Biorthogonal Fourier transform for multichirp-rate signal detection over dispersive wireless channel

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.

A new integral transform: biorthogonal Mellin transform

“…对于零 初频、无时延的 LFM 信号, 其 BFT 为辛格函数, 峰值搜索可得 LFM 信号调频斜率. BFT 具备线性、 可逆、斜移不变等性质, 目前已应用于通信信号检测 [13] 、雷达干扰抑制 [14] 等领域. 考虑到, LFM 信 号也是一种 PFM 信号, 以式 (1) 替换 BFT 中的基函数, 可解决所有类型 PFM 信号检测及处理问题.…”

Detection and Parameter Estimation of Multicomponent LFM Signal based on Nonlinear Transformation under the Impulsive Noise

“…Early the linear frequency modulated (LFM) signal has been widely employed in radar signal processing [1][2][3][4], especially in target detection, tracking, location and radar imaging fields, for its excellent characteristic of long time interval and wide frequency band. In recent years, wireless sensor networks, as well as military ad hoc network, have the requirement of integration with self-localization, sensing, and communication functions [5][6][7][8][9]. At present, broadband wireless communications in high-speed vehicles, such as aircraft and high-speed trains, are much in demand.…”

Regeneration scanning method for M ‐WFRFT communication signals

“…The fractional Fourier transform (FRFT) [1–3] is a new signal transformation method based on the traditional Fourier transform. FRFT can provide a better explanation of a signal from a partial time period.…”