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Hybrid pulse position modulation and binary phase shift keying subcarrier intensity modulation for free space optics in a weak and saturated turbulence channel Monire Faridzadeh,1 Asghar Gholami,1 Zabih Ghassemlooy,2 and Sujan Rajbhandari2,* 1
Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran 2 Optical Communications Research Group, School of Computing, Engineering and Information Sciences, Northumbria University, Newcastle upon Tyne, UK *Corresponding author:
[email protected] Received February 23, 2012; revised June 22, 2012; accepted June 24, 2012; posted June 25, 2012 (Doc. ID 163525); published July 25, 2012 In this paper a hybrid modulation scheme based on pulse position modulation (PPM) and binary phase shift keying subcarrier intensity modulation (BPSK-SIM) schemes for free-space optical communications is proposed. The analytical bit error rate (BER) performance is investigated in weak and saturated turbulence channels and results are verified with the simulation data. Results show that performance of PPM-BPSK-SIM is superior to BPSK-SIM in all turbulence regimes; however, it outperforms 2-PPM for the turbulence variance σ 21 > 0.2. PPM-BPSK-SIM offers a signal-to-noise ratio (SNR) gain of 50 dB in the saturation regime compared to BPSK at a BER of 10−6 . The SNR gain in comparison to PPM improves as the strength of the turbulence level increases. © 2012 Optical Society of America OCIS codes: 060.2605, 060.4510, 010.1300, 010.1330, 060.0060.
1. INTRODUCTION In the last decade, we have seen a growing level of research and development activities in the emerging field of free-space optical (FSO) communication systems. The FSO technology is an attractive complementary alternative to the radio frequency (RF) wireless and wired (including optical fiber) for the “last mile” communications as it does not require the right of way and digging trenches. High security, a license-free frequency spectrum, low installation costs, and the immunity to electromagnetic interference are some of other key features of FSO technologies [1–4]. The availability of the FSO link is very much dependent on the atmospheric conditions. Atmospheric factors such as fog, haze, rain, and aerosols attenuate the optical intensity by photon absorption and scattering, thus degrading the FSO link performance. Fog with particle sizes that are comparable to optical wavelengths (850–1550 nm) contribute the highest levels of attenuation [1]. In heavy fog conditions, the FSO link experiences attenuation greater than 300 dB ∕ km, which results in a substantial link range reduction from a few kilometers to less than a hundred meters [5]. In such circumstances, one solution would be to utilize a hybrid FSO/ RF (40 GHz) scheme. Using such a scheme increases the link availability from 96.8% to 99.92% [6,7]. However, this is achieved at the cost of reduced data rate and loss of data during switch-over from FSO to RF or vice versa [2,8]. In a clear atmospheric condition, the link attenuation is very low ( = 1 0 pI q exp > > 2σ 2l ; : I 2πσ 2l
I ≥ 0;
pI
1 −I exp I0 I0
B. Negative Exponential Model Beyond the strong turbulence regime, the number of independent scattering becomes large. Theoretical and experimental results have shown that the irradiance of the received signal in the saturation regime is best described by the negative exponential distribution given as [9]
(3)
3. MODULATION SCHEMES In FSO communications the average emitted optical power is limited due to the skin and eye safety constrains. Hence, modulation schemes are often compared in terms of the average received optical power required to achieve the required BER performance. Although both power and bandwidth efficiencies are important factors in selecting a modulation scheme, the simplicity in implementation is as equally important. Complex modulation schemes might render it impracticable, regardless of the power and bandwidth efficiencies [2]. In the next section, we first introduce PPM and BPSK-SIM followed by the proposed PPM-BPSK-SIM scheme. A. PPM PPM is an orthogonal pulse time modulation technique with an inherent power efficiency that makes it a prime candidate for a number of applications, including optical fiber and deepspace optical communications. However, PPM suffers from poor bandwidth efficiency due to its short pulse duration (i.e., higher bandwidth) and stringent synchronization requirements, which introduce more system complexity [23]. In PPM a block of M log2 L data bits is mapped to a symbol that consists of L-slots and a single pulse of one slot duration T s T b M ∕ L, where T b is the bit duration. The position of the pulse within a symbol (T symb T b M) corresponds to the decimal value of M-bit. Therefore, the electrical signal at the output of the photodetector in one symbol period is defined as [2,24] L−1 X
it RI
! C k gt − kT s nt;
(4)
k0
where R is the photodetector responsivity and C k is codeword of PPM. gt is the rectangular pulse shape of one time slot duration, nt is the additive white Gaussian noise (AWGN) with zero mean and variance σ 2L−ppm N 0 Rb L ∕ 2M, N 0 is the double-sided power spectral density of the Gaussian noise, and Rb is the bit rate. I is the intensity of the received signal with a peak intensity in the absence of turbulence I 0 LP av , P av is the average transmitted optical power [25]. At the receiver, detection is carried out by choosing the index of the slot containing the maximum received signal in a symbol; hence, the conditional slot error rate (SER) is obtained as [23,24] 0
1 I Q@qA: 2σ 2L−ppm
(2)
where I 0 is received optical intensity in the absence of turbulence.
I ≥ 0:
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P SER
(5)
By averaging SER over the turbulence duration, the unconditional symbol error rate (SYER) for L 2 is obtained as follows: Z P SYER
0
1 I Q@qApIdI: 2σ 22−ppm 0
∞
(6)
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B. BPSK-SIM SIM is a technique adopted from the RF communication in which the RF subcarriers pre-modulated with the data are used to modulate the optical carrier signal. Each subcarrier modulated by any standard RF digital/analog based modulation schemes could be employed for subcarrier modulation. Here, we have used BPSK with a coherent demodulation, which offers high immunity to the intensity fluctuation and does not require adaptive thresholding scheme at the receiver as information is contained in the phase of the carrier signal [1]. In addition, the coherent demodulation scheme is relatively less complex when using a low noise RF oscillator [26]. However, the requirement for an additional DC bias level to avoid signal clipping and the fact that the optical source is ‘ON’ during the transmission of both digital “1” and “0”, makes BPSK-SIM less power efficient [2]. By using a direct detection scheme at the receiver, the received signal can be modeled as [1] it RI1 ζmt nt;
minimum bandwidth of 2Rs (slot rate) centered at the RF subcarrier frequency. The output of the filter is multiplied with the reference carrier signal cosωt followed by a low pass filter, a match filter, and a sampler. The signal for one symbol period at the sampler output is given by
iD t
L RX I nD t; 2 k1 k
(10)
where nD t is AWGN with the variance of σ 2ppm ∕ 2. Finally, signal recovery is carried out by finding the index of the largest sample within one symbol. In order to evaluate the performance of the proposed modulation technique, the BER is calculated for L 2, which is equal to the slot error probability for 2-PPM. Assuming transmitting a bit “1” sequence, the received signal in one symbol period at each slot at the sampler output is given as
(7)
where ζ is the optical modulation index while I 0 P av . The unconditional bit error probability of BPSK-SIM is obtained as [1] Z ∞ p (8) Q I ∕ 2σ 2 pIdI: Pe 0
C. Hybrid PPM-BPSK-SIM This scheme combines the power efficiency and the low sensitivity to the irradiance fluctuation of PPM and BPSK-SIM, respectively. The block diagram of the proposed scheme is shown in Fig. 1. The transmitter M-bit input data is first converted into the PPM format. Following parallel-to-serial conversion and a standard RF modulator, PPM codewords are applied to the BPSK modulator. A DC bias is added to the BPSK signal prior to intensity modulating the light source. By employing a direct detection scheme at the receiver, the photodetector output current for one symbol stream is obtained as ! L X it R I k 1 ζ cosωt C k πgt − k − 1T s nt: k1
1 i1 t − RI 1 n1 t; 2
1 i2 t RI 2 n2 t: 2
(11)
The probability of choosing the wrong slot is P eslot Pi1 > i2 . Hence, the conditional BER for the 2-PPMBPSK-SIM scheme is obtained as I1 I2 : 2σ 2−ppm
Pe Q
(12)
D. 2-PPM-BPSK-SIM in Lognormal and Negative Exponential Atmospheric Turbulence Assuming z I 1 I 2 I 3 … I N expU is the sum of N lognormal random variables with log intensity variance σ z and mean μz , PDF of z is defined as [2] 1 lnz − μu 2 ; pz p exp 2σ 2u z 2πσ 2u
(13a)
expσ 2l − 1 ; μu lnN − 0.5 ln 1 N
(13b)
where (9)
In order to limit the noise contribution, the regenerated electrical signal is passed through a bandpass filter with a
Fig. 1. Block diagram of L-PPM-BPSK-SIM FSO communication system: (a) transmitter and (b) receiver.
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Values
Responsivity R Bit rate Rb Carrier frequency F c Sampling frequency F s Modulation index ξ PRBS length
1 1 Mbps 4 MHz 20 MHz 1 20
expσ 2l : σ 2u ln 1 N
SNR gain (dB)
Table 1. Simulation Parameters Parameters
∞
o
Q
(14)
Under negative exponential atmospheric turbulence, z is the sum of N negative exponential random variables with PDF of [2] pz I 0 −N zN−1
exp−z ∕ I 0 ΓN
z ≥ 0:
compared to BPSK-SIM
0
0.3
0.6
0.9
1.2
σ2l
(13c)
I0z pzdz: 2σ 2−ppm
0
compared to 2-PPM
Therefore, the unconditional BER is obtained by averaging (12) over the atmospheric turbulence with PDF of pz given by Z
4
-4
p2−ppm−bpsk
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(15)
The unconditional BER is calculated using (14) and (15).
4. RESULTS AND DISCUSSION To evaluate the performance of the PPM-BPSK-SIM modulation scheme, we have carried out analytical and simulation error probabilities for L 2 at different turbulence levels and compared the results with PPM and BPSK-SIM modulation schemes. In order to make fair comparisons between modulation schemes, the average transmitted optical power and the data rate are made to be constant. The most significant simulation parameters are listed in Table 1. The theoretical and simulation BER results for 2-PPM-BPSK-SIM, 2-PPM, and BPSK-SIM in the weak turbulence channel σ 2l f0; 0.3g
Fig. 3. SNR gain against the turbulence strength at a BER of 10−6 for 2-PPM-BPSK-SIM when compared with 2-PPM, BPSK-SIM in the lognormal atmospheric turbulence channel.
are depicted in Fig. 2. Results illustrate a good agreement between theoretical and simulation data, thus validating the accuracy of the analysis and results obtained. As expected, increasing the strength of atmospheric turbulence decreases the system performance. The SNR gain of 2-PPM-BPSK-SIM compared with 2-PPM and BPSK-SIM schemes under the lognormal model for a range of log intensity variance at a desired BER of 10−6 is plotted in Fig. 3. Notice a 3 dB gain for 2-PPM compared to 2-PPM-BPSKSIM in the absence of turbulence, which is expected as a pulse occupies one of two possible slot durations in 2-PPM. However, the signal is transmitted in both possible slot durations in 2-PPM-BPSK. BPSK-SIM shows identical performance to BPSK in the absence of turbulence. However, the clear advantage of PPM-BPSK-SIM over BPSK and PPM can be observed at higher turbulence levels (σ 2l > 0.2) with the SNR gain increasing with the turbulence strength. For example, for σ 2l 1.2 there is 7 dB and 10 dB SNR gain using 2-PPM-BPSK-SIM in comparison with 2-PPM and BPSK SIM schemes, respectively. Accordingly, the performance of the proposed modulation scheme is investigated in the saturation regime under the negative exponential model, and BER plots for 2PPMBPSKSIM, 2-PPM, and BPSK-SIM are shown in Fig. 4. As expected, 2-PPM-BPSKSIM offers enhanced performance in comparison to other modulation schemes in the strong atmospheric turbulence regime with the SNR gain of ∼50 dB at a BER of 10−6 . BER simulation results for 4-PPM-BPSK-SIM under the lognormal atmospheric turbulence for σ 21 f0.5 and 0.9g, is plotted in Fig. 5. The proposed modulation shows enhanced performance in the
0
10
2PPM-BPSK-theory PPM-sim PPM-BPSK-SIM-sim PPM BPSK-SIM BPSK-SIM-sim
σ2l =0.3 -2
10
0
BPSK-SIM 2-PPM 2-PPM-BPSK 2-PPM-BPSK-sim 2-PPM-sim BPSK-SIM-sim
-2
BER
BER
10
10
-4
10
10
No turbulence
-4
-6
10
0
5
10
15
20
25
30
SNR(dB)
Fig. 2. Theoretical and simulated BER against the SNR (dB) for 2PPM-BPSK in the lognormal and negative exponential turbulence channel.
10
-6
0
20
40
60
80
100
120
SNR(dB)
Fig. 4. BER against the SNR (dB) for 2-PPM-BPSK, 2-PPM, and BPSK-SIM in the saturation regime.
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0
10
BER results for the L-PPM-BPSK-SIM modulation scheme for L 2; 4, and 8 under lognormal (σ 21 0.5) and negative exponential atmospheric turbulence conditions. As shown, by increasing L the system performance decreases whereas the bandwidth increases.
BPSK 4-PPM-BPSK 4-PPM
-2
10 BER
σ2l =0.9
5. CONCLUSION -4
10
σ2l =0.5 -6
10
0
10
20
30
40
50
SNR(dB)
Fig. 5. BER against the SNR (dB) for 4-PPM-BPSK, 4-PPM, and BPSK-SIM in the lognormal atmospheric turbulence channel.
strong turbulence regime for the higher bit resolution as well. Figure 6 shows the BER simulation results under the negative exponential atmospheric turbulence. As illustrated in Fig. 6, 35 dB reduction in the required SNR is achieved compared with 4-PPM at a BER of 10−6 . Finally, Fig. 7 compares the simulated 0
10
BPSK 4-PPM 4-PPM-BPSK sim
-1
10
REFERENCES
Negative exponential -2
BER
10
-3
10
-4
10
0
20
40
60
80
100
SNR(dB)
Fig. 6. BER against the SNR (dB) for 4-PPM-BPSK, 4-PPM, and BPSK-SIM in the negative exponential atmospheric turbulence channel.
0
10
2-PPMBPSK 4-PPMBPSK 8-PPMBPSK
-1
10
Negative exponential
-2
BER
10
-3
10
-4
10
σ2l =0.3
0
10
20
30
40
50
60
In this paper, a new modulation scheme so called the hybrid PPM-BPSK-SIM has been proposed, and its performance was investigated for different turbulence levels. The analytical unconditional BER under the lognormal and negative exponential models were calculated for 2-PPM-BPSK-SIM and verified using computer simulations. Comparing the predicted results of 2-PPM-BPSK-SIM with BPSK and 2-PPM showed that in the turbulence-free channel, 2-PPM-BPSK-SIM has the same performance as BPSK-SIM, but is inferior to 2-PPM. In the atmospheric turbulence channel, 2-PPM-BPSK-SIM offers BER performance superior to that of other modulation schemes investigated in this paper, and its superiority is enhanced for higher turbulence levels. In the saturation regime, ∼50 dB SNR gain was achieved in comparison with BPSK-SIM at a BER of 10−6 . Hence, the proposed modulation is recommended for long haul FSO links. Simulated BER performance for the L-PPM-BPSK-SIM modulation scheme for L 2; 4, and 8 under lognormal (σ 21 0.5) and negative exponential atmospheric turbulence conditions were also carried out, showing performance degradation for higher values of L.
70
SNR(dB)
Fig. 7. Simulated BER against the SNR (dB) for 2-, 4-, and 8PPM-BPSK-SIM in the lognormal and saturation turbulence regime.
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