Abstract

In this paper, we consider the design of space code for an intensity modulated direct detection multi-input-multi-output optical wireless communication (IM/DD MIMO-OWC) system, in which channel coefficients are independent and non-identically log-normal distributed, with variances and means known at the transmitter and channel state information available at the receiver. Utilizing the existing space code design criterion for IM/DD MIMO-OWC with a maximum likelihood (ML) detector, we design a diversity-optimal space code (DOSC) that maximizes both large-scale diversity and small-scale diversity gains and prove that the spatial repetition code (RC) with a diversity-optimized power allocation is diversity-optimal among all the high dimensional nonnegative space code schemes under a commonly used optical power constraint. In addition, we show that one of significant advantages of the DOSC is to allow low-complexity ML detection. Simulation results indicate that in high signal-to-noise ratio (SNR) regimes, our proposed DOSC significantly outperforms RC, which is the best space code currently available for such system.

© 2016 Optical Society of America

1. Introduction

As an emerging technology, intensity modulated direct detection optical wireless communication (IM/DD OWC) [1–4 ] has become an attractive area of research. To provide more robust error performance in presence of atmospheric turbulence, the design of diversity transmitters for IM/DD MIMO-OWC was proposed [5–13 ]. Unfortunately, the currently well developed diversity techniques for MIMO radio frequency (MIMO-RF) [14–17 ] and coherent MIMOOWC [18–22 ] can not be straightforwardly generalized to IM/DD MIMO-OWC because of the following two reasons. The first reason is that the transmitter design of IM/DD MIMO-OWC must be nonnegative to satisfy the unipolarity requirement of intensity modulation. As a result, the existing MIMO-RF [14] and coherent MIMO-OWC diversity techniques [21, 22] are not directly applicable to IM/DD MIMO-OWC. Although a full diversity gain can be provided by adding proper direct-current components into the code designs for MIMO-RF and coherent MIMO-OWC [5, 8, 9], the numerical error performance of some modified orthogonal space time block codes is even worse than that of the space-only repetition code (RC) [6, 7, 10, 11]. The second reason is that the channel coefficients of IM/DD MIMO-OWC are also nonnegative [23]. In fact, the results in [12, 13] indicate that because of this characteristic of channels, a properly designed space-only transmission of IM/DD MIMO-OWC enables a full diversity gain. As a simple space-only scheme, RC, which repeats the same symbol across all the space dimensions [6, 7, 10, 11], is the best currently available full diversity space code [6, 7, 10–13 ] for IM/DD MIMO-OWC, which does not need the transmitter to exactly know channel state information. Here, a natural question is whether there exists a full diversity spatial transmission scheme outperforming RC, which, as far as the best knowledge of authors, is still a longstanding open problem.

Therefore, in this paper, we consider the design of space code for IM/DD MIMO-OWC systems. For such system, it is known that when the transmitter has perfect channel state information, the transmitter aperture selection method was proposed in [24–27 ] and shown to outperform RC. Unfortunately, perfect channel state information at the transmitter is not easily attainable in practice. For this reason, we specifically consider an IM/DD MIMO-OWC system in presence of log-normal fading [28, 29] with a practical assumption that different channel coefficients are independent and have nonidentical variances resulted from diverse atmospheric factors [30, 31]. For this scenario, an error performance design criterion of a space code with an ML detector has been established in [12, 13]. Using this criterion, the design problem of a diversity-optimal space code (DOSC) maximizing both large-scale and small-scale diversity gains is formulated into a max-min optimization problem with continuous-discrete mixed design variables. In [12, 13], linear DOSC is designed for a specific 2 × 2 IM/DD MIMO-OWC with given unipolar pulse amplitude modulation (PAM). Unfortunately, the technique in [12,13] using the Farey sequence in number theory is very difficult to be extended to a general IM/DD MIMO-OWC. In addition, significantly different from the specific linear design for a 2 × 2 IM/DD MIMO-OWC in [12,13], our design in this paper is to consider the DOSC for a general IM/DD MIMO-OWC system within the nonnegative orthant of a multi-dimensional real space without any other additional assumptions on the signal set. By fully using the full large-scale diversity condition on the space code design [12, 13], we will arrange all the space signal vectors in an increasing order and develop a novel geometrically-weighted inequality to attain a closed-form solution to the design problem. It will be proved that RC with a diversity-optimal power allocation is the DOSC for a general IM/DD MIMO-OWC system among all the nonnegative high-dimensional space constellations. In addition, it will be shown that this diversity-optimal design has a fast ML detection algorithm.

2. System model and design criterion for space code

In this section, we first introduce the system model considered in this paper, and then, review our recently proposed design criterion for the space code of IM/DD MIMO-OWC systems [12, 13].

2.1. System model

Let us consider an M × N IM/DD MIMO-OWC system which has M receiver apertures and N transmitter apertures. These N transmitter apertures transmit a space signal s = [s 1, s 2, ··· , sN]T randomly and independently selected with equal probability from a constellation 𝒮 = {s k, 0 ≤ k ≤ 2K − 1} to be designed. To meet the nonnegativity condition of intensity modulation, the symbol sn for n = 1, 2, ··· , N to be transmitted from the n-th transmitter aperture is nonnegative, say, 𝒮+N. These symbols are then transmitted to the M receiver apertures through an M × N channel matrix H, whose entries are flat-fading path coefficients and also nonnegative. Therefore, the received signal, denoted by an M × 1 vector y, can be represented by

y=Hs+n,
where the entries of H are assumed to be independent and log-normal distributed, i.e., hmn = e zmn, where zmn~𝒩(μmn,σmn2), m = 1, ··· , M, n = 1, ··· , N. The probability density function (PDF) of hmn is fH(hmn)=12πhmnσmne(lnhmnμmn)22σmn2, where σmn2 is decided by diverse factors such as altitude, the light wavelength, the link distance and the root mean square wind speed [30,31]. These factors usually lead to non-identical σmn2 for different m and n in practical scenarios. The PDF of H is f(H)=Πm=1MΠn=1NfH(hmn). From [23,30,32,33], the noise vector n is modelled as signal-independent, additive, white and Gaussian noise with zero mean and co-variance matrix σn2MIM×M.

To facilitate our analysis, in this paper we make the following two assumptions:

  1. Power constraint. In practice, the power constraint for intensity modulated optical sources is usually imposed on the mean value of the unipolar optical signals [23, 34–37 ], i.e., 12Kk=02K1n=1Nsnk1.
  2. Channel information. The receiver knows the values of channel coefficients. The transmitter knows μmn, the mean values of the logarithm of channel coefficients, and the following vector in terms of the channel variances, 1σ¯[σ¯1,,σ¯N]T, where σ¯n=m=1Mσmn2 and σ¯=n=1Nσ¯n.

2.2. Design criterion for space code

For presentation clarity, let us now introduce our recently established space code design criterion for the IM/DD MIMO-OWC system [12, 13] below:

Design criterion: If e = (e 1, e 2,··· ,eN)T = ŝs is positive up to a real-valued scale for any s, ŝ𝒮 satisfying sŝ, then, in high SNR=ρ regimes, the average pair-wise error probability P(sŝ) for a space code of an M × N IM/DD MIMO-OWC system (1) is bounded by CL(lnρ)MNe𝒟large8(lnρ+lnσ¯ln(Mk=1Nek2))2P(ss^)PD(ss^)+𝒪(e𝒟large8ln2ρ), where 𝒟 large = σ̄, CL=m=1Mn=1Nσmn(4π)MNeMN/2Q(12(k=1Nek2)1/2) with Q being the standard Q-function and

PD(ss^)=CD𝒢(e)(ρ/ln2ρ)σ¯4ln(Nσ¯M)34ln𝒟small(e)(lnρ)MNe𝒟large8ln2ρln2ρ
with CD=NMN2m=1Mn=1Nσmneσ¯8ln2(Nσ¯M), 𝒟small(e)=n=1N|en|σ¯n and 𝒢(e)=exp(12m=1Mn=1N(ln|en|σmn)2)(Nσ¯M)lnln𝒟small(e)2.

It should be noted that the results in [12, 13] are for the case when μmn = 0 for any m, n. However, the channel fading not only attenuates the received optical power, but also attenuates the signal. In addition, different channel links may suffer from attenuations. Therefore, in the following, we provide a signal design criterion with μmn taken into consideration. By following the performance analysis techniques in [12,13], we can, without much difficulty, attain the corresponding dominant behavior of the average pair-wise error probability in high SNR regimes as follows:

P˜D(ss^)=PD(ss^)n=1N|en|m=1Mμmnσmn2(ρ/ln2ρ)14n=1Nm=1Mμmnσmn2
where PD (sŝ) is defined in (2).

From (2) and (3), we can observe that in high SNR regimes, the following three major factors significantly affect the decaying speed of D (sŝ).

  1. Large-scale diversity gain. In a high SNR regime, the first main factor that determines the exponential decaying speed of D (sŝ) is 𝒟 large. Therefore, 𝒟 large is named large-scale diversity gain [12, 13]. The maximum 𝒟 large or full large-scale diversity gain σ̄ is achieved when e = ŝs is positive up to a scale for any pair of distinct s, ŝ𝒮.
  2. Small-scale diversity gain. The second main factor is 𝒟small(e)=n=1N|en|σ¯n, which controls the polynomial decaying speed of ρln2ρ, and thus, is defined as small-scale diversity gain [12, 13]. When a full large-scale diversity gain has been assured, the worst-case small-scale diversity gain mine 𝒟 small (e) should be further maximized.
  3. Coding gain. Since 𝒢=(e)n=1N|en|m=1Mμmnσmn2 only affects the horizontal shift of the error curve, this term is defined as coding gain. Under the condition that both large-scale diversity and small-scale diversity gains have been optimized, maxe𝒢(e)n=1N|en|m=1Mμmnσmn2 should be minimized if there are still design freedoms to be optimized.

3. Diversity-optimal power loading for space code

Our primary purpose in this section is to devise a diversity-optimal constellation 𝒮 that maximizes both the large-scale diversity and the small-scale diversity gains. Then, this proposed design will be shown to admit ML detection with low-complexity.

3.1. Diversity-optimal space code

In this subsection, we specifically aim at solving the following optimization problem:

Design problem: For any given positive integers N and K, design a space constellation 𝒮={sk,0k2K1}+N such that min0k2k12K1n=1N|snk2snk1|σ¯n is maximized under conditions that ∀k 2 > k 1, sk2sk1+N, and 12Kk=02K1n=1Nsnk=1.

Here, it is noticed that min0k1k22K1n=1N|snk2snk1|σ¯n has continuous and discrete mixed design variables. Thus, one of the main technical challenges is to analytically solve the inner minimization problem with respect to the discrete variables, i.e., min0k1k22K1n=1N|snk2snk1|σ¯n. From the above-mentioned design criterion, we know that a full large-scale diversity gain is assured by the condition that ŝs is positive up to a scale for any pair of distinct ŝ and s. This condition enables us to rearrange all the elements of 𝒮, s0,,s2K1+N, such that s 0 < ··· < s 2K−1, where notation “x < y” denotes that all the entries of yx are positive. Therefore, for 0 ≤ k 1 < k 2 ≤ 2K − 1, it holds that s nk2s n(k1+1) > s nk1, giving us n=1N|snk2snk1|σ¯n=n=1N(snk2sn(k1+1)+sn(k1+1)snk1)σ¯nn=1N(sn(k1+1)snk1)σ¯n, where the equality holds if and only if k 2 = k 1 + 1. Therefore, we can attain that min0k1<k22K1n=1N|snk2snk1|σ¯n=min0k2K1n=1N(sn(k+1)snk)σ¯n. This observation leads us to the equivalent form of our original design problem:

Problem 1: For arbitrarily fixed positive integers N and K, find an N-dimensional constellation 𝒮={sk,0k2K1}+N to maximize min0k2K2n=1N(sn(k+1)snk)σ¯n subject to constraints that s k+1s k > 0 and 12Kk=02K1n=1Nsnk=1.

Now, it can be seen that the positivity of the error vectors (up to a scale) not only assures a full large-scale diversity gain, but also plays an important role in equivalently simplifying the inner minimization problem with respect to the discrete variables in the design problem.

For the purpose of attaining a closed-form solution to Problem 1, we first establish a power-product inequality. It is known that logt is concave with respect to positive t. In addition, the Jensen’s inequality [38] tells us that for λn ≥ 0 with n=1Nλn=1, logt satisfies n=1Nλnlogtnlogn=1Nλntn, where the equality holds if and only if t 1 = ··· = tN. Now, let tn = (s n(k+1)snk)/σ̄n and λn=σ¯nσ¯. Then, we have n=1Nλnlogtn=n=1Nσ¯nσ¯log(sn(k+1)snk)n=1Nσ¯nσ¯logσ¯n=1σ¯logn=1N(sn(k+1)snk)σ¯n1σ¯logn=1Nσ¯nσ¯n and logn=1Nλntn=logn=1N(sn(k+1)snk)σ¯. Then, combining these two inequalities with n=1Nλnlog(tn)logn=1Nλntn produces logn=1N(sn(k+1)snk)σ¯nlogn=1Nσ¯nσ¯n+log(n=1N(sn(k+1)snk)/σ¯)σ¯, yielding

n=1N(sn(k+1)snk)σ¯n(n=1N(sn(k+1))snk)σ¯n=1N(σ¯nσ¯)σ¯n.
Now, we claim that for any constellation 𝒮 satisfying the power constraint, the following inequality is true,
min0k2K2n=1N(sn(k+1)snk)σ¯n2σ¯n=1Nσ¯nσ¯n((2K1)σ¯)σ¯
Otherwise, if there exists a constellation 𝒮 = 𝒮̃ = {ŝ k, 0 ≤ k ≤ 2K − 1} such that min0k2K2n=1N(s˜n(k+1)s˜nk)σ¯n2σ¯n=1Nσ¯nσ¯n((2K1)σ¯)σ¯, then, ∀k ∈ {0, 1, ··· , 2K − 2}, it holds
n=1N(s˜n(k+1)s˜nk)σ¯n>2σ¯n=1Nσ¯nσ¯n((2K1)σ¯)σ¯
Then, substituting the inequality (4) into (6) yields that ∀k ∈ {0, 1,...,2K − 2}, n=1Ns˜n(k+1)n=1Ns˜nk>2/(2K1). It follows that n=1Ns˜nk>2k/(2K1)+kn=1Ns˜n0 for k = 1, 2,··· ,2K − 1. Now, summing all these inequalities yields that k=02K1n=1Ns˜nk>2k=02K1k/(2K1)+(1+2K(2K1)/2)n=1Ns˜n0=2K+(1+2K(2K1)/2)n=1Ns˜n02K, which contradicts with our power constraint 12Kk=02K1n=1Nsnk=1. Thus, inequality (5) is indeed true. By computations, we can have that the upper-bound in (5) is achieved by
𝒮opt={kw}k=0k=2K1
where w=2[σ¯1,,σ¯N]Tσ¯(2K1). Therefore, the optimal solution to Problem 1 is determined by 𝒮 opt. Now, for a general IM/DD MIMO-OWC system, the DOSC has been designed. To further appreciate the diversity-optimal design, we make the following three comments:
  1. Diversity-optimal constellation. The proposed diversity-optimal design reveals the fact that the diversity-optimal space constellation is actually a diversity-optimal power-loaded version of the one-dimensional PAM constellation {k : 0 ≤ k ≤ 2K − 1}. Here, it should be emphasized that the DOSC is attained among all the full large-scale diversity space code schemes. Hence, this diversity-optimality of our design is for all space code schemes in the sense of maximizing both the small-scale and large-scale diversity gains. It can be seen that after both diversity gains have been optimized, there are no design freedoms left. Therefore, the diversity-optimality of our proposed result is irrelevant to the values of μmn.
  2. RC diversity-optimality. The existing experimental evidences [7,10] have strongly demonstrated that RC as a spatial diversity transmission scheme is diversity-optimal in the sense of error performance for IM/DD MIMO-OWC over log-normal fading channels with equal variances. However, its mathematical proof remains open for a long time due to the lack of an explicit signal design criterion. As a specific case of the diversity-optimal design, when σ̄ 1 = ··· = σ̄N, the resulting DOSC is exactly RC. Hence, we actually solve this long-standing open problem under a much weaker condition.
  3. Power loading. The diversity-optimal design only requires the knowledge of σ¯nσ¯ for n = 1, 2, ··· , N rather than each variance σmn2, m = 1, ··· , M, n = 1, ··· , N itself. Essentially, the diversity-optimal structure of space code is the diversity-optimal power-loaded space-repetition of the symbols selected from {k : 0 ≤ k ≤ 2K − 1}.

3.2. Fast ML detection for diversity-optimal space code

Notice that for the DOSC 𝒮 opt, the resulting MIMO channel model becomes

y=Hwk+n,0k2K1

3.2.1. Classical ML receiver of MIMO channels

For a general MIMO channel model y = Hs + n with s𝒮, the output of the classical ML receiver is attained as s^=argmins𝒮yHs22. To determine the optimal estimate, the receiver has to exhaustively search all the 2K elements in 𝒮. Therefore, the complexity of the classical ML receiver is O(2K).

3.2.2. Fast ML detector for proposed diversity-optimal design

For our proposed diversity-optimal design 𝒮opt, the optimal estimate of s = w k for the model (8) with the ML detector is equivalent to finding a nonnegative integer k such that

k^=argmin0k2K1yHwk22=argmin0k2K1(k2Hwk222kyTHw+y22)=argmin0k2K1(Hw22×|kyTHw/Hw22|2(yTHw)2/Hwk22+y22)=argmin0k2K1|kyTHw/Hw22|
where the last equality holds for the fact that both y and Hw are independent of k. The observation tells us that the optimal ML receiver for our diversity-optimal design is equivalent to a linear zero-forcing receiver. Hence, the optimal estimate of the transmitted signal can be efficiently obtained by using the following algorithm:

Algorithm 1 (Fast ML detection): Given the received signal y and the nonzero channel matrix H, the output of the ML detector for the DOSC 𝒮 opt is determined as follows:

s^k={0,yTHw/Hw22<0;yTHw/Hw22+12w,0yTHw/Hw222K1;(2K1)w,yTHw/Hw22>2K1.

From Algorithm 1, we can see that the complexity of the ML detector for our proposed transmission scheme is just O(MN). Therefore, the ML detector for our proposed diversity-optimal design has much lower complexity.

4. Simulation results and discussions

In this section, we carry our computer simulations to examine the performance of our diversity-optimal design by comparing with RC [6, 7, 10–13 ], which is the best space code presently available in the literature for this system. Since the average optical power is normalized, the SNR is defined by 1σn2. The channel realizations are generated by producing Gaussian random variables zmn~𝒩(μmn,σmn2) first for m = 1, ··· , M, n = 1, ··· , N and then, letting hmn = exp(zmn). The channel realizations are independently generated from time slot to time slot.

All the schemes to compare are described as follows:

  1. Repetition code (RC). The space vector of RC for M × N IM/DD MIMO-OWC with K bits per channel use is given by sk=2×1N×1N(2K1) with 0 ≤ k ≤ 2K − 1.
  2. Diversity-optimal space code (DOSC). The signal vector of the proposed design in (7) is determined as sk=2k[σ¯1,,σ¯N]Tσ¯(2K1), for 0 ≤ k ≤ 2K − 1.

It can be seen that the above two schemes have the same bit rate, i.e., K bits per channel use and normalized average optical power, i.e., 12Kk=02K1n=1Nsnk=1. To make the comparison as fair as possible, all the receivers are based on ML detection, which is equivalent to the zero-forcing receiver. More details of the simulations shown by Figs. 14 are described as follows:

 

Fig. 1 Performance comparison of DOSC and RC with M = 1, N = 2 and K = 2.

Download Full Size | PPT Slide | PDF

 

Fig. 2 Performance comparison of DOSC and RC with M = N = 2 and varied K.

Download Full Size | PPT Slide | PDF

 

Fig. 3 Performance comparison of DOSC and RC with M = 1, N = K = 2 and varied μn.

Download Full Size | PPT Slide | PDF

 

Fig. 4 Performance comparison of DOSC and RC with N = 2, K = 3 and varied M.

Download Full Size | PPT Slide | PDF

As illustrated in Fig. 1, we find that if maxn1n2,σ̄n1σ̄n2 σ̄ n1/σ̄ n2 is sufficiently large, then, the more SNR gain of our diversity-optimal design over RC is attained. Furthermore, the gap between two error curves becomes larger against increasing SNR. When σ̄ 2/σ̄ 1 = 0.5/0.001 = 500, as illustrated by Fig. 1, substantial SNR gains can be observed. For example, when looking at the target codeword symbol error rate of 10−6, we can see that our DOSC obtains about the 4 dB SNR gain over RC, which will be expected to become larger if SNR is sufficiently high. This is, again, for the reason that the DOSC provides larger small-scale diversity gain than RC, and the small-scale diversity gain governs the polynomial decaying speed of the error curves. In addition, for M = 1, N = 2 and σ12=1, σ22=0.001, the attained gain, about 4 dB for target error rate of 10−6, is robust to the bit rate as illustrated by Fig. 2. Furthermore, from Fig. 3, when μn is varied and the other parameters are fixed, substantial gains can still be attained. However, when μ 1 = 0 and μ 2 becomes smaller, the corresponding error curves of RC and our diversity-optimal design will have a horizontal shift to the right and the performance advantage of our proposed design will become noticeable in a higher SNR regime. For example, when μ 1 = 0 and μ 2 = −1.5, the path long-term attenuation factors exp(μ 1) and exp(μ 2) are far from different. Recall that the small-scale diversity gain of an IM/DD MIMO-OWC system is defined at high SNRs and here the upper end of the SNR range is not sufficiently high. Hence, even when μ 1 = 0 and μ 2 becomes very small with fixed σ12 and σ22, the attained small-scale diversity advantage of our diversity-optimal design is expected to be more noticeable against increasing SNRs.

To put the influence of aperture number on the error performance into perspective, we vary the receiver aperture number M and fix the transmitter number to be N = 2. The performance comparison is illustrated by Fig. 4. From Fig. 4, we can see that for fixed σmn2, μmn, N and K, the performance advantage of our diversity-optimal design over RC depends on M and decreases against increasing M. For instance, when M = 1, the attained gain is about 3 dB at the target error rate of 10−8. However, for the case with M = 8, the attained gain by our diversity-optimal design is smaller than 0.1 dB for the same target error rate. The main reason is that our proposed design is only diversity-optimal and improves the error performance in the high SNR regime. When M is large, the diversity gain provided by our diversity-optimal design will be noticeable when SNR is sufficiently high.

5. Conclusion and future work

In this paper, we have designed the DOSC in the sense of maximizing both the large-scale and small-scale diversity gains for a general IM/DD MIMO-OWC system in presence of independent and non-identical log-normal fading. By fully taking advantage of the full large-scale diversity condition and developing a novel power-product inequality, we have attained a closed-form solution to the DOSC design problem. It has been shown that RC with a diversity-optimal power allocation is the DOSC. Simulation results have indicated that substantial performance gains are attained by our diversity-optimal design over RC, which is the best space code currently available in literature for IM/DD MIMO-OWC systems. In future, we will consider the following two research directions: 1) the error performance of our proposed DOSC will be verified via experimental approaches and 2) an asymptotic error performance formula will be established, addressing the overall influence of σmn2 and μmn on the optimal design of space code.

Acknowledgments

This work was supported in part by Grant No. 2013AA013603 from China National “863” Program, by Grant 61271253 from China NSFC and by NSERC.

References and links

1. D. K. Borah, A. C. Boucouvalas, C. C. Davis, S. Hranilovic, and K. Yiannopoulos, “A review of communication-oriented optical wireless systems,” EURASIP J. Wireless Commun. Netw. 91(1), 1–28 (2012).

2. M. A. Khalighi and M. Uysal, “Survey on free space optical communication: A communication theory perspective,” Commun. Surveys Tuts. 16(4), 2231–2258 (2014). [CrossRef]  

3. S. Chaudhary and A. Amphawan, “The role and challenges of free-space optical systems,” J. Opt. Commun. 35(4), 327–334 (2014). [CrossRef]  

4. A. K. Majumdar, Free-space Optical (FSO) Platforms: Unmanned Aerial Vehicle (UAV) and Mobile (Springer, 2015).

5. M. K. Simon and V. A. Vilnrotter, “Alamouti-type space-time coding for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. 4(1), 35–39 (2005). [CrossRef]  

6. S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun. 6(8), 2813–2819 (2007). [CrossRef]  

7. M. Safari and M. Uysal, “Do we really need OSTBCs for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. 7(11), 4445–4448 (2008). [CrossRef]  

8. H. Wang, X. Ke, and L. Zhao, “MIMO free space optical communication based on orthogonal space time block code,” Science Chin. Series F: Inf. Sci. 52(8), 1483–1490 (2009). [CrossRef]  

9. R. Tian-Peng, C. Yuen, Y. Guan, and T. Ge-Shi, “High-order intensity modulations for OSTBC in free-space optical MIMO communications,” IEEE Commun. Lett. 2(6), 607–610 (2013). [CrossRef]  

10. E. Bayaki and R. Schober, “On space-time coding for free-space optical systems,” IEEE Trans. Commun. 58(1), 58–62 (2010). [CrossRef]  

11. M. Abaza, R. Mesleh, A. Mansour, and E.-H. M. Aggoune, “Diversity techniques for a free-space optical communication system in correlated log-normal channels,” Opt. Eng. 53(1), 259–268 (2014). [CrossRef]  

12. Y.-Y. Zhang, H.-Y. Yu, J.-K. Zhang, Y.-J. Zhu, J.-L. Wang, and T. Wang, “Full large-scale diversity space codes for MIMO optical wireless communications,” in Proc. IEEE Int. Symp. Inf. Theory (IEEE, 2015), pp. 1671–1675.

13. Y.-Y. Zhang, H.-Y. Yu, J.-K. Zhang, Y.-J. Zhu, J.-L. Wang, and T. Wang, “Space codes for MIMO optical wireless communications: Error performance criterion and code construction,” http://arxiv.org/abs/1509.07470 (2015).

14. V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-time codes for high date rate wireless communication: performance criterion and code construction,” IEEE Trans. Inf. Theory 44(2), 744–765 (1998). [CrossRef]  

15. J.-K. Zhang, J. Liu, and K. M. Wong, “Trace-orthonormal full diversity cyclotomic space-time codes,” IEEE Trans. Signal Process. 55(2), 618–630 (2007). [CrossRef]  

16. J. Liu, J.-K. Zhang, and K. M. Wong, “Full diversity codes for MISO systems equipped with linear or ML detectors,” IEEE Trans. Inf. Theory 54(10) 4511–4527 (2008). [CrossRef]  

17. D. Xia, J.-K. Zhang, and S. Dumitrescu, “Energy-efficient full diversity collaborative unitary space-time block code designs via unique factorization of signals,” IEEE Trans. Inf. Theory 59(3), 1678–1703 (2013). [CrossRef]  

18. S. M. Aghajanzadeh and M. Uysal, “Diversity–multiplexing trade-off in coherent free-space optical systems with multiple receivers,” J. Opt. Commun. Netw 2(12), 1087–1094 (2010). [CrossRef]  

19. E. Bayaki and R. Schober, “Performance and design of coherent and differential space-time coded FSO systems,” J. Lightwave Technol. 30(11), 1569–1577 (2012). [CrossRef]  

20. M. Niu, X. Song, J. Cheng, and J. F. Holzman, “Performance analysis of coherent wireless optical communications with atmospheric turbulence,” Opt. Express 20(6), 6515–6520 (2012). [CrossRef]   [PubMed]  

21. X. Song, J. Cheng, and M.-S. Alouini, “High SNR BER comparison of coherent and differentially coherent modulation schemes in lognormal fading channels,” arXiv preprint arXiv:1407.7097 (2014).

22. M. Niu, J. Cheng, and J. F. Holzman, “Alamouti-type STBC for atmospheric optical communication using coherent detection,” IEEE Photonics J. 6(1), 1–17 (2014). [CrossRef]  

23. J. R. Barry, Wireless Infrared Communications (Kluwer Academic, 1994). [CrossRef]  

24. A. García-Zambrana, C. Castillo-Vázquez, B. Castillo-Vázquez, and A. Hiniesta-Gómez, “Selection transmit diversity for FSO links over strong atmospheric turbulence channels,” IEEE Photonics Technol. Lett. 21(14), 1017–1019 (2009). [CrossRef]  

25. A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Space-time trellis coding with transmit laser selection for FSO links over strong atmospheric turbulence channels,” Opt. Express 18(6), 5356–5366 (2010). [CrossRef]   [PubMed]  

26. A. García-Zambrana, B. Castillo-Vázquez, and C. Castillo-Vázquez, “Average capacity of FSO links with transmit laser selection using non-uniform OOK signaling over exponential atmospheric turbulence channels,” Opt. Express 18(19), 20445–20454 (2010). [CrossRef]   [PubMed]  

27. C. Abou-Rjeily, “On the optimality of the selection transmit diversity for MIMO-FSO links with feedback,” IEEE Commun. Lett. 15(6), 641–643 (2011). [CrossRef]  

28. N. C. Beaulieu and Q. Xie, “An optimal lognormal approximation to lognormal sum distributions,” IEEE Trans. Commun. Technol. 53(2), 479–489 (2004).

29. D. Giggenbach and H. Henniger, “Fading-loss assessment in atmospheric free-space optical communication links with on-off keying,” Opt. Eng. 47(4), 046001 (2008). [CrossRef]  

30. S. Karp, R. M. Gagliardi, S. E. Moran, and L. B. Stotts, Optical Channels (Springer, 1988). [CrossRef]  

31. L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001). [CrossRef]  

32. D. Marcuse, “Calculation of bit-error probability for a lightwave system with optical amplifiers and post-detection Gaussian noise,” J. Lightwave Technol. 9(4), 505–513 (1991). [CrossRef]  

33. M. K. Simon and M.-S. Alouini, Digital Communication Over Fading Channels (John Wiley and Sons, 2000). [CrossRef]  

34. J. Armstrong and B. J. C. Schmidt, “Comparison of asymmetrically clipped optical OFDM and DC-biased optical OFDM in AWGN,” IEEE Commun. Lett. 12(5), 343–345 (2008). [CrossRef]  

35. J. Karout, E. Agrell, K. Szczerba, and M. Karlsson, “Optimizing constellations for single-subcarrier intensity-modulated optical systems,” IEEE Trans. Inf. Theory 58(7), 4645–4659 (2012). [CrossRef]  

36. Q. Gao, J. Manton, G. Chen, and Y. Hua, “Constellation design for a multicarrier optical wireless communication channel,” IEEE Trans. Commun. 62(1), 214–225 (2014). [CrossRef]  

37. X. Ling, J. Wang, X. Liang, Z. Ding, and C. Zhao, “Offset and power optimization for DCO-OFDM in visible light communication systems,” IEEE Trans. Signal Process. 31(1), 278 (2015).

38. T. M. Cover and J. A. Thomas, Information Theory (John Wiley and Sons, 1991).

References

  • View by:
  • |
  • |
  • |

  1. D. K. Borah, A. C. Boucouvalas, C. C. Davis, S. Hranilovic, and K. Yiannopoulos, “A review of communication-oriented optical wireless systems,” EURASIP J. Wireless Commun. Netw. 91(1), 1–28 (2012).
  2. M. A. Khalighi and M. Uysal, “Survey on free space optical communication: A communication theory perspective,” Commun. Surveys Tuts. 16(4), 2231–2258 (2014).
    [Crossref]
  3. S. Chaudhary and A. Amphawan, “The role and challenges of free-space optical systems,” J. Opt. Commun. 35(4), 327–334 (2014).
    [Crossref]
  4. A. K. Majumdar, Free-space Optical (FSO) Platforms: Unmanned Aerial Vehicle (UAV) and Mobile (Springer, 2015).
  5. M. K. Simon and V. A. Vilnrotter, “Alamouti-type space-time coding for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. 4(1), 35–39 (2005).
    [Crossref]
  6. S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun. 6(8), 2813–2819 (2007).
    [Crossref]
  7. M. Safari and M. Uysal, “Do we really need OSTBCs for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. 7(11), 4445–4448 (2008).
    [Crossref]
  8. H. Wang, X. Ke, and L. Zhao, “MIMO free space optical communication based on orthogonal space time block code,” Science Chin. Series F: Inf. Sci. 52(8), 1483–1490 (2009).
    [Crossref]
  9. R. Tian-Peng, C. Yuen, Y. Guan, and T. Ge-Shi, “High-order intensity modulations for OSTBC in free-space optical MIMO communications,” IEEE Commun. Lett. 2(6), 607–610 (2013).
    [Crossref]
  10. E. Bayaki and R. Schober, “On space-time coding for free-space optical systems,” IEEE Trans. Commun. 58(1), 58–62 (2010).
    [Crossref]
  11. M. Abaza, R. Mesleh, A. Mansour, and E.-H. M. Aggoune, “Diversity techniques for a free-space optical communication system in correlated log-normal channels,” Opt. Eng. 53(1), 259–268 (2014).
    [Crossref]
  12. Y.-Y. Zhang, H.-Y. Yu, J.-K. Zhang, Y.-J. Zhu, J.-L. Wang, and T. Wang, “Full large-scale diversity space codes for MIMO optical wireless communications,” in Proc. IEEE Int. Symp. Inf. Theory (IEEE, 2015), pp. 1671–1675.
  13. Y.-Y. Zhang, H.-Y. Yu, J.-K. Zhang, Y.-J. Zhu, J.-L. Wang, and T. Wang, “Space codes for MIMO optical wireless communications: Error performance criterion and code construction,” http://arxiv.org/abs/1509.07470 (2015).
  14. V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-time codes for high date rate wireless communication: performance criterion and code construction,” IEEE Trans. Inf. Theory 44(2), 744–765 (1998).
    [Crossref]
  15. J.-K. Zhang, J. Liu, and K. M. Wong, “Trace-orthonormal full diversity cyclotomic space-time codes,” IEEE Trans. Signal Process. 55(2), 618–630 (2007).
    [Crossref]
  16. J. Liu, J.-K. Zhang, and K. M. Wong, “Full diversity codes for MISO systems equipped with linear or ML detectors,” IEEE Trans. Inf. Theory 54(10) 4511–4527 (2008).
    [Crossref]
  17. D. Xia, J.-K. Zhang, and S. Dumitrescu, “Energy-efficient full diversity collaborative unitary space-time block code designs via unique factorization of signals,” IEEE Trans. Inf. Theory 59(3), 1678–1703 (2013).
    [Crossref]
  18. S. M. Aghajanzadeh and M. Uysal, “Diversity–multiplexing trade-off in coherent free-space optical systems with multiple receivers,” J. Opt. Commun. Netw 2(12), 1087–1094 (2010).
    [Crossref]
  19. E. Bayaki and R. Schober, “Performance and design of coherent and differential space-time coded FSO systems,” J. Lightwave Technol. 30(11), 1569–1577 (2012).
    [Crossref]
  20. M. Niu, X. Song, J. Cheng, and J. F. Holzman, “Performance analysis of coherent wireless optical communications with atmospheric turbulence,” Opt. Express 20(6), 6515–6520 (2012).
    [Crossref] [PubMed]
  21. X. Song, J. Cheng, and M.-S. Alouini, “High SNR BER comparison of coherent and differentially coherent modulation schemes in lognormal fading channels,” arXiv preprint arXiv:1407.7097 (2014).
  22. M. Niu, J. Cheng, and J. F. Holzman, “Alamouti-type STBC for atmospheric optical communication using coherent detection,” IEEE Photonics J. 6(1), 1–17 (2014).
    [Crossref]
  23. J. R. Barry, Wireless Infrared Communications (Kluwer Academic, 1994).
    [Crossref]
  24. A. García-Zambrana, C. Castillo-Vázquez, B. Castillo-Vázquez, and A. Hiniesta-Gómez, “Selection transmit diversity for FSO links over strong atmospheric turbulence channels,” IEEE Photonics Technol. Lett. 21(14), 1017–1019 (2009).
    [Crossref]
  25. A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Space-time trellis coding with transmit laser selection for FSO links over strong atmospheric turbulence channels,” Opt. Express 18(6), 5356–5366 (2010).
    [Crossref] [PubMed]
  26. A. García-Zambrana, B. Castillo-Vázquez, and C. Castillo-Vázquez, “Average capacity of FSO links with transmit laser selection using non-uniform OOK signaling over exponential atmospheric turbulence channels,” Opt. Express 18(19), 20445–20454 (2010).
    [Crossref] [PubMed]
  27. C. Abou-Rjeily, “On the optimality of the selection transmit diversity for MIMO-FSO links with feedback,” IEEE Commun. Lett. 15(6), 641–643 (2011).
    [Crossref]
  28. N. C. Beaulieu and Q. Xie, “An optimal lognormal approximation to lognormal sum distributions,” IEEE Trans. Commun. Technol. 53(2), 479–489 (2004).
  29. D. Giggenbach and H. Henniger, “Fading-loss assessment in atmospheric free-space optical communication links with on-off keying,” Opt. Eng. 47(4), 046001 (2008).
    [Crossref]
  30. S. Karp, R. M. Gagliardi, S. E. Moran, and L. B. Stotts, Optical Channels (Springer, 1988).
    [Crossref]
  31. L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).
    [Crossref]
  32. D. Marcuse, “Calculation of bit-error probability for a lightwave system with optical amplifiers and post-detection Gaussian noise,” J. Lightwave Technol. 9(4), 505–513 (1991).
    [Crossref]
  33. M. K. Simon and M.-S. Alouini, Digital Communication Over Fading Channels (John Wiley and Sons, 2000).
    [Crossref]
  34. J. Armstrong and B. J. C. Schmidt, “Comparison of asymmetrically clipped optical OFDM and DC-biased optical OFDM in AWGN,” IEEE Commun. Lett. 12(5), 343–345 (2008).
    [Crossref]
  35. J. Karout, E. Agrell, K. Szczerba, and M. Karlsson, “Optimizing constellations for single-subcarrier intensity-modulated optical systems,” IEEE Trans. Inf. Theory 58(7), 4645–4659 (2012).
    [Crossref]
  36. Q. Gao, J. Manton, G. Chen, and Y. Hua, “Constellation design for a multicarrier optical wireless communication channel,” IEEE Trans. Commun. 62(1), 214–225 (2014).
    [Crossref]
  37. X. Ling, J. Wang, X. Liang, Z. Ding, and C. Zhao, “Offset and power optimization for DCO-OFDM in visible light communication systems,” IEEE Trans. Signal Process. 31(1), 278 (2015).
  38. T. M. Cover and J. A. Thomas, Information Theory (John Wiley and Sons, 1991).

2015 (1)

X. Ling, J. Wang, X. Liang, Z. Ding, and C. Zhao, “Offset and power optimization for DCO-OFDM in visible light communication systems,” IEEE Trans. Signal Process. 31(1), 278 (2015).

2014 (5)

Q. Gao, J. Manton, G. Chen, and Y. Hua, “Constellation design for a multicarrier optical wireless communication channel,” IEEE Trans. Commun. 62(1), 214–225 (2014).
[Crossref]

M. Niu, J. Cheng, and J. F. Holzman, “Alamouti-type STBC for atmospheric optical communication using coherent detection,” IEEE Photonics J. 6(1), 1–17 (2014).
[Crossref]

M. A. Khalighi and M. Uysal, “Survey on free space optical communication: A communication theory perspective,” Commun. Surveys Tuts. 16(4), 2231–2258 (2014).
[Crossref]

S. Chaudhary and A. Amphawan, “The role and challenges of free-space optical systems,” J. Opt. Commun. 35(4), 327–334 (2014).
[Crossref]

M. Abaza, R. Mesleh, A. Mansour, and E.-H. M. Aggoune, “Diversity techniques for a free-space optical communication system in correlated log-normal channels,” Opt. Eng. 53(1), 259–268 (2014).
[Crossref]

2013 (2)

D. Xia, J.-K. Zhang, and S. Dumitrescu, “Energy-efficient full diversity collaborative unitary space-time block code designs via unique factorization of signals,” IEEE Trans. Inf. Theory 59(3), 1678–1703 (2013).
[Crossref]

R. Tian-Peng, C. Yuen, Y. Guan, and T. Ge-Shi, “High-order intensity modulations for OSTBC in free-space optical MIMO communications,” IEEE Commun. Lett. 2(6), 607–610 (2013).
[Crossref]

2012 (4)

D. K. Borah, A. C. Boucouvalas, C. C. Davis, S. Hranilovic, and K. Yiannopoulos, “A review of communication-oriented optical wireless systems,” EURASIP J. Wireless Commun. Netw. 91(1), 1–28 (2012).

E. Bayaki and R. Schober, “Performance and design of coherent and differential space-time coded FSO systems,” J. Lightwave Technol. 30(11), 1569–1577 (2012).
[Crossref]

M. Niu, X. Song, J. Cheng, and J. F. Holzman, “Performance analysis of coherent wireless optical communications with atmospheric turbulence,” Opt. Express 20(6), 6515–6520 (2012).
[Crossref] [PubMed]

J. Karout, E. Agrell, K. Szczerba, and M. Karlsson, “Optimizing constellations for single-subcarrier intensity-modulated optical systems,” IEEE Trans. Inf. Theory 58(7), 4645–4659 (2012).
[Crossref]

2011 (1)

C. Abou-Rjeily, “On the optimality of the selection transmit diversity for MIMO-FSO links with feedback,” IEEE Commun. Lett. 15(6), 641–643 (2011).
[Crossref]

2010 (4)

2009 (2)

H. Wang, X. Ke, and L. Zhao, “MIMO free space optical communication based on orthogonal space time block code,” Science Chin. Series F: Inf. Sci. 52(8), 1483–1490 (2009).
[Crossref]

A. García-Zambrana, C. Castillo-Vázquez, B. Castillo-Vázquez, and A. Hiniesta-Gómez, “Selection transmit diversity for FSO links over strong atmospheric turbulence channels,” IEEE Photonics Technol. Lett. 21(14), 1017–1019 (2009).
[Crossref]

2008 (4)

D. Giggenbach and H. Henniger, “Fading-loss assessment in atmospheric free-space optical communication links with on-off keying,” Opt. Eng. 47(4), 046001 (2008).
[Crossref]

J. Armstrong and B. J. C. Schmidt, “Comparison of asymmetrically clipped optical OFDM and DC-biased optical OFDM in AWGN,” IEEE Commun. Lett. 12(5), 343–345 (2008).
[Crossref]

M. Safari and M. Uysal, “Do we really need OSTBCs for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. 7(11), 4445–4448 (2008).
[Crossref]

J. Liu, J.-K. Zhang, and K. M. Wong, “Full diversity codes for MISO systems equipped with linear or ML detectors,” IEEE Trans. Inf. Theory 54(10) 4511–4527 (2008).
[Crossref]

2007 (2)

J.-K. Zhang, J. Liu, and K. M. Wong, “Trace-orthonormal full diversity cyclotomic space-time codes,” IEEE Trans. Signal Process. 55(2), 618–630 (2007).
[Crossref]

S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun. 6(8), 2813–2819 (2007).
[Crossref]

2005 (1)

M. K. Simon and V. A. Vilnrotter, “Alamouti-type space-time coding for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. 4(1), 35–39 (2005).
[Crossref]

2004 (1)

N. C. Beaulieu and Q. Xie, “An optimal lognormal approximation to lognormal sum distributions,” IEEE Trans. Commun. Technol. 53(2), 479–489 (2004).

1998 (1)

V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-time codes for high date rate wireless communication: performance criterion and code construction,” IEEE Trans. Inf. Theory 44(2), 744–765 (1998).
[Crossref]

1991 (1)

D. Marcuse, “Calculation of bit-error probability for a lightwave system with optical amplifiers and post-detection Gaussian noise,” J. Lightwave Technol. 9(4), 505–513 (1991).
[Crossref]

Abaza, M.

M. Abaza, R. Mesleh, A. Mansour, and E.-H. M. Aggoune, “Diversity techniques for a free-space optical communication system in correlated log-normal channels,” Opt. Eng. 53(1), 259–268 (2014).
[Crossref]

Abou-Rjeily, C.

C. Abou-Rjeily, “On the optimality of the selection transmit diversity for MIMO-FSO links with feedback,” IEEE Commun. Lett. 15(6), 641–643 (2011).
[Crossref]

Aggoune, E.-H. M.

M. Abaza, R. Mesleh, A. Mansour, and E.-H. M. Aggoune, “Diversity techniques for a free-space optical communication system in correlated log-normal channels,” Opt. Eng. 53(1), 259–268 (2014).
[Crossref]

Aghajanzadeh, S. M.

S. M. Aghajanzadeh and M. Uysal, “Diversity–multiplexing trade-off in coherent free-space optical systems with multiple receivers,” J. Opt. Commun. Netw 2(12), 1087–1094 (2010).
[Crossref]

Agrell, E.

J. Karout, E. Agrell, K. Szczerba, and M. Karlsson, “Optimizing constellations for single-subcarrier intensity-modulated optical systems,” IEEE Trans. Inf. Theory 58(7), 4645–4659 (2012).
[Crossref]

Alouini, M.-S.

M. K. Simon and M.-S. Alouini, Digital Communication Over Fading Channels (John Wiley and Sons, 2000).
[Crossref]

X. Song, J. Cheng, and M.-S. Alouini, “High SNR BER comparison of coherent and differentially coherent modulation schemes in lognormal fading channels,” arXiv preprint arXiv:1407.7097 (2014).

Amphawan, A.

S. Chaudhary and A. Amphawan, “The role and challenges of free-space optical systems,” J. Opt. Commun. 35(4), 327–334 (2014).
[Crossref]

Andrews, L. C.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).
[Crossref]

Armstrong, J.

J. Armstrong and B. J. C. Schmidt, “Comparison of asymmetrically clipped optical OFDM and DC-biased optical OFDM in AWGN,” IEEE Commun. Lett. 12(5), 343–345 (2008).
[Crossref]

Barry, J. R.

J. R. Barry, Wireless Infrared Communications (Kluwer Academic, 1994).
[Crossref]

Bayaki, E.

E. Bayaki and R. Schober, “Performance and design of coherent and differential space-time coded FSO systems,” J. Lightwave Technol. 30(11), 1569–1577 (2012).
[Crossref]

E. Bayaki and R. Schober, “On space-time coding for free-space optical systems,” IEEE Trans. Commun. 58(1), 58–62 (2010).
[Crossref]

Beaulieu, N. C.

N. C. Beaulieu and Q. Xie, “An optimal lognormal approximation to lognormal sum distributions,” IEEE Trans. Commun. Technol. 53(2), 479–489 (2004).

Borah, D. K.

D. K. Borah, A. C. Boucouvalas, C. C. Davis, S. Hranilovic, and K. Yiannopoulos, “A review of communication-oriented optical wireless systems,” EURASIP J. Wireless Commun. Netw. 91(1), 1–28 (2012).

Boucouvalas, A. C.

D. K. Borah, A. C. Boucouvalas, C. C. Davis, S. Hranilovic, and K. Yiannopoulos, “A review of communication-oriented optical wireless systems,” EURASIP J. Wireless Commun. Netw. 91(1), 1–28 (2012).

Calderbank, A. R.

V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-time codes for high date rate wireless communication: performance criterion and code construction,” IEEE Trans. Inf. Theory 44(2), 744–765 (1998).
[Crossref]

Castillo-Vázquez, B.

Castillo-Vázquez, C.

Chaudhary, S.

S. Chaudhary and A. Amphawan, “The role and challenges of free-space optical systems,” J. Opt. Commun. 35(4), 327–334 (2014).
[Crossref]

Chen, G.

Q. Gao, J. Manton, G. Chen, and Y. Hua, “Constellation design for a multicarrier optical wireless communication channel,” IEEE Trans. Commun. 62(1), 214–225 (2014).
[Crossref]

Cheng, J.

M. Niu, J. Cheng, and J. F. Holzman, “Alamouti-type STBC for atmospheric optical communication using coherent detection,” IEEE Photonics J. 6(1), 1–17 (2014).
[Crossref]

M. Niu, X. Song, J. Cheng, and J. F. Holzman, “Performance analysis of coherent wireless optical communications with atmospheric turbulence,” Opt. Express 20(6), 6515–6520 (2012).
[Crossref] [PubMed]

X. Song, J. Cheng, and M.-S. Alouini, “High SNR BER comparison of coherent and differentially coherent modulation schemes in lognormal fading channels,” arXiv preprint arXiv:1407.7097 (2014).

Cover, T. M.

T. M. Cover and J. A. Thomas, Information Theory (John Wiley and Sons, 1991).

Davis, C. C.

D. K. Borah, A. C. Boucouvalas, C. C. Davis, S. Hranilovic, and K. Yiannopoulos, “A review of communication-oriented optical wireless systems,” EURASIP J. Wireless Commun. Netw. 91(1), 1–28 (2012).

Ding, Z.

X. Ling, J. Wang, X. Liang, Z. Ding, and C. Zhao, “Offset and power optimization for DCO-OFDM in visible light communication systems,” IEEE Trans. Signal Process. 31(1), 278 (2015).

Dumitrescu, S.

D. Xia, J.-K. Zhang, and S. Dumitrescu, “Energy-efficient full diversity collaborative unitary space-time block code designs via unique factorization of signals,” IEEE Trans. Inf. Theory 59(3), 1678–1703 (2013).
[Crossref]

Gagliardi, R. M.

S. Karp, R. M. Gagliardi, S. E. Moran, and L. B. Stotts, Optical Channels (Springer, 1988).
[Crossref]

Gao, Q.

Q. Gao, J. Manton, G. Chen, and Y. Hua, “Constellation design for a multicarrier optical wireless communication channel,” IEEE Trans. Commun. 62(1), 214–225 (2014).
[Crossref]

García-Zambrana, A.

Ge-Shi, T.

R. Tian-Peng, C. Yuen, Y. Guan, and T. Ge-Shi, “High-order intensity modulations for OSTBC in free-space optical MIMO communications,” IEEE Commun. Lett. 2(6), 607–610 (2013).
[Crossref]

Giggenbach, D.

D. Giggenbach and H. Henniger, “Fading-loss assessment in atmospheric free-space optical communication links with on-off keying,” Opt. Eng. 47(4), 046001 (2008).
[Crossref]

Guan, Y.

R. Tian-Peng, C. Yuen, Y. Guan, and T. Ge-Shi, “High-order intensity modulations for OSTBC in free-space optical MIMO communications,” IEEE Commun. Lett. 2(6), 607–610 (2013).
[Crossref]

Henniger, H.

D. Giggenbach and H. Henniger, “Fading-loss assessment in atmospheric free-space optical communication links with on-off keying,” Opt. Eng. 47(4), 046001 (2008).
[Crossref]

Hiniesta-Gómez, A.

A. García-Zambrana, C. Castillo-Vázquez, B. Castillo-Vázquez, and A. Hiniesta-Gómez, “Selection transmit diversity for FSO links over strong atmospheric turbulence channels,” IEEE Photonics Technol. Lett. 21(14), 1017–1019 (2009).
[Crossref]

Holzman, J. F.

M. Niu, J. Cheng, and J. F. Holzman, “Alamouti-type STBC for atmospheric optical communication using coherent detection,” IEEE Photonics J. 6(1), 1–17 (2014).
[Crossref]

M. Niu, X. Song, J. Cheng, and J. F. Holzman, “Performance analysis of coherent wireless optical communications with atmospheric turbulence,” Opt. Express 20(6), 6515–6520 (2012).
[Crossref] [PubMed]

Hopen, C. Y.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).
[Crossref]

Hranilovic, S.

D. K. Borah, A. C. Boucouvalas, C. C. Davis, S. Hranilovic, and K. Yiannopoulos, “A review of communication-oriented optical wireless systems,” EURASIP J. Wireless Commun. Netw. 91(1), 1–28 (2012).

Hua, Y.

Q. Gao, J. Manton, G. Chen, and Y. Hua, “Constellation design for a multicarrier optical wireless communication channel,” IEEE Trans. Commun. 62(1), 214–225 (2014).
[Crossref]

Karlsson, M.

J. Karout, E. Agrell, K. Szczerba, and M. Karlsson, “Optimizing constellations for single-subcarrier intensity-modulated optical systems,” IEEE Trans. Inf. Theory 58(7), 4645–4659 (2012).
[Crossref]

Karout, J.

J. Karout, E. Agrell, K. Szczerba, and M. Karlsson, “Optimizing constellations for single-subcarrier intensity-modulated optical systems,” IEEE Trans. Inf. Theory 58(7), 4645–4659 (2012).
[Crossref]

Karp, S.

S. Karp, R. M. Gagliardi, S. E. Moran, and L. B. Stotts, Optical Channels (Springer, 1988).
[Crossref]

Kavehrad, M.

S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun. 6(8), 2813–2819 (2007).
[Crossref]

Ke, X.

H. Wang, X. Ke, and L. Zhao, “MIMO free space optical communication based on orthogonal space time block code,” Science Chin. Series F: Inf. Sci. 52(8), 1483–1490 (2009).
[Crossref]

Khalighi, M. A.

M. A. Khalighi and M. Uysal, “Survey on free space optical communication: A communication theory perspective,” Commun. Surveys Tuts. 16(4), 2231–2258 (2014).
[Crossref]

Liang, X.

X. Ling, J. Wang, X. Liang, Z. Ding, and C. Zhao, “Offset and power optimization for DCO-OFDM in visible light communication systems,” IEEE Trans. Signal Process. 31(1), 278 (2015).

Ling, X.

X. Ling, J. Wang, X. Liang, Z. Ding, and C. Zhao, “Offset and power optimization for DCO-OFDM in visible light communication systems,” IEEE Trans. Signal Process. 31(1), 278 (2015).

Liu, J.

J. Liu, J.-K. Zhang, and K. M. Wong, “Full diversity codes for MISO systems equipped with linear or ML detectors,” IEEE Trans. Inf. Theory 54(10) 4511–4527 (2008).
[Crossref]

J.-K. Zhang, J. Liu, and K. M. Wong, “Trace-orthonormal full diversity cyclotomic space-time codes,” IEEE Trans. Signal Process. 55(2), 618–630 (2007).
[Crossref]

Majumdar, A. K.

A. K. Majumdar, Free-space Optical (FSO) Platforms: Unmanned Aerial Vehicle (UAV) and Mobile (Springer, 2015).

Mansour, A.

M. Abaza, R. Mesleh, A. Mansour, and E.-H. M. Aggoune, “Diversity techniques for a free-space optical communication system in correlated log-normal channels,” Opt. Eng. 53(1), 259–268 (2014).
[Crossref]

Manton, J.

Q. Gao, J. Manton, G. Chen, and Y. Hua, “Constellation design for a multicarrier optical wireless communication channel,” IEEE Trans. Commun. 62(1), 214–225 (2014).
[Crossref]

Marcuse, D.

D. Marcuse, “Calculation of bit-error probability for a lightwave system with optical amplifiers and post-detection Gaussian noise,” J. Lightwave Technol. 9(4), 505–513 (1991).
[Crossref]

Mesleh, R.

M. Abaza, R. Mesleh, A. Mansour, and E.-H. M. Aggoune, “Diversity techniques for a free-space optical communication system in correlated log-normal channels,” Opt. Eng. 53(1), 259–268 (2014).
[Crossref]

Moran, S. E.

S. Karp, R. M. Gagliardi, S. E. Moran, and L. B. Stotts, Optical Channels (Springer, 1988).
[Crossref]

Navidpour, S. M.

S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun. 6(8), 2813–2819 (2007).
[Crossref]

Niu, M.

M. Niu, J. Cheng, and J. F. Holzman, “Alamouti-type STBC for atmospheric optical communication using coherent detection,” IEEE Photonics J. 6(1), 1–17 (2014).
[Crossref]

M. Niu, X. Song, J. Cheng, and J. F. Holzman, “Performance analysis of coherent wireless optical communications with atmospheric turbulence,” Opt. Express 20(6), 6515–6520 (2012).
[Crossref] [PubMed]

Phillips, R. L.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).
[Crossref]

Safari, M.

M. Safari and M. Uysal, “Do we really need OSTBCs for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. 7(11), 4445–4448 (2008).
[Crossref]

Schmidt, B. J. C.

J. Armstrong and B. J. C. Schmidt, “Comparison of asymmetrically clipped optical OFDM and DC-biased optical OFDM in AWGN,” IEEE Commun. Lett. 12(5), 343–345 (2008).
[Crossref]

Schober, R.

E. Bayaki and R. Schober, “Performance and design of coherent and differential space-time coded FSO systems,” J. Lightwave Technol. 30(11), 1569–1577 (2012).
[Crossref]

E. Bayaki and R. Schober, “On space-time coding for free-space optical systems,” IEEE Trans. Commun. 58(1), 58–62 (2010).
[Crossref]

Seshadri, N.

V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-time codes for high date rate wireless communication: performance criterion and code construction,” IEEE Trans. Inf. Theory 44(2), 744–765 (1998).
[Crossref]

Simon, M. K.

M. K. Simon and V. A. Vilnrotter, “Alamouti-type space-time coding for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. 4(1), 35–39 (2005).
[Crossref]

M. K. Simon and M.-S. Alouini, Digital Communication Over Fading Channels (John Wiley and Sons, 2000).
[Crossref]

Song, X.

M. Niu, X. Song, J. Cheng, and J. F. Holzman, “Performance analysis of coherent wireless optical communications with atmospheric turbulence,” Opt. Express 20(6), 6515–6520 (2012).
[Crossref] [PubMed]

X. Song, J. Cheng, and M.-S. Alouini, “High SNR BER comparison of coherent and differentially coherent modulation schemes in lognormal fading channels,” arXiv preprint arXiv:1407.7097 (2014).

Stotts, L. B.

S. Karp, R. M. Gagliardi, S. E. Moran, and L. B. Stotts, Optical Channels (Springer, 1988).
[Crossref]

Szczerba, K.

J. Karout, E. Agrell, K. Szczerba, and M. Karlsson, “Optimizing constellations for single-subcarrier intensity-modulated optical systems,” IEEE Trans. Inf. Theory 58(7), 4645–4659 (2012).
[Crossref]

Tarokh, V.

V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-time codes for high date rate wireless communication: performance criterion and code construction,” IEEE Trans. Inf. Theory 44(2), 744–765 (1998).
[Crossref]

Thomas, J. A.

T. M. Cover and J. A. Thomas, Information Theory (John Wiley and Sons, 1991).

Tian-Peng, R.

R. Tian-Peng, C. Yuen, Y. Guan, and T. Ge-Shi, “High-order intensity modulations for OSTBC in free-space optical MIMO communications,” IEEE Commun. Lett. 2(6), 607–610 (2013).
[Crossref]

Uysal, M.

M. A. Khalighi and M. Uysal, “Survey on free space optical communication: A communication theory perspective,” Commun. Surveys Tuts. 16(4), 2231–2258 (2014).
[Crossref]

S. M. Aghajanzadeh and M. Uysal, “Diversity–multiplexing trade-off in coherent free-space optical systems with multiple receivers,” J. Opt. Commun. Netw 2(12), 1087–1094 (2010).
[Crossref]

M. Safari and M. Uysal, “Do we really need OSTBCs for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. 7(11), 4445–4448 (2008).
[Crossref]

S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun. 6(8), 2813–2819 (2007).
[Crossref]

Vilnrotter, V. A.

M. K. Simon and V. A. Vilnrotter, “Alamouti-type space-time coding for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. 4(1), 35–39 (2005).
[Crossref]

Wang, H.

H. Wang, X. Ke, and L. Zhao, “MIMO free space optical communication based on orthogonal space time block code,” Science Chin. Series F: Inf. Sci. 52(8), 1483–1490 (2009).
[Crossref]

Wang, J.

X. Ling, J. Wang, X. Liang, Z. Ding, and C. Zhao, “Offset and power optimization for DCO-OFDM in visible light communication systems,” IEEE Trans. Signal Process. 31(1), 278 (2015).

Wang, J.-L.

Y.-Y. Zhang, H.-Y. Yu, J.-K. Zhang, Y.-J. Zhu, J.-L. Wang, and T. Wang, “Full large-scale diversity space codes for MIMO optical wireless communications,” in Proc. IEEE Int. Symp. Inf. Theory (IEEE, 2015), pp. 1671–1675.

Wang, T.

Y.-Y. Zhang, H.-Y. Yu, J.-K. Zhang, Y.-J. Zhu, J.-L. Wang, and T. Wang, “Full large-scale diversity space codes for MIMO optical wireless communications,” in Proc. IEEE Int. Symp. Inf. Theory (IEEE, 2015), pp. 1671–1675.

Wong, K. M.

J. Liu, J.-K. Zhang, and K. M. Wong, “Full diversity codes for MISO systems equipped with linear or ML detectors,” IEEE Trans. Inf. Theory 54(10) 4511–4527 (2008).
[Crossref]

J.-K. Zhang, J. Liu, and K. M. Wong, “Trace-orthonormal full diversity cyclotomic space-time codes,” IEEE Trans. Signal Process. 55(2), 618–630 (2007).
[Crossref]

Xia, D.

D. Xia, J.-K. Zhang, and S. Dumitrescu, “Energy-efficient full diversity collaborative unitary space-time block code designs via unique factorization of signals,” IEEE Trans. Inf. Theory 59(3), 1678–1703 (2013).
[Crossref]

Xie, Q.

N. C. Beaulieu and Q. Xie, “An optimal lognormal approximation to lognormal sum distributions,” IEEE Trans. Commun. Technol. 53(2), 479–489 (2004).

Yiannopoulos, K.

D. K. Borah, A. C. Boucouvalas, C. C. Davis, S. Hranilovic, and K. Yiannopoulos, “A review of communication-oriented optical wireless systems,” EURASIP J. Wireless Commun. Netw. 91(1), 1–28 (2012).

Yu, H.-Y.

Y.-Y. Zhang, H.-Y. Yu, J.-K. Zhang, Y.-J. Zhu, J.-L. Wang, and T. Wang, “Full large-scale diversity space codes for MIMO optical wireless communications,” in Proc. IEEE Int. Symp. Inf. Theory (IEEE, 2015), pp. 1671–1675.

Yuen, C.

R. Tian-Peng, C. Yuen, Y. Guan, and T. Ge-Shi, “High-order intensity modulations for OSTBC in free-space optical MIMO communications,” IEEE Commun. Lett. 2(6), 607–610 (2013).
[Crossref]

Zhang, J.-K.

D. Xia, J.-K. Zhang, and S. Dumitrescu, “Energy-efficient full diversity collaborative unitary space-time block code designs via unique factorization of signals,” IEEE Trans. Inf. Theory 59(3), 1678–1703 (2013).
[Crossref]

J. Liu, J.-K. Zhang, and K. M. Wong, “Full diversity codes for MISO systems equipped with linear or ML detectors,” IEEE Trans. Inf. Theory 54(10) 4511–4527 (2008).
[Crossref]

J.-K. Zhang, J. Liu, and K. M. Wong, “Trace-orthonormal full diversity cyclotomic space-time codes,” IEEE Trans. Signal Process. 55(2), 618–630 (2007).
[Crossref]

Y.-Y. Zhang, H.-Y. Yu, J.-K. Zhang, Y.-J. Zhu, J.-L. Wang, and T. Wang, “Full large-scale diversity space codes for MIMO optical wireless communications,” in Proc. IEEE Int. Symp. Inf. Theory (IEEE, 2015), pp. 1671–1675.

Zhang, Y.-Y.

Y.-Y. Zhang, H.-Y. Yu, J.-K. Zhang, Y.-J. Zhu, J.-L. Wang, and T. Wang, “Full large-scale diversity space codes for MIMO optical wireless communications,” in Proc. IEEE Int. Symp. Inf. Theory (IEEE, 2015), pp. 1671–1675.

Zhao, C.

X. Ling, J. Wang, X. Liang, Z. Ding, and C. Zhao, “Offset and power optimization for DCO-OFDM in visible light communication systems,” IEEE Trans. Signal Process. 31(1), 278 (2015).

Zhao, L.

H. Wang, X. Ke, and L. Zhao, “MIMO free space optical communication based on orthogonal space time block code,” Science Chin. Series F: Inf. Sci. 52(8), 1483–1490 (2009).
[Crossref]

Zhu, Y.-J.

Y.-Y. Zhang, H.-Y. Yu, J.-K. Zhang, Y.-J. Zhu, J.-L. Wang, and T. Wang, “Full large-scale diversity space codes for MIMO optical wireless communications,” in Proc. IEEE Int. Symp. Inf. Theory (IEEE, 2015), pp. 1671–1675.

Commun. Surveys Tuts. (1)

M. A. Khalighi and M. Uysal, “Survey on free space optical communication: A communication theory perspective,” Commun. Surveys Tuts. 16(4), 2231–2258 (2014).
[Crossref]

EURASIP J. Wireless Commun. Netw. (1)

D. K. Borah, A. C. Boucouvalas, C. C. Davis, S. Hranilovic, and K. Yiannopoulos, “A review of communication-oriented optical wireless systems,” EURASIP J. Wireless Commun. Netw. 91(1), 1–28 (2012).

IEEE Commun. Lett. (3)

J. Armstrong and B. J. C. Schmidt, “Comparison of asymmetrically clipped optical OFDM and DC-biased optical OFDM in AWGN,” IEEE Commun. Lett. 12(5), 343–345 (2008).
[Crossref]

C. Abou-Rjeily, “On the optimality of the selection transmit diversity for MIMO-FSO links with feedback,” IEEE Commun. Lett. 15(6), 641–643 (2011).
[Crossref]

R. Tian-Peng, C. Yuen, Y. Guan, and T. Ge-Shi, “High-order intensity modulations for OSTBC in free-space optical MIMO communications,” IEEE Commun. Lett. 2(6), 607–610 (2013).
[Crossref]

IEEE Photonics J. (1)

M. Niu, J. Cheng, and J. F. Holzman, “Alamouti-type STBC for atmospheric optical communication using coherent detection,” IEEE Photonics J. 6(1), 1–17 (2014).
[Crossref]

IEEE Photonics Technol. Lett. (1)

A. García-Zambrana, C. Castillo-Vázquez, B. Castillo-Vázquez, and A. Hiniesta-Gómez, “Selection transmit diversity for FSO links over strong atmospheric turbulence channels,” IEEE Photonics Technol. Lett. 21(14), 1017–1019 (2009).
[Crossref]

IEEE Trans. Commun. (2)

Q. Gao, J. Manton, G. Chen, and Y. Hua, “Constellation design for a multicarrier optical wireless communication channel,” IEEE Trans. Commun. 62(1), 214–225 (2014).
[Crossref]

E. Bayaki and R. Schober, “On space-time coding for free-space optical systems,” IEEE Trans. Commun. 58(1), 58–62 (2010).
[Crossref]

IEEE Trans. Commun. Technol. (1)

N. C. Beaulieu and Q. Xie, “An optimal lognormal approximation to lognormal sum distributions,” IEEE Trans. Commun. Technol. 53(2), 479–489 (2004).

IEEE Trans. Inf. Theory (4)

J. Karout, E. Agrell, K. Szczerba, and M. Karlsson, “Optimizing constellations for single-subcarrier intensity-modulated optical systems,” IEEE Trans. Inf. Theory 58(7), 4645–4659 (2012).
[Crossref]

V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-time codes for high date rate wireless communication: performance criterion and code construction,” IEEE Trans. Inf. Theory 44(2), 744–765 (1998).
[Crossref]

J. Liu, J.-K. Zhang, and K. M. Wong, “Full diversity codes for MISO systems equipped with linear or ML detectors,” IEEE Trans. Inf. Theory 54(10) 4511–4527 (2008).
[Crossref]

D. Xia, J.-K. Zhang, and S. Dumitrescu, “Energy-efficient full diversity collaborative unitary space-time block code designs via unique factorization of signals,” IEEE Trans. Inf. Theory 59(3), 1678–1703 (2013).
[Crossref]

IEEE Trans. Signal Process. (2)

J.-K. Zhang, J. Liu, and K. M. Wong, “Trace-orthonormal full diversity cyclotomic space-time codes,” IEEE Trans. Signal Process. 55(2), 618–630 (2007).
[Crossref]

X. Ling, J. Wang, X. Liang, Z. Ding, and C. Zhao, “Offset and power optimization for DCO-OFDM in visible light communication systems,” IEEE Trans. Signal Process. 31(1), 278 (2015).

IEEE Trans. Wireless Commun. (3)

M. K. Simon and V. A. Vilnrotter, “Alamouti-type space-time coding for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. 4(1), 35–39 (2005).
[Crossref]

S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun. 6(8), 2813–2819 (2007).
[Crossref]

M. Safari and M. Uysal, “Do we really need OSTBCs for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. 7(11), 4445–4448 (2008).
[Crossref]

J. Lightwave Technol. (2)

E. Bayaki and R. Schober, “Performance and design of coherent and differential space-time coded FSO systems,” J. Lightwave Technol. 30(11), 1569–1577 (2012).
[Crossref]

D. Marcuse, “Calculation of bit-error probability for a lightwave system with optical amplifiers and post-detection Gaussian noise,” J. Lightwave Technol. 9(4), 505–513 (1991).
[Crossref]

J. Opt. Commun. (1)

S. Chaudhary and A. Amphawan, “The role and challenges of free-space optical systems,” J. Opt. Commun. 35(4), 327–334 (2014).
[Crossref]

J. Opt. Commun. Netw (1)

S. M. Aghajanzadeh and M. Uysal, “Diversity–multiplexing trade-off in coherent free-space optical systems with multiple receivers,” J. Opt. Commun. Netw 2(12), 1087–1094 (2010).
[Crossref]

Opt. Eng. (2)

M. Abaza, R. Mesleh, A. Mansour, and E.-H. M. Aggoune, “Diversity techniques for a free-space optical communication system in correlated log-normal channels,” Opt. Eng. 53(1), 259–268 (2014).
[Crossref]

D. Giggenbach and H. Henniger, “Fading-loss assessment in atmospheric free-space optical communication links with on-off keying,” Opt. Eng. 47(4), 046001 (2008).
[Crossref]

Opt. Express (3)

Science Chin. Series F: Inf. Sci. (1)

H. Wang, X. Ke, and L. Zhao, “MIMO free space optical communication based on orthogonal space time block code,” Science Chin. Series F: Inf. Sci. 52(8), 1483–1490 (2009).
[Crossref]

Other (9)

Y.-Y. Zhang, H.-Y. Yu, J.-K. Zhang, Y.-J. Zhu, J.-L. Wang, and T. Wang, “Full large-scale diversity space codes for MIMO optical wireless communications,” in Proc. IEEE Int. Symp. Inf. Theory (IEEE, 2015), pp. 1671–1675.

Y.-Y. Zhang, H.-Y. Yu, J.-K. Zhang, Y.-J. Zhu, J.-L. Wang, and T. Wang, “Space codes for MIMO optical wireless communications: Error performance criterion and code construction,” http://arxiv.org/abs/1509.07470 (2015).

X. Song, J. Cheng, and M.-S. Alouini, “High SNR BER comparison of coherent and differentially coherent modulation schemes in lognormal fading channels,” arXiv preprint arXiv:1407.7097 (2014).

A. K. Majumdar, Free-space Optical (FSO) Platforms: Unmanned Aerial Vehicle (UAV) and Mobile (Springer, 2015).

J. R. Barry, Wireless Infrared Communications (Kluwer Academic, 1994).
[Crossref]

S. Karp, R. M. Gagliardi, S. E. Moran, and L. B. Stotts, Optical Channels (Springer, 1988).
[Crossref]

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).
[Crossref]

M. K. Simon and M.-S. Alouini, Digital Communication Over Fading Channels (John Wiley and Sons, 2000).
[Crossref]

T. M. Cover and J. A. Thomas, Information Theory (John Wiley and Sons, 1991).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1 Performance comparison of DOSC and RC with M = 1, N = 2 and K = 2.
Fig. 2
Fig. 2 Performance comparison of DOSC and RC with M = N = 2 and varied K.
Fig. 3
Fig. 3 Performance comparison of DOSC and RC with M = 1, N = K = 2 and varied μn .
Fig. 4
Fig. 4 Performance comparison of DOSC and RC with N = 2, K = 3 and varied M.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

y = Hs + n ,
P D ( s s ^ ) = C D 𝒢 ( e ) ( ρ / ln 2 ρ ) σ ¯ 4 ln ( N σ ¯ M ) 3 4 ln 𝒟 small ( e ) ( ln ρ ) M N e 𝒟 large 8 ln 2 ρ ln 2 ρ
P ˜ D ( s s ^ ) = P D ( s s ^ ) n = 1 N | e n | m = 1 M μ m n σ m n 2 ( ρ / ln 2 ρ ) 1 4 n = 1 N m = 1 M μ m n σ m n 2
n = 1 N ( s n ( k + 1 ) s nk ) σ ¯ n ( n = 1 N ( s n ( k + 1 ) ) s nk ) σ ¯ n = 1 N ( σ ¯ n σ ¯ ) σ ¯ n .
min 0 k 2 K 2 n = 1 N ( s n ( k + 1 ) s nk ) σ ¯ n 2 σ ¯ n = 1 N σ ¯ n σ ¯ n ( ( 2 K 1 ) σ ¯ ) σ ¯
n = 1 N ( s ˜ n ( k + 1 ) s ˜ nk ) σ ¯ n > 2 σ ¯ n = 1 N σ ¯ n σ ¯ n ( ( 2 K 1 ) σ ¯ ) σ ¯
𝒮 opt = { k w } k = 0 k = 2 K 1
y = Hw k + n , 0 k 2 K 1
k ^ = arg min 0 k 2 K 1 y Hw k 2 2 = arg min 0 k 2 K 1 ( k 2 Hw k 2 2 2 k y T Hw + y 2 2 ) = arg min 0 k 2 K 1 ( Hw 2 2 × | k y T Hw / Hw 2 2 | 2 ( y T Hw ) 2 / Hw k 2 2 + y 2 2 ) = arg min 0 k 2 K 1 | k y T Hw / Hw 2 2 |
s ^ k = { 0 , y T Hw / Hw 2 2 < 0 ; y T Hw / Hw 2 2 + 1 2 w , 0 y T Hw / Hw 2 2 2 K 1 ; ( 2 K 1 ) w , y T Hw / Hw 2 2 > 2 K 1 .

Metrics