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

Xiang Liu

doi:10.1364/OE.15.002927

1. Introduction

Optical differential phase-shift keying (DPSK) has attracted extensive study due to its promising applications in high-speed optical transport systems by offering high receiver sensitivity and high tolerance to major nonlinear impairments as compared to traditional on-off-keying (OOK) [1, 2]. DPSK also allows for direct-detection that avoids the need of an optical local oscillator (OLO) and optical polarization/phase tracking between the OLO and the signal as required in coherent homodyne-detection phase-shift keying (PSK). Optical binary DPSK (DBPSK), being the simplest form of DPSK, has been used in many record-setting long-haul high-speed transmissions [1]. For future wavelength-division-multiplexed (WDM) optical transport networks, it is desired to further increase the overall transmission capacity as well as the data rate per wavelength channel. Multilevel modulation formats, by offering higher spectral efficiency and higher tolerance to chromatic dispersion and polarization-mode dispersion (PMD) than a binary format, become natural candidates for future optical transport systems. Recently, differential quadrature phase-shift-keying (DQPSK) or quaternary DPSK [3] has been demonstrated for long-distance transmission with doubled spectral efficiency [4, 5] and PMD tolerance [6] than binary DPSK. 8-ary DPSK, a 3-bit/symbol format, has also been demonstrated [7]. Further increase in spectral efficiency can be achieved by using multilevel or m-ary DPSK formats with more phase states and/or combining DPSK with amplitude-shift keying (ASK) [8]. However, there exists a receiver sensitivity degradation in the direct-detection DPSK as compared to the coherent homodyne-detection PSK [9], which is often referred to as the differential detection penalty. Moreover, the differential detection penalty increases with the increase of the number of phase states and approaches 3 dB at low bit error rates (BERs) in the linear regime as the number of phase states becomes very large. It is thus particularly desired to remove or reduce the differential detection penalty in receiving multilevel DPSK signals.

To reduce the differential-detection penalty, two common methods had been used in wireless communications, i.e., multiple-symbol differential detection (MSDD) [10] and data-aided multi-symbol phase estimation (MSPE) [11]. Recently, the MSDD concept was extended to optical DBPSK [12, 13] and optical DQPSK [14]. MSDD uses at least twice as many optical delay interferometers (ODIs) to extract more information regarding the phase differences among different symbols. More recently, a data-aided MSPE scheme for optical DQPSK, which requires the same optical complexity as conventional direct-detection, but relies on analog electronic processing to extract an improved phase reference, thereby improving the receiver sensitivity has been proposed [15,16]. Two analog implementations, one using the conventional DQPSK demodulator [16] and the other using a modified demodulator [15], were reported. The data-aided MSPE scheme was also extended to the detection of a DQPSK/ASK signal [17] and improved its receiver sensitivity. A digital implementation of the data-aided MSPE scheme was recently proposed and experimentally demonstrated with a 40-Gb/s DQPSK signal through offline digital signal processing (DSP) [18].

In this paper, we generalize the framework of the data-aided MSPE scheme in the direct-detection of any m-ary DPSK and m-ary-DPSK/ASK signals. Both analog and digital implementations are described. This paper is organized as follows. Section 2 provides detailed derivations of a data-aided MSPE algorithm for optical DQPSK and shows the performance improvement it brings in the linear and nonlinear regimes. Section 3 describes a data-aided MSPE algorithm for optical 8-ary DPSK and the resulting receiver sensitivity improvement. Section 4 presents a generalized data-aided MSPE scheme for optical m-ary DPSK. A simple yet universal receiver platform for multilevel DPSK consisting of a pair of optical I/Q demodulators and a DSP unit is also presented. Section 5 discusses the extension of the data-aided MSPE scheme to DPSK/ASK. An interesting electronic method that compensates for the unequal nonlinear phase shifts experienced by symbols with different amplitude levels and substantially improves the nonlinear tolerance will also be introduced. Finally, Section 6 concludes this paper.

Fig. 1. Schematic of a data-aided MSPE receiver for optical DQPSK. BD: balanced detector. DFF: decision flip-flop. LOU: logic operation unit.

Download Full Size | PDF

2. Data-aided MSPE in optical DQPSK

2.1 Theory

For direct-detection of optical DQPSK, two ODIs, each having a delay of T (T being the symbol period of the signal) and an appropriate phase offset between its two interference paths, and two balanced detectors are needed, as shown in left portion of Fig. 1. The two ODIs are often referred to the in-phase (I) and quadrature (Q) demodulators. In conventional differential detection, the phase reference is simply the previous symbol. The decision variables obtained by the direct detection for I and Q data tributaries are [16]

u_{I} (n) = Re [u (n)] = Re [e^{j \frac{π}{4}} ∙ y (n) ∙ {(n - 1)}^{*}], u_{Q} (n) = Im [u (n)] = Im [e^{j \frac{π}{4}} ∙ y (n) ∙ {(n - 1)}^{*}],

where y(n) is the normalized optical field of the n-th bit before demodulation, and “^*” represents complex conjugate.

In MSPE, multiple previous symbols, with their phase modulations removed, are used collectively to obtain a new phase reference z(n-1) that is more accurate than y(n-1) through the following weighted summation

z (n - 1) = y (n - 1) + w ∙ z (n - 2) ∙ \exp [j ∙ Δϕ (n - 1)],

where w is a weighting factor or forgetting factor, and Δϕ(n-1)= ϕ(n-1)- ϕ(n-2)∈{0, 0.5π, π, 1.5 π} is the optical phase difference between the (n-1)-th and the (n-2)-th symbols. The purpose of the last term in Eq. (2) is to remove the phase modulation of each of the previous symbols, and it can be estimated by using previously recovered data, in which case the MSPE process is called data-aided MSPE. For optical DQPSK, using recovered I and Q data tributaries, c_I and c_Q, we have

\exp [- j . Δϕ (n)] = \bar{c_{I} (n) \oplus c_{Q} (n)} ∙ {(- 1)}^{\bar{c_{I} (n)}} + j . c_{I} (n) \oplus c_{Q} (n) ∙ {(- 1)}^{\bar{c_{I} (n)}},

where ⊕ denotes XOR logic operation. The following conversion table is used in deriving the above equation.

Table 1. Relation between the differential phase and the recovered data in optical DQPSK.

View Table | View all tables in this article

With the new phase reference z(n-1), we obtain the improved complex decision variable for the optical DQPSK signal, x(n), as

x (n) = e^{j \frac{π}{4}} ∙ y (n) ∙ z {(n - 1)}^{*},

In wireless communications, the signal field is readily accessible, so the MSPE can be straightforwardly applied by using Eqs. (4) and (2). However, in optical direct-detection DPSK, the complex optical signal field is not available. It is thus desirable to express the improved decision variable in terms of the measurable quantities from the conventional direct detection, namely u_I and u_Q. To accomplish this, we first rewrite Eq.(4) using Eqs. (1–2) as

x (n) = e^{j \frac{π}{4}} ∙ y (n) ∙ {y (n - 1) + w ∙ z (n - 2) ∙ \exp [j ∙ Δϕ (n - 1)]} *

When the signal performance is limited by phase noise rather than amplitude noise, y(n) ≈ e ^jϕ(n) , which is usually applicable to optical multilevel DPSK including DQPSK. We can use the following approximation,

\frac{1}{y {(n - 1)}^{*}} \approx y (n - 1) .

Eq. (5) can then be expressed as

x (n) \approx u (n) + w ∙ u (n) ∙ y (n - 1) ∙ z {(n - 2)}^{*} ∙ \exp [- j ∙ Δϕ (n - 1)]

Thus, we can obtain the real (I) and imaginary (Q) parts of the improved complex decision variable for the optical DQPSK signal, x_I and x_Q, from the measurable quantities and past decisions by

x_{I} (n) = Re [x (n)], x_{Q} (n) = Im [x (n)], and

Equation (8) provides the basis for the analog implementation of the data-aided MSPE for optical DQPSK. Extending the MSPE concept to the digital domain, we can write the improved phase reference z(n-1) as

z (n - 1) = y (n - 1) + \sum_{p = 1}^{N} {w^{p} \prod_{q = 1}^{p} [y (n - 1 - q) ∙ e^{j ∙ Δϕ (n - q)}]},

where N is the number of past decisions (or data) used in the MSPE process. The forgetting factor w can be conveniently set to 1. The improved I and Q decision variables, x_I and x_Q, are then

x_{I} (n) = Re [x (n)], x_{Q} (n) = Im [x (n)], and

Equation (10) provides the basis for the digital implementation of the data-aided MSPE for optical DQPSK. One advantage of the digital implementation is that N can be suitably selected to reduce laser noise induced penalty when w approaches 1. In the analog implementation, the circuit complexity is insensitive to the forgetting factor w. In the digital implementation, it can be seen from the recursive relation shown in Eqs. (8) and (10) that the computational complexity of the data-aided MSPE, in terms of the number of complex multiplications and additions, increases roughly linearly with the number of past decision used.

2.2 Implementation

The right portion of Fig. 1 shows a schematic analog implementation of the data-aided MSPE for optical DQPSK. To perform the computations described in Eq. (8), three analog complex four-quadrant multipliers, denoted as (×), two multipliers, and two adders are used. A logic operation unit (LOU) performs the operations described in Eq. (3) using past decisions. The path lengths of the inputs to the circuit elements are appropriately matched. The computations may also be performed in the digital domain with the help of high-speed analog-to-digital converters (ADCs) [19] and DSP [18]. Figure 2 shows a schematic digital implementation of the data-aided MSPE for optical DQPSK based on Eq. (10), which is actually applicable any m-ary DPSK as to be described later. In the digital domain, a finite number of past data or decisions, e.g. 8, are used to compute the improved decision variables. Note that the DSP-based receiver may allow “soft”-FEC [20] to be used to further increase receiver sensitivity.

Fig. 2. Schematic of a digital implementation of the data-aided MSPE for optical m-ary DPSK. AGC: automatic gain controller.

Download Full Size | PDF

2.3 Performance improvement

To verify the sensitivity improvement due to the data-aided MSPE, we perform Monte-Carlo simulations to obtain the BERs at different optical signal-to-noise ratio (OSNR) values. The OSNR is defined as the ratio between the signal power and the noise power in two polarization states within a 0.1-nm bandwidth. We consider a 20-Gb/s DQPSK signal with a pseudo-random bit stream (PRBS) of length of 2⁷-1. The transmitter was assumed to be ideal and the receiver had a 3^rd-order Gaussian optical filter with a 3-dB bandwidth of 12.5 GHz and a Gaussian electrical filter with a 3-dB bandwidth of 8 GHz. For simplicity, only the noise component that has the same polarization as the signal is considered in the demodulation process. The simulated transmission link consisted of 8x 100-km standard single-mode fiber (SSMF). To effectively emulate long-haul transmission with degraded noise and enhanced self-phase modulation (SPM), we assumed that the SPM induced nonlinear phase shift increased with signal launch power into each fiber span and the OSNR. This is similar to assuming a 25-dB SSMF span loss, an additional loss of 13 dB after each span, a fiber nonlinear coefficient of 1.2/W/km, and an optical amplifier noise figure of 6 dB. At a signal launch power of 8 dBm, the SPM induced nonlinear phase shift is 1 rad. and the OSNR is 16 dB after the transmission. The dispersion of each fiber span is fully compensated by a dispersion compensating fiber, which is inserted in an EDFA following the span. The fiber PMD was neglected. When studying the linear transmission performance, we further neglected the fiber nonlinearity.

To quantify the quality of the recovered signal, we use the common Q-factor, which is directly related to the BER through

BER = \frac{1}{2} erfc (\frac{1}{\sqrt{2}} ∙ 10^{Q \frac{(d B)}{20}}),

where the Q-factor is in units of dB and erfc() is the complementary error function. Figure 3 shows the Q-factor as a function of OSNR with w=0.8. In the linear regime where fiber nonlinearity is neglected, the data-aided MSPE receiver outperforms the conventional receiver by ~1.8 dB at BER~10^-4. Note that the Q-factor improvement in the linear regime is virtually the same as the receiver sensitivity improvement in the linear regime. In the nonlinear regime, we consider the Gordon-Mollenauer nonlinear phase noise [21] due to interaction of amplified spontaneous emission (ASE) noise and SPM. ASE noise is added distributed in a transmission link with eight amplified optical spans. The mean nonlinear phase shift increases with the signal power or the received OSNR, and is about 1 radian when the received OSNR is 13 dB. The optimal performance is reached when the mean nonlinear phase shift is about 1 radian, which is reasonable [21]. The Q-factor improvement in the regime of moderate SPM is ~2.1 dB.

When the digital implementation of the MSPE scheme is applied, a finite number of past decisions are used. Figure 4 shows simulated Q-factor improvement by the data-aided MSPE as a function of the number of the past decisions used (N) with a received OSNR of 10 dB. As can be expected, the sensitivity improvement increases with the increase of N, and exceeds 1.5 dB at BER~10^-4 when N ≥4. In the analog implementation, the forgetting factor w is equivalent to the number of past decision used as N=(1+w)/(1-w) [11]. Since the theoretical sensitivity difference between the direct-detection DQPSK and the homodyne detection QPSK assuming matched optical filters is about 2.3 dB [9], the sensitivity of the data-aided MSPE receiver clearly approaches that of the homodyne detection receiver with the increase of w or N. Note that in the analog implementation, w may be limited (e.g., to <0.8) due to RF loss and maximum allowable RF power after the adders. It was also found the sensitivity improvement remains in the presence of moderate chromatic dispersion [17].

Fig. 3. Simulated Q-factor (derived directly from BER) performance of the data-aided MSPE DQPSK receiver as compared to the conventional DQPSK receiver. The bit rate is 20 Gb/s and w=0.8.

Download Full Size | PDF

Fig. 4. Improvement in the Q-factor (derived directly from BER) by the data-aided MSPE for a DQPSK signal as a function of the number of past decisions used. OSNR= 10 dB and w=1.

Download Full Size | PDF

3. Data-aided MSPE in optical 8-ary DPSK

The next multilevel DPSK beyond DQPSK is 8-ary DPSK that carries 3 bits/symbol. 8-ary DPSK also offers further improve tolerance to chromatic dispersion and PMD [7]. A data-aided MSPE algorithm for 8-ary DPSK and the performance improvement it brings will be discussed in this section.

3.1 Theory

For direct-detection of optical 8-ary DPSK, a straightforward but complex demodulation scheme is to use three ODIs, each having a delay of T and an appropriate phase offset between its two interference paths, followed by three balanced detectors [7]. A simplified demodulation scheme requiring only two ODIs was recently proposed [22]. The two decision variables obtained from the simplified demodulation process are

u_{I} (n) = Re [u (n)] = Re [e^{j \frac{π}{8}} ∙ y (n) ∙ y {(n - 1)}^{*}], u_{Q} (n) = Im [u (n)] = Im [e^{j \frac{π}{8}} ∙ y (n) ∙ y {(n - 1)}^{*}] .

Following a similar derivation as presented in the previous section, we can obtain the improved complex decision variable for the 8-ary DPSK signal by

x (n) \approx u (n) + w ∙ u (n) ∙ x (n - 1) ∙ \exp [- j ∙ Δϕ (n - 1)] ∙ \exp (\frac{- j π}{8}) .

The three data tributaries carried by the 8-ary DPSK signal are then [22]

c_{I} (n) = [x_{I} (n) > 0], c_{Q} (n) = ⌊ x_{Q} (n) > 0 ⌋, and

where “a>0” is a logic operation that outputs 1(0) if a>(≤)0, and ⊕ denotes the XOR operation. The relation between the differential phase and the recovered data is shown in Table 2.

Table 2. Relation between the differential phase and the recovered data in optical 8-ary DPSK.

View Table | View all tables in this article

Based on the relation described in Table 2, the phase factor term used to remove the phase modulation of past symbols in Eq. (13) can be expressed as

\exp (- j Δ ϕ (n)) = A + jB, and

where “×” and “⊕”, respectively, denote AND and XOR logic operations.

Equations (12)–(15) provide the basis for a simple recursive implementation of the data-aided MSPE for optical 8-ary DPSK. The optical complexity is the same as that for conventional direct-detection DQPSK: only a pair of I and Q demodulators are required. The general schematic implementation shown in Fig. 2 is applicable to the data-aided MSPE scheme for 8-ary DPSK.

3.2 Performance improvement

To quantify the performance improvement made by the data-aided MSPE, we perform Monte-Carlo simulations with a 30-Gb/s 8-ary DPSK signal. The simulation conditions are the same as those used in the previous section. Fig. 5 shows the signal BER performances as a function of the received OSNR without and with the consideration of the Gordon-Mollenauer nonlinear phase noise. When the fiber nonlinearity is considered, nonlinear phase shift reaches 1 rad when the signal power is such that the OSNR is 19 dB. With N=8, the data-aided MSPE improves the 8-ary DPSK performance by 2.14 and 2.3 dB, respectively, in both the linear and nonlinear regimes, essentially eliminating the differential detection penalty.

Fig. 5. Simulated BER performances of a 30-Gb/s 8-ary DPSK signal received with the data-aided MSPE receiver (N=8 and w=1) as compared to those with the conventional receiver.

Download Full Size | PDF

4. Data-aided MSPE in optical m-ary DPSK

4.1 Theory

In this section, we further extend the data-aided MSPE scheme to any optical m-ary DPSK in which the number of phase states m can be larger than 8. With the I/Q demodulations shown in Fig. 2, the I and Q decision variables are

u_{I} = Re ⌊ e^{\frac{jπ}{m}} y (n) ∙ y {(n - 1)}^{*} ⌋, u_{Q} = Im ⌊ e^{\frac{jπ}{m}} y (n) ∙ y {(n - 1)}^{*} ⌋ .

Following similar analyses described in the previous sections, the improved complex decision variable for an m-ary DPSK signal can be written as

x (n) \approx u (n) + w ∙ u (n) ∙ x (n - 1) ∙ \exp [- j ∙ Δϕ (n - 1)] ∙ \exp (\frac{- j π}{m}),

where Δϕ(n-1)= ϕ(n-1)-ϕ(n-2)∈{[0:m-1]π/m} represents the original optical phase difference between the (n-1)-th bit and the (n-2)-th bit. The phase factor exp[- jΔϕ (n-1)] can be obtained based on the recovered data tributaries and the demodulation and decoding schemes used. For digital implementation, we have

x (n) = u (n) + \sum_{p = 1}^{N} {w^{p} e^{\frac{- j ∙ p π}{m}} u (n) \prod_{q = 1}^{p} [u (n - q) ∙ e^{- j ∙ Δ ϕ (n - q)}]} .

The needed computations can be performed in the DSP unit shown in Fig. 2.

4.2 Unified receiver for m-ary DPSK

We now show that the unified receiver platform for m-ary DPSK, whose optical complexity is the same as that of the conventional direct-detection DQPSK as shown in Fig. 2, can recover all the data tributaries of a m-ary DPSK signal. An m-ary DPSK signal carries log₂(m) data tributaries, which generally can be decoded from m/2 decision variables through

c_{1} = c_{I} = (x_{I} > 0),

where ν (ϕ) is the decision variable associated with a demodulator (or ODI) with a phase offset of ϕ. The number of the decision variables used for the n-th data tributary is 2^n-2 for 2<n≤log(m), so the total number of decision variables used in Eq. (19) is

1 + 1 + \sum_{n = 3}^{\log_{2} (m)} 2^{n - 2} = 1 + 1 + \sum_{i = 1}^{\log_{2} (m) - 2} 2^{i} = 1 + \sum_{i = 0}^{\log_{2} (m) - 2} 2^{i} = 1 + \frac{1 - 2^{\log_{2} (m) - 1}}{1 - 2} = 2^{\log_{2} (m) - 1} = \frac{m}{2} .

More specifically, the m/2 decision variables correspond to demodulators with the following m/4 pairs of orthogonal phase offsets

(\frac{π}{m}, \frac{π}{m} - \frac{π}{2}), (\frac{3 π}{m}, \frac{3 π}{m} - \frac{π}{2}), \dots, (\frac{(\frac{m}{2} - 1) π}{m}, - \frac{π}{m}) .

Evidently, the first pair of orthogonal phase offsets corresponds to the first two decision variables, x_I and x_Q. While remaining (m/2-2) needed decision variables can be obtained by using (m/2-2) additional ODIs with appropriate phase offsets shown above, the resulting optical complexity may become forbiddingly large. We show below that the needed (m/2-2) additional decision variable can be obtained through linear combinations of the first two decision variables, x_I and x_Q, so just one pair of orthogonal ODIs, together with digital signal processing, is sufficient to demodulate the m-ary DPSK signal.

The decision variables associated with ϕ=(πp/m), where p=3,5,…,m/2-1, can be expressed as

ν (\frac{πp}{m}) = Re [e^{\frac{jπp}{m}} ∙ y (n) ∙ {y (n - 1)}^{*}]

Similarly, we can express their orthogonal counterparts as

ν (\frac{πp}{m} - \frac{π}{2}) = Im [e^{\frac{jπp}{m}} ∙ y (n) ∙ {y (n - 1)}^{*}]

When the data-aided MSPE is applied, u_I and u_Q in the above two equations are replaced with the improved decision variables x_I and x_Q. Thus, we have obtained the rest (m/2-2) decision variables by using the real and imaginary parts of the measured complex decision variable and Eqs. (20) and (21). In effect, the complex decision variable contains completed information on the differential phase between adjacent symbols, and is sufficient for deriving all the needed decision variables. Any phase error in the ODIs can also be electronically compensated [18]. Notice that an appropriate pre-coding of the original data tributaries before optical modulation is needed to ensure that the decoded data tributaries are the original ones. The pre-coding function can be determined based on the optical modulation scheme, the optical demodulation scheme, and the decoding scheme described in Eq. (19). The above formulas form the basis of a simple receiver platform for data-aided MSPE in m-ary DPSK using only one pair of optical I/Q demodulators.

4.3 Laser linewidth requirement

As briefly mentioned in Section 2.1, the MSPE receiver based on digital implementation is tolerant to laser noise when w approaches 1. Here, we estimate the laser noise tolerance. Assuming that 8 past decisions (N=8) are used, the laser noise tolerance of the MSPE receiver would be ~4 times lower than that of a conventional differential detection receiver for the same signal. For an OSNR penalty of 0.5 dB at BER~10^-4, the tolerable laser linewidth is ~8.5 MHz for 20-Gb/s DQPSK or ~2 MHz for 30-Gb/s 8-ary DPSK with conventional differential direct detection based on analyses similar to those reported in Refs. [23] and [24]. Detailed derivations are beyond the scope of this paper. This indicates that the laser linewidth requirements for 20-Gb/s DQPSK and 30-Gb/s 8-ary DPSK with the data-aided MSPE are, respectively, ~2 MHz and ~0.5 MHz, which may be satisfied with conventional DFB lasers. Notice that the laser noise requirements for the MSPE-based receivers are much relaxed as compared to those for traditional homodyne receivers, especially when the number of phase levels is large [24]. With more phase levels and/or lower signal data rates, narrower laser linewidth and/or fewer past decisions used in the MSPE are needed.

5. Data-aided MSPE in optical DPSK/ASK

The simultaneous modulation of phase and amplitude provides a means to achieve high spectral efficiency with reasonable power efficiency. Optical m-ary DPSK can be combined with pulse amplitude modulation (PAM) or ASK. A combination of optical DQPSK and ASK has been demonstrated [8]. In this section, we extend the data-aided MSPE scheme to m-ary-DPSK/ASK signals. Figure 6 shows a schematic of data-aided MSPE receiver for optical mary-DPSK/ASK.

Fig. 6. Schematic of a data-aided MSPE receiver for optical DQPSK/ASK. TIA: transimpedance amplifier.

Download Full Size | PDF

5.1 Theory

Due to the presence of amplitude modulation, the approximation described in Eq. (6) is no longer accurate for DPSK/ASK. We can express the normalized received optical field y(n) as

y (n) = ∣ y (n) ∣ e^{jϕ (n)} = \sqrt{P (n)} ∙ e^{jϕ (n)},

where P(n) is the normalized the signal power for the n-th symbol. We then have the following relation

\frac{1}{{y (n - 1)}^{*}} = \frac{1}{P (n)} y (n - 1) .

Using the above relation together with some simplifications, the improved complex decision variable for an m-ary-DPSK/ASK signal can be written as

x (n) = u (n) + w ∙ u (n) ∙ \frac{x (n - 1)}{P (n - 1)} ∙ e^{- j ∙ Δ ϕ (n - 1)} ∙ e^{\frac{- j π}{m}} .

For digital implementation, we have

x (n) = u (n) + \sum_{p = 1}^{N} {w^{p} e^{\frac{- j ∙ p π}{m}} u (n) \prod_{q = 1}^{p} [\frac{u (n - q)}{P (n - q)} ∙ e^{- j ∙ Δ ϕ (n - q)}]} .

With the above improved complex decision variable, all the log₂(m) data tributaries associated with the DPSK modulation can be recovered using the formulas presented in the previous section. The data tributaries associated with the ASK modulation can be straightforwardly recovered based on the power of each symbol P(n).

The simplest m-ary-DPSK/ASK modulation is the combination of DQPSK with a 2-level ASK. The performance of the data-aided MSPE for a 3-bit/symbol 30-Gb/s DQPSK/ASK signal was evaluated in Ref. [17]. The extinction ratio of the ASK modulation for the DQPSK/ASK was 4 dB. Other simulation conditions are the same as those used in previous sections. Fig. 7 shows the BER performance of the DQSPK tributary of the DQPSK/ASK signal using two MSPE schemes, the first (MSPE-1) without the multiplication of P(n-1)^-1 and the second (MSPE-2) with the multiplication of P(n-1)^-1 in Eq. (24). At BER=10^-4, the sensitivity improvements are 1 dB and 1.4 dB for MSPE-1 and MSPE-2, respectively. This conforms the benefit of including the factor P(n-1)^-1 in the MSPE of DQPSK/ASK. It is also found that the MSPE remains effective in the presence of chromatic dispersion [17].

Fig. 7. Simulated BER performance of the data-aided MSPE DQPSK/ASK receivers as compared to the conventional receiver. The bit rate is 30 Gb/s.

Download Full Size | PDF

5.2 Electronic compensation of nonlinear phase shift in DPSK/ASK

In optical fiber transmission, the SPM effect due to fiber nonlinearity causes different nonlinear phase shifts for symbols at different amplitude levels. It is desired to compensate for the nonlinear phase shifts to improve the transmission performance [25]. This can be achieved by replacing the directly measured complex decision variable, u(n), with a compensated complex variable u(n)

ν (n) = u (n) ∙ \exp {- j ∙ c_{NL} [P (n) - P (n - 1)]},

where c_NL is the average nonlinear phase shift experienced by the signal over the fiber transmission. This nonlinear phase shift compensation scheme can be straightforwardly implemented with DSP prior to the MSPE. Initial simulations suggest that substantial improvement in SPM tolerance can be achieved by using the electronic compensation scheme in DPSK/ASK. The Gordon-Mollenauer nonlinear phase noise could also be suppressed prior to the MSPE, in a similar way as that reported in a recent experiment where the optical field of a 40-Gb/s QPSK signal after a nonlinear transmission was recovered by coherent detection QPSK and the nonlinear phase noise was partially compensated by an offline signal processing [26].

6. Conclusion

We have presented a generalized framework of data-aided multi-symbol phase estimation for improving the receiver sensitivity of direct-detection optical m-ary DPSK. Derivations of the data-aided MSPE algorithms for DQPSK, 8-ary DPSK, m-ary DPSK, and DPSK/ASK have been provided for both analog and digital implementations. Numerical simulations have been performed to confirm the sensitivity improvements afforded by the data-aided MSPE. Also presented is a simple yet universal DSP-assisted receiver platform for m-ary DPSK consisting of just one pair of optical I/Q demodulators. Laser linewidth requirement for the MSPE receiver was estimated. An electronic nonlinear phase shift compensation scheme for DPSK/ASK was briefly discussed. The data-aided MSPE scheme, by enabling the performances of direct-detection m-ary DPSK signals to approach those of coherent homodyne detection without resorting to an optical local oscillator, may find promising applications in future advanced optical receivers as well as transport systems.

Acknowledgments

The author wishes to thank C. R. Giles and A. R. Chraplyvy for their support, and S. Chandrasekhar, R. Essiambre, M. Nazarathy, and D. van den Borne for valuable discussions.

References and links

1. A. H. Gnauck and P. J. Winzer, “Optical phase-shift-keyed transmission,” J. Lightwave Technol. 23,115–130 (2005). [CrossRef]

2. C. Xu, X. Liu, and X. Wei, “Differential phase-shift keying for high spectral efficiency optical transmissions,” IEEE J. Sel. Top. Quantum Electron. 10,281–293 (2004). [CrossRef]

3. R. Griffin, R. Johnstone, R. Walker, S. Wadsworth, A. Carter, and M. Wale, “Integrated DQPSK transmitter for dispersion-tolerant and dispersion-managed DWDM transmission,” in Proceedings of Optical Fiber Communications Conference2003, Paper FP6.

4. P. S. Cho, V. S. Grigoryan, Y. A. Godin, A. Salamon, and Y. Achiam, “Transmission of 25-Gb/s RZDQPSK signals with 25-GHz channel spacing over 1000 km of SMF-28 fiber,” IEEE Photon. Technol. Lett. 15,473–475 (2003). [CrossRef]

5. A. H. Gnauck, P. J. Winzer, S. Chandrasekhar, and C. Dorrer, “Spectrally efficient (0.8 b/s/Hz) 1-Tb/s (25 × 42.7 Gb/s) RZ-DQPSK transmission over 28 100-km SSMF spans with 7 optical add/drops,” in Proceedings of European Conference on Optical Communications2004, post-deadline paper Th4.4.1.

6. J.-X. Cai, M. Nissov, C. R. Davidson, W. Anderson, Y. Cai, A. N. Pilipetskii, D. G. Foursa, W. W. Patterson, P. C. Corbett, A. J. Lucero, and Neal S. Bergano, “Improved margin in long-haul 40 Gb/s systems using bit-synchronously modulated RZ-DQPSK,” in Proceedings of Optical Fiber Communications Conference2006, paper PDP33.

7. C. Kim and G. Li, “Direct-detection optical differential 8-level phase-shift keying (OD8PSK) for spectrally efficient transmission,” Opt. Express 12,3415–3421 (2004). [CrossRef] [PubMed]

8. S. Hayase, N. Kikuchi, K. Sekine, and S. Sasaki, “Chromatic dispersion and SPM tolerance of 8-state/symbol (binary ASK and QPSK) modulated signal,” in Proceedings of Optical Fiber Communications Conference2004, paper ThM3.

9. K.-P. Ho, Phase-modulated optical communication systems (Springer, New York, 2005).

10. D. Divsalar and M. K. Simon, “Multiple-symbol differential detection of MPSK,” IEEE Trans. Commun. 38,300–308 (1990). [CrossRef]

11. H. Leib, “Data-aided noncoherent demodulation of DPSK,” IEEE Trans. Commun. 43,722–725 (1995). [CrossRef]

12. Y. Yadin, A. Bilenca, and M. Nazarathy, “Soft detection of multichip DPSK over the nonlinear fiber-optic channel,” IEEE Photon. Technol. Lett. 17,2001–2003 (2005). [CrossRef]

13. X. Liu, “Digital implementation of soft detection for 3-chip-DBPSK with improved receiver sensitivity and dispersion tolerance,” in Proceedings of Optical Fiber Communications Conference2006, paper OTuI2.

14. M. Nazarathy and E. Simony, “Multichip differential phase encoded optical transmission,” IEEE Photon. Technol. Lett. 17,1133–1135 (2005). [CrossRef]

15. D. van den Borne, S. Jansen, G. Khoe, H. de Wardt, S. Calabro, and E. Gottwald, “Differential quadrature phase shift keying with close to homodyne performance based on multi-symbol phase estimation,” IEE Seminar on Optical Fiber Comm. and Electronic Signal. Processing, Ref. No. 2005–11310 (2005).

16. X. Liu, “Data-aided multi-symbol phase estimation for receiver sensitivity enhancement in optical DQPSK,” in Proceedings of OSA Topic Meeting on Coherent Optical Technologies and Applications (COTA)2006, paper CThB4.

17. X. Liu, “Receiver sensitivity improvement in optical DQPSK and DQPSK/ASK through data-aided multisymbol phase estimation,” in Proceedings of European Conference on Optical Communications2006, paper We2.5.6.

18. X. Liu, S. Chandrasekhar, A. H. Gnauck, C. R. Doerr, I. Kang, D. Kilper, L. L. Buhl, and J. Centanni, “DSP-enabled compensation of demodulator phase error and sensitivity improvement in direct-detection 40-Gb/s DQPSK,” in Proceedings of European Conference on Optical Communications2006, postdeadline paper Th4.4.5.

19. J. Lee, P. Roux, U.-V. Koc, T. Link, Y. Baeyens, and Y.-K. Chen, “A 5-b 10-GSample/s A/D converter for 10-Gb/s optical receivers,” IEEE J. Solid-State Circuits 39,1671–1679 (2004). [CrossRef]

20. T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, “Forward error correction based on block turbo code with 3-bit soft decision for 10-Gb/s optical communication systems,” IEEE J. Sel. Top. Quantum Electron. 10,376–386 (2004). [CrossRef]

21. J. P. Gordon and L. F. Mollenauer, “Phase noise in photonic communications systems using linear amplifiers,” Opt. Lett. 15,1351–1353 (1990). [CrossRef] [PubMed]

22. Y. Han, C. Kim, and G. Li, “Simplified receiver implementation for optical differential 8-level phase-shift keying,” Electron. Lett. 40,1372–1373 (2004). [CrossRef]

23. S. Savory and A. Hadjifotiou, “Laser linewidth requirements for optical DQPSK systems,” IEEE Photon. Technol. Lett. 16,930–932 (2004). [CrossRef]

24. J. M. Kahn, “Modulation and diction techniques for optical communication systems,” in Proceedings of OSA Topic Meeting on Coherent Optical Technologies and Applications (COTA)2006, paper CThC1.

25. X. Liu, X. Wei, R. E. Slusher, and C. J. McKinstrie, “Improving transmission performance in differential phase-shift-keyed systems by use of lumped nonlinear phase-shift compensation,” Opt. Lett. 27,1616–1618 (2002). [CrossRef]

26. G. Charlet, N. Maaref, J. Renaudier, H. Mardoyan, P. Tran, and S. Bigo, “Transmission of 40Gb/s QPSK with coherent detection over ultra long haul distance improved by nonlinearity mitigation,” in Proceedings of European Conference on Optical Communications 2006, post-deadline paper Th4.3.4.

	Δϕ(n)=0	Δϕ(n)=π/2	Δϕ(n)=π	Δϕ(n)=1.5π
exp[-jΔϕ(n)]	1	-j	-1	J
c_I(n)	1	0	0	1
c_Q(n)	1	1	0	0

Δϕ(n)	0	π/4	π/2	3π/4	π	5π/4	3π/2	7π/4
√2 exp[-jΔϕ(n)]	√2	1-j	-√2 j	-1-j	-√2	-1+j	√2 j	1+j
c_I(n)	1	1	0	0	0	0	1	1
c_Q(n)	1	1	1	1	0	0	0	0
c₃(n)	1	0	0	1	1	0	0	1

	Δϕ(n)=0	Δϕ(n)=π/2	Δϕ(n)=π	Δϕ(n)=1.5π
exp[-jΔϕ(n)]	1	-j	-1	J
c_I(n)	1	0	0	1
c_Q(n)	1	1	0	0

Δϕ(n)	0	π/4	π/2	3π/4	π	5π/4	3π/2	7π/4
√2 exp[-jΔϕ(n)]	√2	1-j	-√2 j	-1-j	-√2	-1+j	√2 j	1+j
c_I(n)	1	1	0	0	0	0	1	1
c_Q(n)	1	1	1	1	0	0	0	0
c₃(n)	1	0	0	1	1	0	0	1

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

Abstract

1. Introduction

2. Data-aided MSPE in optical DQPSK

2.1 Theory

2.2 Implementation

2.3 Performance improvement

3. Data-aided MSPE in optical 8-ary DPSK

3.1 Theory

3.2 Performance improvement

4. Data-aided MSPE in optical m-ary DPSK

4.1 Theory

4.2 Unified receiver for m-ary DPSK

4.3 Laser linewidth requirement

5. Data-aided MSPE in optical DPSK/ASK

5.1 Theory

5.2 Electronic compensation of nonlinear phase shift in DPSK/ASK

6. Conclusion

Acknowledgments

References and links

Cited By

Figures (7)

Tables (2)

Equations (45)

Optics Express