1. Introduction
Free-space optical (FSO) communications links have the potential to deliver very high bandwidth due to the high carrier frequency as compared with RF links. They have the advantages of being rapidly deployable and less expensive to install than optical fiber systems. The low divergence of laser beams means that FSO systems are intrinsically low in probability of intercept in comparison to RF, and being ‘line-of-sight’ avoids wasteful use of both the frequency domain (bandwidth allocation) and the spatial domain. Another advantage of FSO communication links over RF communications is the large unregulated bandwidth as compared with the heavy traffic and expensive bandwidth allocations for RF links.
However, one of the main factors reducing SNR in FSO communications is scintillation noise due to turbulence. Atmospheric turbulence produces temporary pockets of air with slightly different temperatures and pressures, and therefore with slightly different indices of refraction. These turbulence cells act as small, weak lenses that refract the light slightly and cause distortions in the wave front as a laser beam propagates through the atmosphere. The resulting variation in the arrival time of various components of the beam produces constructive and destructive interference at the receiver, causing fluctuations in laser beam intensity. These rapid fluctuations are known as scintillation and occur on a time scale comparable to the time it takes these cells to move across the beam path due to the wind (typically on the order of a millisecond). These intensity fluctuations become amplitude fluctuations in the case of analog modulation of the laser beam. In addition, atmospheric turbulence can cause beam break-up and beam wander which can cause very large swings in the average received power, on the order of tens of dB, on frequency scales from dc up to several kilohertz. This causes the average received AC signal to not be clamped at zero due to inadequate AC coupling.
There are many applications in which data is collected from an analog sensor or system and transmitted long distances to the end user. Typically the data would subsequently be digitized and transmitted over an RF or fiber optic communication link. Problems occur if the platform containing the sensor system is size, weight, or power (SWaP) constrained, since high speed digitizers can greatly add to the SWaP burden. Also, if the data or required communication is of a sensitive nature and secure communication links are not available, the user runs the risk of having the communication detected and/or intercepted. In these cases, it would be of great benefit to have the capability of transmitting unprocessed analog sensor data over a secure channel. Free-space lasercomm using analog or RF modulation of the transmitted laser beam can provide a method for transmitting un-digitized data over a high speed communication link that has a very low probability of detection and intercept, as well as being highly resistant to jamming efforts due to the relatively narrow field-of-view of the receivers. However, atmospheric turbulence as discussed above makes this process problematic.
Methods to correct the aberrations caused by atmospheric turbulence and to thus enable transmission of analog data over a FSO link are currently being explored. This work deals with scenarios in which a frequency-modulated waveform is transmitted through an FSO channel. Several applications of the DWT are employed in the receiver end to demodulate the transmitted data.
The chapter is organized as follows. Section 2 reviews recent advances in using analog FM to transmit data over the free space channel. Section 3 describes the mathematical modeling of the received FSO signal. Section 4 is dedicated to de-noising of the FSO signal using the DWT and Section 5 is devoted to the simulation experiments. Finally, we present the summary and conclusions in Section 6.
2. Applications
The transmission of RF modulated laser beams through optical fibers and the characterization of the information transmitted have been the subject of research for many years [1-3]. More recently, however, the potential advantages of the free space channel have led to research into its use as a medium for transmission of RF analog data. Refai
Since 2005, there have been several reports in the literature on demonstrations of FSO analog links, with increasing range and performance. In a bench top demonstration, Refai
Analog modulation has been successfully applied to FSO transmission of video signals. Baseband AM provides optimum use of bandwidth, and transmission of composite video has been demonstrated using amplitude modulation [9], although this suffers from signal degradation due to atmospheric scintillation. A technique employing dual wavelengths has been demonstrated to be effective in mitigating scintillation noise by using common mode rejection to remove co-channel noise [10, 11], but the utility of this is limited by the complexity of the system and linearity constraints in the amplitude domain. This constraint was removed by using frequency modulation of a sub-carrier to transmit audio/video signals over a 1.5km terrestrial path [12, 13]. This work has now been extended to include bidirectional audio transmission, and has been demonstrated at ranges up to 3km in the maritime environment using a modulating retro-reflector [14]. Burris
3. Mathematical modeling of received FSO signal
The received FSO signal can be described as
in which
in which
In the following section we use the Discrete Wavelet Transformation (DWT) to process
4. De-noising of FSO signal using discrete wavelet transform
This section deals with the application of the Discrete Wavelet Transformation (DWT) to the de-noising of the received FSO waveform
The DWT is a powerful iterative technique for decomposition of a signal into
A specific strength of the DWT is its ability to decompose a signal into low-frequency and high-frequency waveforms at any desired level. This property can be directly applied into the received FSO waveform of (1) in order to identify and remove the unwanted low-frequency signal
The process of removing the low-frequency noise
Hence, the received FSO signal (1) after cancellation of
where
Application of (2) in (5) results in a low-frequency signal
It is observed from (6) that the square process has enhanced the difference between the low and high frequency components of the received signal; hence, it is more effective to use DWT for signal separation. Subsequently, by finding the DWT
where in (7) it is assumed that
5. Simulation experiments
This section presents the results of simulation experiments. We present the results in two sets of experiments. Experiment I uses a 1-D time signal and deals with the sensitivity of the algorithm to the variations of
In this experiment the received waveform (1) was synthesized by generating an FM signal with the carrier frequency
with
where
This quantity is a measure of the abrupt variation of the scintillation noise
Figures 3 through 9 represent the results of this experiment. Figure 3 illustrates the FM/FSO signal
As a demonstration of the efficiency of this algorithm, we consider the situation in which the transmitted message
6. Summary and conclusions
Atmospheric noise signals are a fundamental limitation of free-space optical communications. In this work we presented the limitations that this imposes, and investigated the use of the discrete wavelet transformation (DWT) to overcome them. Simulation experiments were performed to validate the use of the DWT in the demodulation of the FM data in the presence of scintillation noise, noise due to insufficient AC-coupling, and AWGN. It was demonstrated that the use of the DWT, as explained in the paper, is quite effective in reducing the joint effects of the atmospheric as well as the additive white Gaussian noises.
Several concluding remarks are in order. It is noted that despite the fact that FM was the modulation type presented in this paper, our algorithm can be extended to other constant-envelope (digital or analog) modulation scheme. This stems from the fact that in constant-envelope modulations, the message is solely modulating the phase of the carrier. Consequently, any changes in the magnitude of the received FSO signal are exclusively due to the noise terms,
Finally, the method presented in this paper is a post-processing of the received data to validate the feasibility of the use of DWT in FM/FSO applications. The next phase of this work should be an FPGA implementation of the algorithm for a real time execution of the whole system in the receiver end.
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