New sign Hadamard-γ-Haar-χ transform in ternary communication system

The application of a sign Hadamard-γ-Haar-χ transform in designing a digital communication system is considered. The nonlinear transform converts binary/ternary vectors into digital spectral domain and is invertible. With its unique and isomorphic properties, the sign Hadamard-γ-Haar-χ transform is suitable for security coding in a communication system. Ternary amplitude frequency shift keying is proposed for the implementation of the system. Power spectral density of the resultant signaling is formulated and analyzed. The noncoherent receiver is designed and proposed as a ternary communication system. The transform is extremely effective in terms of computational costs when compared with known sign Walsh transform in application inside ternary communication system.