# Blind Detection for Serial Relays in Free Space Optical Communication Systems
## 1 Introduction  
Optical wireless communication refers to the transmission of data in an unguided propagation media through the use of optical carriers [1; 2; 3; 4; 5]. Optical wireless communications (OWCs) can be divided into five categories; ultra-short range OWC, short-range OWC, medium range OWC, long-range OWC and ultra-long range OWC [1; 2; 4]. Long range OWC systems are referred to as Free Space Optical (FSO), which is the OWC used between buildings [1; 2; 4]. Free-space optical (FSO) communications have recently been adopted due to its high data rate (up to 10 Gbps), large bandwidth, transmission distance up to several kilometers, frequency above 300 GHz, which is a license-free spectrum, easily and quickly deployed and finally, reinstallation capability of the system [1; 2; 3; 4; 6]. The FSO challenges include atmospheric attenuation such as snow, dust, fog and rain, atmospheric turbulence, beam divergence loss, ambient light, misalignment and complexity of the system [1; 2; 3; 4; 7; 8; 9; 10]. Due to the complexity generated from phase and frequency modulation and dueto the high implementation cost, on-off keying (OOK) intensity modulation with direct detection (IM/DD) is implemented within the most current commercial FSO systems [11; 12; 13; 14; 15; 16]. To evaluate the atmospheric turbulence effect, two methods were used. The first method is the Channel State Information (CSI) method, where pilot signals were sent to detect the channel condition [7; 13]. For the mentioned systems, the receiver would require knowledge of the CSI to adjust the detection threshold [17]. To increase the bandwidth efficiency of FSO channels and to decrease the complexity, the second method was introduced in [13; 17; 18; 19]. The second method is the blind detection method. The blind detection does not use pilot signals. It decreases the complexity of the receiver and increases the throughput [7; 13]. A blind practical method for detecting wireless optical communication was introduced in [18]. In [20], the authors proposed an iterative sequence detector based on [18]. Due to the Bit Error Rate (BER) in [18; 20] being floored for a small size observation window, the authors of [7] introduced an improved data detection methodology. This methodology, introduced in [7], used the specification of channel probability density function (PDF) and proposed a new algorithm that decreased the error floor. The authors of [13] have also derived an analytical expression of a conditional BER of the system proposed on [18]; however, the average BER was not derived. One of the mitigation techniques used for the atmospheric turbulence effect and path loss attenuation is the assisted relay technique [2; 6]. The assisted relay technique helps in shortening the hops, and thus, improving the performance significantly [2; 6]. Table 1 accommodates some of the key pros and cons of the previous literature that used the blind detection method with FSO communication systems. In this paper, we employed a blind detection method for a serial decode and forward relay of the FSO system over a log-normal channel. The novelty of this work is as follows:  
* The combined advantages of blind detection and assisted relays motivated the research group to investigate the combined system in more details. * Approximated average BER, which was not derived earlier in [7; 13], is derived within the paper. Although the derivation of the analytical model is more difficult than the Monte Carlo simulation, it allows a better understanding of the proposed system and an easier comparison between the proposed model and other ones. * The Monte Carlo simulation verifies the correctness of the derived expression. * The obtained results show the closeness of the employed method using small windows compared with channel state information. * The new results would promote the use of blind detection for more applications. The remainder of this paper is organized as follows. Section 2 describes the system model.