# A Review-Unguided Optical Communications: Developments, Technology Evolution, and Challenges
## 7 UOC Near-Future Network Scenarios and Research Challenges
### UOC--Today's Research Challenges
#### 7.2.1 Performance with Non-Kolmogorov Optical Turbulence  
Turbulence in the atmosphere can cause both phase and intensity fluctuations in UOC links, thereby lowering the data rate. An optical propagation atmospheric channel model was used to evaluate UOC system performance, such as SNR and BER. Most of the accepted models are based on the conventional Kolmogorov's power spectral density with constant wind speed and weak turbulence. However, recent investigations revealed that the Kolmogorov theory in many cases is not enough to explain the channel model when turbulence is high and wind speed is variable. UOC system performance could be evaluated better using a non-Kolmogorov power spectrum, which has a generalized exponent rather than a constant value of \(11/3\), and a generalized amplitude factor rather than one of 0.033. This will have a significant role in designing the UOC system correctly. The essential results describing the effects of using non-Kolmogorov theory for optical propagation and the effects on communication system performance parameters are briefly summarized below. This model's theoretical power spectrum has a generalized power law spectrum that can take values between 3 and 4, which depends on the specific scenario and atmospheric turbulence characteristics. The non-Kolmogorov power spectrum model [468; 469] can be written as  
\[\mathcal{D}_{n}(k,\alpha)=A(\alpha)C_{n}^{2}l^{-\alpha},\frac{2\pi}{L_{0}} \leq k\leq\frac{2\pi}{l_{0}},3<\alpha<4 \tag{49}\]  
where \(\alpha\) is the spectral power law exponent; \(\kappa\) is the magnitude of the 3D wave number; and \(C_{n}^{2}\) is equal to \(\beta C_{n}^{2}\), which is the parameter of generalized refractive-index structure, where \(A(\alpha)=\frac{1}{4\pi^{2}}\left[(\alpha-1)cos\left(\frac{\pi\alpha}{2} \right)\right.\). \(\Gamma(x)\) is the gamma function. An essential parameter for assessing the performance of a communication system is the scintillation index, which is calculated by adding the radial and longitudinal components for a Gaussian beam wave (the suffix r for radial and l for longitudinal) [490] as defined in Equation (50):  
\[\sigma_{I}^{2}(r,L)=\sigma_{I,r}^{2}(r,L)+\sigma_{I,l}^{2}(L) \tag{50}\]  
To evaluate a communication system's performance, it is also essential to know about the signal intensity's statistical distributions under a specific turbulence condition. A Gamma-Gamma distribution PDF is generally accepted for a high-turbulence domain [491]. In the presence of a non-Kolmogorov turbulence model, the mean SNR <SNR> at the detector output (shot-noise limited system) can be stated as [489]  
\[\langle SNR\rangle=\frac{SNR_{0}}{\sqrt{1+\sigma_{I}^{2}(r,L,\alpha)SNR_{0}^{ 2}}}, \tag{51}\]where \(SNR_{0}\) is the \(SNR\) with no turbulence, and the scintillation parameter includes radial distance \(r\), path length \(L\), and the exponent value \(\alpha\) of the power spectrum.  
\[Pr(E)=\langle\text{BER}\rangle=\frac{1}{2}\int_{0}^{\infty}p_{1}(u)\text{erfc} \bigg{(}\frac{\langle SNR\rangle u}{2\sqrt{2}}\bigg{)}du \tag{52}\]  
In Equation (52), erfc is the complementary error function and \(p_{1}\) (u) is the Gamma-Gamma distribution. BER as a function of SNR for several wind speeds without turbulence and the mean SNR as a function of SNR for different wind speeds with non-Kolmogorov turbulence are presented in [490]. Parameters relevant to UOC system performance such as probability of fade, scintillation index, mean BER, and mean SNR for a collimated Gaussian beam as a function of several exponent values and anisotropic parameters are discussed in [489]. Readers who are interested in the details of the derivation and graphical representations are urged to study these works.