterparts, at links with strong PMD, whereas the opposite holds true at the weak PMD regime. It is shown that the successive application of CMA and DD-LMS with 20 complex, half-symbol-period-spaced taps per finite impulse response filter is adequate to reduce the outage probability of coherent PDM QPSK systems to less than 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> , for a mean differential group delay of more than twice the symbol period.

Outage Probability Due to PMD in Coherent PDM QPSK Systems With Electronic Equalization

Polarization-division-multiplexed (PDM) quadrature phase-shift-keying (QPSK) coherent optical systems employ blind adaptive electronic equalizers for polarization-mode dispersion compensation. In this letter, we compare the performance of fractionally spaced, linear electronic equalizers, composed of four parallel finite impulse response (FIR) filters of various lengths, using the outage probability as a performance criterion. The constant modulus algorithm is applied for the adaptation of FIR filter coefficients. A parallel programming implementation of the multicanonical Monte Carlo method is adopted for the estimation of the tails of the outage probability distribution. It is shown that less than 20 complex, half-symbol-period-spaced taps per FIR filter suffice, in order to reduce the outage probability of PDM QPSK coherent optical systems to less than 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> , for a mean differential group delay up to twice the symbol period.

Dual-Stage Cascaded Frequency Offset Estimation for Digital Coherent Receivers

Frequency offset estimation is a key function in carrier phase recovery to enable digital coherent reception. We propose a novel, feed-forward, dual-stage frequency offset estimator, and demonstrate its performance through both simulation and experiment. Our simulation results show that the estimation range can be as large as ± 9 GHz for a 10.7-GBaud polarization-multiplexed (PolMux) quadrature phase-shift keying (QPSK) system. In addition, the widest range of ±0.5 times the system symbol rate is achieved for the first time in an experimental 42.8-Gb/s coherent PolMux QPSK receiver.

Nonlinear signal–noise interactions in dispersion-managed links with various modulation formats

Purpose of this paper is to highlight the principles of the nonlinear signal–noise interaction (NSNI) in dispersion-managed long-haul optical links and provide a quantitative understanding of the system parameters for which NSNI sets the nonlinear performance of the most popular intensity and phase modulation formats, namely on–off keying, differential binary and quadrature phase-shift keying and coherent quadrature phase-shift keying.

Impact of Quadrature Imbalance in Optical Coherent QPSK Receiver

In this letter, we present the impact of quadrature imbalance in an optical coherent quadrature phase-shift-keying (QPSK) receiver. Arbitrary conjugate misalignment was realized in all-fiber optical hybrid and two correction algorithms of quadrature imbalance, the ellipse correction method, and the Gram-Schmidt orthogonalization method, were independently applied. Bit-error-rate curves versus optical signal-to-noise ratio (OSNR) were measured for the 20-Gb/s optical QPSK signal. We show that OSNR penalty is reduced from ~6 to 1 dB at ~20deg conjugate misalignment with the help of correction algorithms.

Intra-channel nonlinearities mitigation in pseudo-linear coherent QPSK transmission systems via nonlinear electrical equalizer

A novel nonlinear electrical equalizer (NLEE) based on Volterra theory is proposed for mitigating intra-channel nonlinearities in pseudo-linear coherent optical communication systems. According to the temporal matching condition of intra-channel nonlinear pulse interactions, we just select specific nonlinear terms and reduce the computation complexity considerably. Numerical simulations of 10GBaud coherent quadrature phase-shift keying (QPSK) transmission show that the simplified NLEE can efficiently mitigate intra-channel nonlinearities.

Unequal bit error probability in coherent QPSK fiber‐optic systems using phase modulator based transmitters

AbstractWe report on the occurrence of unequal bit error probability in a coherent quadrature phase shift keying (QPSK) fiber‐optic system. The bit error rates (BER) of two QPSK bits are derived individually based on the developed system model, and they turn out to differ by more than an order of magnitude for a phase modulator based transmitter. The phenomenon, previously unreported, arises because such a transmitter introduces a controlled form of inter‐symbol‐interference (ISI), and the receiver low‐pass filters affect this ISI differently for the two bits. The optimum bandwidth of the receiver low‐pass filter is obtained from the analytic derivation, which is about 0.7 times the symbol rate. We propose two simple system modifications, one in the transmitter and one in the receiver, to compensate for the phenomenon and equalize the two BER's. Those modifications improve the system performance by about 2 dB without adding any extra hardware. Copyright © 2007 John Wiley &amp; Sons, Ltd.

Analysis of the Effect of the I/Q Base-Band Filter Mismatch in an OFDM Modem

In digital communication modems in which a very high rate system clock is used, it is necessary to use analog base-band shaping filters in the inphase (I) and quadrature (Q) paths of the modulator. However, this type of implementation inherently produces a mismatch of the I and Q paths. In the present paper, results of the analysis of the transmitter (TX) I/Q mismatch in an Orthogonal Frequency Division Multiplexing (OFDM) system with Differential Coherent Quadrature Phase Shift Keying (DQPSK) modulation is presented. Theoretical analysis shows that the Signal-to-Noise (SNR) degradation due to the I/Q mismatch can be represented by a mismatch transfer function on the basis of which one can compute the maximum affordable amplitude and phase mismatch of the TX filters transfer functions.

Performance of an adaptive rate modem using quasi-analytic simulation techniques

The symbol error probability (SEP) of a digital signal processor implemented /spl pi//M M-ary differentially coherent phase-shift keying (MDPSK) modem, using quasi-analytical (QA) simulation techniques, is the subject of this investigation. We study M values of 4, 8, 16, 32, and 64 for use in a fast adaptive data rate mobile radio communication system. The proposed modulation scheme /spl pi//M-MDPSK, is a generalization of /spl pi//4 differentially coherent quadrature phase-shift keying, which is used in the North American time-division multiple-access wireless standard. A QA simulation approach is developed so that real system impairments can be studied without having to resort to lengthy Monte Carlo simulation. In particular, it is found that implementation losses, most notable at M=32 and 64, which result from practical transmit and receive filtering, and symbol timing error, can be largely overcome by using a fixed equalization filter and increased accuracy of symbol timing recovery. We focus on an additive white Gaussian noise channel since, in a fast adaptive rate system, the Doppler spread mobile channel is approximately Gaussian on short time intervals. However, the quasi-analytic technique developed here is directly extendable to a fast Rayleigh fading channel. Specifically, we find that for M=64, the inclusion of a fixed seven-tap zero forcing equalizer at the matched filter output, decreases the SEP degradation at P/sub e/=10/sup -4/ from 7.5 dB down to 0.24 dB. The symbol timing error using a finite-precision interpolator is held to within 1/64 symbol period.

Phase precoding for frequency-selective Rayleigh and Rician slowly fading channels

This paper presents a novel phase precoding (pre-equalization) technique to equalize frequency-selective Rayleigh and Rician slowly fading channels for personal communication systems using phase modulation. In order to achieve intersymbol interference (ISI)-free transmission, the precoding technique pre-distorts the signal transmitted from a base station to a portable unit. The novelty of the technique lies in using a spiral curve design: (1) to ensure the stability of the precoder even in equalizing a non-minimum-phase channel; (2) to obtain an ISI-free received signal; and (3) to keep a constant transmitted signal amplitude. Using the precoder can improve the bit-error-rate (BER) transmission performance without increasing the complexity of the portable unit receiver. The BER performance of coherent quadrature phase-shift-keying (QPSK) with the channel pre-equalization is analyzed theoretically for both Rayleigh and Rician fading channels. Analytical and simulation results demonstrate that coherent QPSK using the proposed channel precoder has a significantly lower BER than that using a conventional decision-feedback equalizer (DFE) because the precoder does not suffer from error propagation.

Miniaturized reverse modulation loop of a CQPSK 120 Mbit/s modem for spacecraft applications

The design and performance of a miniaturized reverse modulation loop (RML) for a 120 Mbit/s coherent quadrature phase shift keying (CQPSK) modem for onboard satellite applications are presented. Analysis of time delays within the RML circuit indicates that any differential time-delay errors can adversely affect the associated BER and should be minimized. The RML circuit, consisting of a modulator, demodulator, and comparator circuit, has been fabricated using quasi-monolithic techniques with dimensions of 1.65*4 cm. The relative phase for all four states of the modulator is in close agreement with design values of 90 degrees +or-1 degrees over a 200 MHz bandwidth at 3.95 GHz. The demodulator and comparator circuits of the RML have successfully recovered a 120 Mbit/s bit stream. The RML circuit is capable of recovering higher bit rates because of relatively uniform amplitude and phase performance over the 3.7- to 4.2 GHz communications satellite band.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Coherent optical QPSK intradyne system: concept and digital receiver realization

A receiver concept based on optical quadrature phase-shift keying (QPSK) and a digital realization of synchronous demodulation including phase synchronization is presented. To keep the signal processing bandwidth low a phase diversity receiver, called an intradyne receiver, with an orthogonal electrical demodulation is proposed. Basic principles of the synchronous orthogonal and digital demodulation are described. After the evaluation of the shot noise limit some aspects of the digital phase-locked loop (PLL) are presented. In a 100-Mb/s transmission system a receiver sensitivity of -51.6 dBm has been measured. The loss in relation to the shot noise limit of -66.3 dBm (18 photons/b) is mostly due to the low local laser power and the influence of the receiver input noise. >

Microprocessor implementation of tactical modems for data transmissions over v.h.f. radios

The advent of the single-chip microprocessor has made possible the use of digital signal processing in low-cost communications circuitry. The all-digital approach has been used in a high-performance data modem for the transmission of burst messages through the voice channel of v.h.f. narrow band f.m. radio sets. The techniques used in this novel design of software modem are illustrated by reference to the version using coherent quadrature phase shift keying (q.p.s.k.) modulation and constraint length 48 convolutional encoding with sequential decoding.