# Performance Analysis of Troposphere Scattering Communication Channel with Chirp-BOK Modulation
###### Abstract  
By utilizing chirp-BOK (binary orthogonal keying) modulation into a troposphere scattering communication system, a lower demodulation threshold can be achieved with excellent linear frequency modulation properties in a strong noise and weak signal environment. Firstly, the bit error rate (BER) formula of chirp-BOK modulation over a Rayleigh fading channel was derived theoretically. Then, the BER performance with different chirp-BOK parameters were numerically calculated. In order to investigate the performance of chirp-BOK over deeping fading troposphere scattering link, a seven-path equal-delay Rayleigh fading model was employed. Finally, the system BER performance was simulated under different tap delay and time-bandwidth product parameters. The results demonstrate that when BER reaches \(10^{-4}\), the optimal configuration of the system achieves a gains approximately from 1.7 dB to 10 dB compared to non-optimized configuration under different Path-Gain-Vector with varying tap delays. troposcatter; chirp signal; multipath channel; bit error rate +
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process of chirp signal, but they lacked the description of rigorous mathematical signal processing. Ref. [7] presented the mathematical formulas for modulation and demodulation process of frequency shift chirp modulation (FSCM), providing a theoretical derivation of optimal receiver with low complexity based on FFT. Ref. [12] analyzed the technical characteristics and performance of FSCM demodulation under the residual frequency offset. Ref. [13] proposed a fractional chirp rate grounded on CSS (FCR-CSS) as a physical layer-inspired approach to enhance the capacity of CSS modulation based on IoT networks. Ref. [14] developed a novel OFDM-chirp modulation scheme with a low peak-to-average power ratio (PAPR). An analysis method was introduced to evaluate the corresponding symbol error rate (SER) under carrier frequency offset (CFO) in a Rayleigh fading channel. Ref. [15] designed a non-coherent distributed transmission (NCDT) CSS system for low-power communication. Ref. [16] proposed a two-dimensional modulation method chirp-MFCSK for the LoRa system. Ref. [17] raised phase shift keying based on a CSS (PSK-CSS) multiple-access system with a single chirp rate. On the ground of the analysis results under multiple access interference, the PSK-CSS system can support synchronous and asynchronous transmissions simultaneously by multiplying different random phases to the data symbols of different users. Owing to the special demands and characteristics of the tropospheric scattering communication system, the channel modeling and the adaptive reliable transmission technique have always been a research hotspot. Ref. [18] provide a reference for the theoretical characteristics of communication channels. Ref. [19] presented the troposcatter propagation principles along with several mathematical models, demonstrating integrated theoretical analysis with experimental measurements. Ref. [20] tested the fading characteristics of scattered signals and established a signal model with radar parameters, finally proposing a suitable beamforming and detection algorithm. In ref. [21], equalization techniques were incorporated into a scattering communication system to mitigate inter code interference and achieved high-speed transmission. Ref. [22] investigated the impact of atmospheric conditions on signal transmission and provided insights into uncertainty estimation, serving as a reference for an alternative statistical channel model for bit error rate (BER) analysis. Ref. [23] proposed an innovative anti-fading method for tropospheric scattering communication based on frequency hopping, which also explored synchronization technologies to improve the system performance.