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We demonstrate M-ary frequency-shift keying (FSK) optical modulation and digital coherent detection, aiming at applications to space communications, where high receiver sensitivity is the most crucial consideration. The proposed FSK transmitter and receiver are based on the coherent orthogonal frequency-division multiplexing (OFDM) technique and feature simple configuration and low computational complexity. By offline bit-error rate measurements using a 256-FSK signal without the forward error-correction code, we obtain the receiver sensitivity as high as 3.5 photons per bit at the bit-error rate of 10−3. The experimental result is in good agreement with simulations.
© 2011 Optical Society of America
1. Introduction
Digital coherent optical receivers enable high spectral efficiency by the use of multi-level optical modulation formats such as M-ary phase-shift keying (PSK) modulation and quadrature amplitude modulation (QAM) [1]. In such a case, however, we inevitably suffer from degradation of the receiver sensitivity to gain the spectral efficiency. In contrast, if we employ orthogonal modulation formats such as M-ary pulse-position modulation (PPM) and frequency-shift keying (FSK) modulation, we can improve the receiver sensitivity, sacrificing the spectral efficiency [2].
In the PPM scheme, we prepare M time slots within one symbol duration T. In the FSK scheme, on the other hand, we prepare M frequency slots for one symbol duration. The minimum bandwidth of each frequency slot is 1/T. In both the cases, one of the slots is loaded with a certain number of photons, generating a symbol that carries log2 M-bit information at the rate of 1/T. With increase in the number of slots M, we can increase bits per symbol even by keeping the number of photons per symbol; therefore, the required number of photons per bit can be reduced, which means that the receiver sensitivity is improved. However, note that the signal bandwidth is expanded up to M/T. In general, bit-error rate (BER) performances of the two schemes are perfectly the same.
Continued attention has been paid to orthogonal optical modulation especially in space communication systems, where the high receiver sensitivity is one of the most crucial considerations [3]. In these orthogonal optical modulation systems, the PPM-based scheme has been more widely investigated, including the recent experiment on 16-PPM with digital coherent detection [4]. On the other hand, FSK has scarcely been studied so far, but 8-FSK has recently been reported in [5], which features parallel direct-modulation of eight semiconductor lasers and direct detection of the 8-FSK signal. However, such parallel configuration of the FSK transmitter and receiver is rather complicated and difficult to increase the number of M.
In this paper, we experimentally demonstrate highly-sensitive digital coherent detection of M-ary FSK signals for the first time to our knowledge, where the orthogonal frequency-division multiplexing (OFDM) technique [6] is introduced to prepare a considerable number of frequency slots. Owing to efficient implementation of digital signal processing (DSP) based on fast Fourier transform (FFT) and inverse FFT (IFFT), we can successfully build the FSK transmitter and receiver with simple configuration and low computational complexity. Using such a scheme, we conduct offline bit-error rate (BER) measurements. The receiver sensitivity as high as 3.5 photons per bit at BER=10−3 is demonstrated by using the uncoded 256-FSK signal where forward error-correction (FEC) is not employed.
2. M-ary orthogonal modulation
The Shannon-Hartley theorem tells us the channel capacity limit C [bit/s] with a specified bandwidth B [Hz] in the presence of noise as [7]
where S/N denotes the signal-to-noise ratio. On the other hand, S/N of light in the shot-noise limit is expressed as [8] where Ps [W] is the power of light, f [Hz] the frequency of light, and h [J·s] the Planck’s constant. The minimum number of photons per bit n [/bit] is therefore written as Noting that the spectral efficiency ɛ [bit/s/Hz] is given as we find thatFigure 1 shows the minimum number of photons per bit n plotted as a function of the spectral efficiency ɛ. When the bandwidth of the transmission system is limited, we pursue higher spectral efficiency at the expense of increasing photon numbers per bit as shown by the red arrow. Multi-level modulation formats have been used commonly for such a purpose [1]. On the other hand, when the available optical power is limited, we aim at lower photon numbers per bit, while the spectral efficiency decreases as shown by the blue arrow. The theoretical lower-limit of the photon number per bit is 0.7. The M-ary orthogonal modulation format is most suitable for such power-limited environment [2].
Fig. 1 Minimum number of photons per bit n as a function of the spectral efficiency ɛ. The red arrow represents the bandwidth-limited region, whereas the blue one the power-limited region. The theoretical lower-limit of the photon number per bit is 0.7.
M-ary pulse-position modulation (PPM) and frequency-shift keying (FSK) belong to the orthogonal modulation format. Figure 2 shows an example of the PPM symbol structure when M = 4. One symbol duration is divided into M time slots; hence, the signal bandwidth is increased by M times. On the other hand, the symbol structure of the M-ary FSK is shown in Fig.3, where the total bandwidth consists of M(= 4) frequency slots. Since the minimum bandwidth of each frequency slot is 1/T, the total bandwidth is expanded over M/T.
Fig. 2 PPM symbol structure when M = 4. One symbol duration is divided into M time slots, and the signal bandwidth is increased by M times.
Fig. 3 FSK symbol structure when M = 4. The total bandwidth consists of M frequency slots. The minimum bandwidth of each frequency slot is 1/T, and the total bandwidth is expanded over M/T.
In each case, we convert the bit sequence into blocks which contain log2 M-bit information. When symbols in such blocks are (1, 1), (1, 0), (0, 1), and (0, 0) for M = 4, we select the fourth, third, second, and first time/frequency slot, respectively, and load the selected slot with a certain number of photons. Such assignment of the time/frequency slot is done in a symbol-by-symbol manner.
As mentioned above, when the number of slots is M, the total bandwidth of the signal is given as M/T. On the other hand, the bit rate equals to log2 M/T, whereas the symbol rate is 1/T. Therefore, the spectral efficiency ɛ is given as log2 M/M. As M increases, the required number of photons per bit can be reduced because the information bit of one symbol increases; however, we cannot prevent the spectral efficiency from decreasing.
3. OFDM-based M-ary FSK transmitter and receiver
Configurations of the proposed M-ary FSK transmitter and receiver are illustrated in Figs.4 (a) and (b), respectively. The principle of operation is entirely based on the coherent orthogonal frequency-division multiplexing (OFDM) technique [6]. The frequency slots shown in Fig.3 are defined by OFDM subcarriers, whose spacing is exactly the same as the symbol rate; therefore, by using the OFDM technique, the bandwidth expansion is most minimized in the FSK scheme.
Fig. 4 Configurations of the proposed M-ary FSK transmitter (a) and receiver (b). The principle of operation is entirely based on the coherent OFDM technique.
Let M = 2ℓ, where ℓ is an integer. In the transmitter shown by Fig.4(a), a block including ℓ serial binary data is converted into a ℓ-bit symbol with a serial-to-parallel converter (S/P). Depending on the symbol, we select one subcarrier out of M with the subcarrier assignment unit. This process is shown in Fig.5. The spectrum of each symbol thus obtained is inverse Fourier-transformed with IFFT. Using a parallel-to-serial converter (P/S) and digital-to-analog converters (DACs), we obtain the complex FSK signal in the time-domain, which drives the in-phase (I) and quadrature (Q) ports of an optical IQ modulator. We also employ the cyclic extension of symbol duration to remove the effect of block interference, which is not shown in Fig.4 for simplicity. One of the advantages of the OFDM-based transmitter is that we can flexibly change the number of subcarriers with software modifications.
Fig. 5 Process of assigning OFDM subcarriers. Depending on the symbol, the subcarrier assignment unit selects one subcarrier out of M.
Figure 4(b) shows the configuration of the FSK receiver. The FSK optical signal is detected by a homodyne phase-diversity receiver [9]. Such receiver can operate under the nearly shot-noise-limited condition as far as a sufficient local-oscillator (LO) power is injected. The real and imaginary parts of the complex amplitude of the signal electric field are digitized with analog-to-digital converters (ADCs) and transformed to block sequences by a serial-to-parallel converter (S/P). The cyclic extension of symbol duration can also be used for symbol synchronization. The time-domain signal in a block is transformed into the frequency domain with FFT. Then, the subcarrier decision unit measures the power of each subcarrier and determines which subcarrer has the maximum power, as shown in Fig.6. Finally, the bit sequence within the block is restored from the determined subcarrier number by using P/S.
Fig. 6 Process of determining the subcarrier in the subcarrier decision unit. The subcarrier having the maximum power is selected among M subcarriers.
4. Experiments and discussions
Figure 7 shows the experimental setup for back-to-back BER measurements of the uncoded M-ary FSK signal, where FEC is not employed.
The transmitter laser was a distributed-feedback laser diode (DFB-LD) having a center wavelength of 1552 nm and a 3-dB linewidth of 150 kHz. An optical FSK signal was generated by using a LiNbO3 optical IQ modulator. The modulator was driven by the electrical FSK signal. Details of offline DSP for electrical FSK-signal generation have been shown in Fig.4(a). We fixed the product of the number of subcarriers and the subcarrier spacing at 5 GHz, while numbers of subcarriers were set to 4, 16, 64, and 256. In addition, we employed 12.5 % cyclic extension of symbol duration. Table 1 shows the relation among the number of subcarriers, the subcarrier spacing, the symbol rate, and the bit rate.
Table 1. Relation among the number of subcarriers, the subcarrier spacing, the symbol rate, and the bit rate. The product of the number of subcarriers and the subcarrier spacing is fixed at 5 GHz.
The incoming signal power was controlled by a variable optical attenuator (VOA). At the receiver, such signal was pre-amplified by an erbium-doped fiber amplifier (EDFA), and phase-diversity coherent detection of the signal was done by using LO with the same characteristics as the transmitter laser. The polarization of the incoming signal was manually controlled so as to match with that of LO. The frequency mismatch between the transmitter laser and LO was set below 10 MHz. Outputs from the receiver were sampled at a rate of 10 Gsample/s with ADCs, and digitized signals were stored for offline DSP. Details of DSP for FSK demodulation have been shown in Fig.4(b). For each number of subcarriers, BERs were measured as a function of the power before the pre-amplifier of the receiver, which was expressed as the photon number per bit.
Figure 8 shows BERs measured as a function of the photon number per bit, when numbers of subcarriers are 4, 16, 64, and 256. From this figure, we find that the receiver sensitivity is improved as the number of subcarriers is increased. When we use 256 subcarriers, the required photons per bit are as small as 3.5 at BER=10−3.
Fig. 8 BERs measured as a function of the photon number per bit. Numbers of subcarriers are 4, 16, 64, and 256.
On the other hand, Fig. 9 shows simulation results where we assume that the spontaneous emission factor nsp of the pre-amplifier is ideally 1.0 and that the phase noise of the transmitter and LO is negligible. Photons per bit required to obtain BER=10−3 are estimated from Figs.8 and 9 and plotted by the red and blue curves, respectively, in Fig.10 as a function of the number of subcarriers. When we assume a more realistic spontaneous emission factor of ns = 1.3, which means the noise figure of 4.2 dB, the calculated receiver sensitivity is represented by the black curve, showing very good agreement with experiments.
Fig. 9 Simulation results on BER characteristics. We assume that the spontaneous emission factor nsp of the pre-amplifier is 1.0 and that the phase noise of the transmitter and LO is negligible. Numbers of subcarriers are 4, 16, 64, 256, and 1024.
Fig. 10 Photon numbers per bit required to obtain BER=10−3. Red curve: experiments, blue curve: simulations with ns = 1.0, and black curve: simulations with ns = 1.3.
Finally, it should be worth while to mention the effect of FEC. In general, FEC can improve the BER performance significantly [10]. The receiver sensitivity as high as 1.5 photons per bit has been demonstrated in the 156-Mbit/s offline homodyne PSK system by introducing the rate-1/2 turbo coding [11]. However, a too large bandwidth overhead for FEC results in drastic increase in computational complexity. Therefore, in order to achieve the ultimate receiver sensitivity in a practical system, it is important to use orthogonal modulation having a large number of M together with FEC having a relatively small bandwidth overhead.
5. Conclusions
We have demonstrated 256-FSK modulation and digital coherent detection, which employ digital signal processing for coherent OFDM. By using such a scheme, the receiver sensitivity as high as 3.5 photons per bit is experimentally obtained at the bit-error rate of 10−3 without FEC. Such receiver sensitivity is in good agreement with the simulation result. Owing to its simple hardware and low computational complexity of DSP, it is suitable for space communication systems, which require high sensitivity, compactness, and low power consumption.
Acknowledgments
This work was supported in part by Grant-in-Aid for Scientific Research (A) (22246046), the Ministry of Education, Science, Sports and Culture, Japan.
References and links
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