Abstract
Free-space optical (FSO) communication is a leading subject that has been in the forefront of both research and commercial activities over the past years. Such attention is driven by the promise of high data rate, license-free operation, and reduced cost as well as being eco-friendly as compared to alternative communication means that are greatly suffering from, among other things, congestion[
To reduce the impact of atmospheric turbulence effects, some potential solutions such as channel coding[
SSK is a special case of SM where no data symbol is transmitted and transmitted information is conveyed through the spatial position of the active transmitter. Another study conducted in Ref. [
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The main contributions of this letter are: (i) SSK is proposed as a high-spectral-efficiency modulation technique for FSO links; (ii) exact moment generation function (MGF) and approximate MGF of the absolute difference of negative-exponential and log-normal channels for SSK are derived, respectively; (iii) tight bounds bit-error rate (BER) are obtained based on the derived MGFs and validated using Monte Carlo (MC) simulations; (iv) performance comparison with state-of-the-art RC MPAM for IM/DD FSO communication system is presented and results show that SSK outperforms RC MPAM for spectral efficiencies of 4 bits/s/Hz or larger over moderate–strong atmospheric turbulence channels.
A SSK system with
Figure 1.Synoptic diagram of the proposed model.
The received signal vector
Channel state information (CSI) is considered available at the receiver side and maximum likelihood (ML) decoder is used to decode the received signals. The decoder decides the estimated active transmitter as[
For strong-turbulence condition, the channel irradiance
A tight upper bound of the BER of SSK can be calculated by[
A tight lower bound of the BER of RC MPAM using maximum ratio combining (MRC) at the receiver is given by[
If
Figure 2.Histogram of the absolute difference of the two negative-exponential RVs.
The pdf of the electrical SNR,
If
Figure 3.Histogram of the absolute difference of two log-normal RVs (
The average lower bound BER probability of SSK over log-normal channels is shown to be equivalent to Eq. (
Figure 4.Comparison of SSK and RCs with spectral efficiency = 3 bits/s/Hz in a negative-exponential channel with
Figure 5.Comparison of SSK and RCs with spectral efficiency = 4 bits/s/Hz in a negative-exponential channel with
Figure 6.Comparison of SSK and RCs with spectral efficiency = 4 bits/s/Hz in a log-normal channel with
Furthermore, the performance of commercially available MIMO systems using RCs with
To achieve a spectral efficiency of 3 bits/s/Hz, an
Figure
Finally, Fig.
It is shown that the SSK system outperforms RC MPAM system for large number of transmitters, however, it might not be feasible in all applications, since the SSK uses a single transmitter at each time instant and all others are off for that time. Hence, single-stream transmitter are needed and the active transmit unit, among the spatially separated units, is selected each time instant based on the incoming bits sequence. As such, transmitter synchronization requirement is omitted and complexity is significantly reduced enabling the use of large number of transmitters.
In conclusion, the ABER performance of FSO links with SSK over negative-exponential and log-normal atmospheric turbulence channels are investigated. Tight upper and lower bounds for ABER expressions corresponding to negative-exponential channels and log-normal channels, respectively, are obtained. In comparison to SISO and RC MPAM techniques, our results are in favor of SSK FSO links for high-spectral-efficiency applications and/or channel high-turbulence effects. Moreover, increasing the number of receivers is shown to yield lower SNR in SSK systems as compared to RC MPAM systems.
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