The multi-weighted type fractional fourier transform scheme and its application over wireless communications

Abstract

Researching on the relationships among different multiple weighted type fractional Fourier transform (multi-WFRFT) schemes, we in this paper provide the modulation order relation of different multi-WFRFT in theory. Moreover, we also prove that the two matrix spaces (i.e., 4-WFRFT and multi-WFRFT) are equivalent. To apply multi-WFRFT into the wireless communication, we design the implementation structure of multi-WFRFT (in particular, for 2 n -WFRFT scheme). Furthermore, the generalized hybrid carrier modulation (GHCM) system has been proposed in this paper, which can be degenerated to the classical hybrid carrier modulation (HCM) system with special parameters. We also verify the modulation order relationship between multi-WFRFT by numerical simulations. Leveraging the theory and structure of multi-WFRFT, we finally discuss its potential applications over secure communication and multiple input multiple output (MIMO) system.

A Weighted Fractional Fourier Transform Signal Synchronous Method based on Delay Multiplication for UAVs System

“…6, which shows that the mean value of WFRFT signals presents segments tendency, and has 2 minimum mean peak value when the local rotation factor is 0.5 and 2.5. According to the periodicity of WFRFT signal, the mean value under local rotation factor[0,2] is the same with local rotation factor [2,4], so the searching scope can be shorten to [0,2], in which has only one minimum mean peak.…”

Multiweighted-Type Fractional Fourier Transform: Unitarity

“…At present, the M-WFRFT is widely used in image encryption and signal processing [7][8][9][10][11][21][22][23][24][25]. Unfortunately, few researchers have discussed its properties, and the proponents of the definition have not explained the properties.…”

Three Term Weighted Type Fractional Fourier Transform Based Generalized Hybrid Carrier and Its Application into PAPR Suppression

“…In this section, we will provide the concept of 3-WFRFT, which is based upon 4-WFRFT. In additional, M-WFRFT (M > 4) proposed in [14], is also based upon 4-WFRFT. However, the relationship between M-WFRFT (M > 4) and 4-WFRFT has been derived in [14], but not that of 3-WFRFT and 4-WFRFT.…”

“…In additional, M-WFRFT (M > 4) proposed in [14], is also based upon 4-WFRFT. However, the relationship between M-WFRFT (M > 4) and 4-WFRFT has been derived in [14], but not that of 3-WFRFT and 4-WFRFT. We, in this paper, will provide the concept of 3-WFRFT and some properties, which maybe helpful to solve the problem.…”