Non-Coherent Capacity of $M$ -ary DCSK Modulation System Over Multipath Rayleigh Fading Channels

Non-coherent capacity bounds for the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -ary differential chaos shift keying (DCSK) modulation system are derived and analyzed over multipath Rayleigh fading channels, deriving conditions on the channel state information/non-channel state information (CSI/NonCSI) and soft-decision/hard-decision (SD/HD), respectively. Meanwhile, the inter-symbol interference is modeled and analyzed mathematically. Through numerical simulations and analyses, it is found that: 1) the influences of the spreading factor <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula> , multipath number <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula> , modulation dimension <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> , CSI/NonCSI, and SD/HD on the non-coherent capacity bounds are significant; 2) there is a relatively broad range of code rates corresponding to the optimal system power in U-shaped capacity curves of the non-coherent reception; and 3) the U-shaped non-coherent capacity bounds are proven to exist by investigating the mechanism of the low density parity check coded the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -ary DCSK system. These results are useful as benchmarks for designing power-efficient coded <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -ary DCSK systems.