Abstract
Biorthogonal Fourier transform (BFT), consistent with the matched signal transform (MST), has been introduced to demodulate the M-ray chirp-rate signal which possesses good orthogonality in the BFT domain. Here, we analyze the characteristics of BFT detection in a further step, including the resolution capability of the multichirp-rate signal, the property of pulse compression, the closed-form bit-error rate in the additive white Gaussian noise (AWGN) channel, and the interference in the time-frequency dispersive channel. Even in the high Doppler environment, the shift in BFT detection is proven to be slight. In addition, we deduce that the orthogonality among received chirp rates in the BFT domain would be affected in the multipath dispersive environment. This causes the mutual interference among different chirp rates in a symbol and over symbols concurrently. The theoretical result shows that the chirp modulation parameter can be adjusted to obtain the trade-off between time and frequency dispersion. By the multipath model of chirp-rate signal, an auxiliary parallel interference cancellation (PIC) method is further introduced in multipath environment. Simulations verify our analyzed performance of BFT detection in the AWGN, Doppler, and multipath channels. The proposed interference cancellation algorithms are also proven to be effective.
Highlights
Chirp signals, i.e., linear frequency modulation (LFM) signals, are implemented in radar and communication
We demonstrate that the orthogonality among the chirp-rate signals in the biorthogonal Fourier transform (BFT) domain will be affected by multipath propagation
We developed an auxiliary parallel interference cancellation (PIC) method based on the dispersive model in BFT domain to mitigate the multipath interference
Summary
I.e., linear frequency modulation (LFM) signals, are implemented in radar and communication. To the signal of linear frequency modulation f (t) = exp jπ Kmt , it has BFT[ f (t)] = 2π δ(β − π Km), where the impulse position at π Km in the BFT domain reflects the chirp rate. Lemma 1 When the chirp-rate signals have different integer BmTs/2, they are orthogonal to each other at the discrete k in BFT domain. The chirp-rate signals have the orthogonality in discrete BFT domain if they have different integer BmTs/2. At β = π Km, the discrete sample for the chirp rate in the BFT domain is deduced as This is the result of D-BFT detection with a frequencyoffset signal, thereby developing the attenuation expression.
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