A multi-carrier off-wave direction finding method based on fast Fourier transform

Abstract

This invention belongs to the field of electronic information technology, specifically relating to a multi-carrier off-wave direction finding method based on Fast Fourier Transform (FFT). The problem this invention aims to solve is how to determine the off-wave direction by utilizing the frequency and phase information of the received signal from the single receiving antenna and the multi-carrier signals simultaneously transmitted by the transmitting antennas, and by constructing two complex amplitude sequences of carriers and processing them using FFT. Using the method proposed in this invention, given the frequency and phase of the transmitted multi-carrier signals, off-wave direction finding can be achieved simply by using a single receiving antenna to receive the multi-carrier signals simultaneously transmitted by two transmitting antennas. This not only reduces the size, weight, power consumption, and system maintenance costs of the radio signal receiver, but also lowers the complexity of off-wave direction finding at the receiver through FFT processing, thereby improving the portability of the off-wave direction finding module.

Description

Technical Field

[0001] This invention belongs to the field of electronic information technology, specifically relating to a multi-carrier off-wave direction finding method based on fast Fourier transform. Background Technology

[0002] Off-wave direction finding of radio signals is of great significance in smart antenna systems that use multiple antennas to transmit radio signals in coordination, and in communication and detection systems that use multiple-input multiple-output electromagnetic wave propagation channel models. The off-wave direction information obtained can not only be used to optimize radio signal transmission efficiency and improve radio signal reception quality, but also for radio navigation and positioning.

[0003] Unlike arrival direction finding, which requires multiple receiving antennas, radio signal departure direction finding only requires a single receiving antenna. Taking two transmitting antennas as an example, when both antennas transmit radio signals simultaneously, the signal received by the receiving antenna is an aliasing of the two transmitted signals. Since departure information is contained in the phase difference between the aliased signals from the two transmitting antennas, signal separation is required before obtaining departure direction information. The phase difference between the separated signals is then determined, and finally, the direction in which the radio signal leaves the two transmitting antennas—the departure direction—is determined by this phase difference.

[0004] When using only a single receiving antenna to separate two superimposed transmitted signals from the received signal, the problem is underdetermined. Prior information related to the two superimposed transmitted signals is needed to achieve correct signal separation. Therefore, when designing an off-wave direction finding system, it is necessary not only to impose specific waveform constraints on the signals transmitted by the transmitting antennas but also to ensure that the signals transmitted by different antennas satisfy specific cooperative relationships. Introducing these waveform constraints and cooperative relationships satisfies the problem-solving conditions for separating two superimposed transmitted signals from the received signal of a single receiving antenna. Summary of the Invention

[0005] The problem this invention aims to solve is how to determine the departure direction by using the received signal from the single receiving antenna and the frequency and phase information of the multi-carrier signals transmitted synchronously by the transmitting antennas, in the case of receiving multi-carrier signals from two transmitting antennas simultaneously using a single receiving antenna, and by constructing two complex amplitude sequences of carriers and processing them with fast Fourier transform.

[0006] The technical solution of this invention is as follows:

[0007] A multi-carrier off-wave direction finding method based on Fast Fourier Transform (FFT) is defined as follows: A single antenna receives multi-carrier signals simultaneously transmitted by two transmitting antennas. The distance between the two transmitting antennas is denoted as d (in units of wavelength of the transmitted signal); the number of carriers in the transmitted signal is N; and the frequency of the nth carrier signal is f. n The phase of the nth carrier signal of the first radio transmitting antenna is n = 1, 2, ..., N; the number of digital signal samples input to the two radio transmitters' digital-to-analog converters is K, and the digital-to-analog conversion rate is f. DAC The analog-to-digital conversion rate of the signal received by the receiving antenna is f. ADC The number of wave-departure directions searched is M, θ m Let m be the wave-departing direction for the m-th search, where m = 1, 2, ..., M, and the search sequence for wave-departing directions is {θ1, θ2, ..., θ...}. M}; including the following steps:

[0008] S1. Based on the carrier signal's frequency, phase, and digital-to-analog conversion rate, the signal transmitted by the first transmitting antenna is set, and the digital-to-analog converter follows the digital-to-analog conversion rate f. DAC The input digital signal sample is:

[0009]

[0010] Where k = 0, 1, 2, ..., K-1; the signal transmitted by the second transmitting antenna is determined by the frequency of the carrier signal and the digital-to-analog conversion rate, and the digital-to-analog converter converts the signal according to the digital-to-analog conversion rate f. st The input digital signal sample is:

[0011]

[0012] Where k = 0, 1, 2, ..., K-1;

[0013] S2. Set up a receiving antenna to receive radio signals, and the analog-to-digital converter operates according to the analog-to-digital conversion rate f. ADC The sampled digital received signal is x(t), t=0,1,2,…,K-1;

[0014] S3. Construct the carrier complex amplitude sequence 1 from the digital received signal, analog-to-digital conversion rate, and the frequency and phase of the nth carrier signal:

[0015]

[0016] The carrier complex amplitude sequence 2 is as follows:

[0017]

[0018] Where n = 1, 2, ..., N;

[0019] S4. Using the Fast Fourier Transform, determine the Fourier transform of carrier complex amplitude sequence 1 as follows:

[0020]

[0021] The Fourier transform of carrier complex amplitude sequence 2 is:

[0022]

[0023] Where n = 1, 2, ..., N;

[0024] S5, the m-th wave-departing direction θ from the search m The Fourier transforms of the complex amplitude sequences 1 and 2 of the carrier wave are used to determine the m-th off-wave direction θ of the search. m The corresponding spectral values ​​are:

[0025]

[0026] Where m = 1, 2, ..., M;

[0027] S6. Determine the sequence of off-wave direction spectrum values ​​to be searched {g(θ1), g(θ2), ..., g(θ)} M The maximum value in )} is g(θ) p Thus, the direction finding of the off-wave is determined to be the corresponding θ. p .

[0028] The beneficial effects of this invention are: using the method proposed in this invention, given the frequency and phase of the transmitted multi-carrier signal, off-wave direction finding can be achieved by using only a single receiving antenna to receive the multi-carrier signal transmitted synchronously by two transmitting antennas. This not only reduces the size, weight, power consumption, and system maintenance cost of the radio signal receiver, but also reduces the complexity of off-wave direction finding at the receiver through fast Fourier transform processing, thereby improving the portability of the off-wave direction finding functional module. Detailed Implementation

[0029] The practicality of the present invention will be analyzed below with reference to the embodiments.

[0030] Example

[0031] In this example, let the distance between the two radio transmitting antennas be half a wavelength, i.e., d = 0.5, the number of carriers in the transmitted signal be N = 121, and the frequency of the nth carrier be f. n= -600+10(n-1)kHz, the phase of the nth carrier signal of the first radio transmitting antenna is an independent random number uniformly distributed between 0 degrees and 360 degrees, n = 1, 2, ..., N; the number of samples of the input signal of the digital-to-analog converter is K = 3000, and the conversion rates of both digital-to-analog and analog-to-digital conversion are 3MHz; the search sequence for the off-wave direction is {θ m =21+0.01(m-1)} degrees, m=1,2,…,M,M=901.

[0032] When the actual departure direction is uniformly distributed between 25 and 26 degrees, 2000 independent experiments were conducted with a carrier power to noise power spectral density ratio of 24 dB for a single receiving antenna. Statistical results show that the standard deviation of the departure direction measured using the method of this invention is 0.0964 degrees.

[0033] As can be seen, the present invention provides a multi-carrier off-wave direction finding method based on fast Fourier transform. Given the frequency and phase of the transmitted multi-carrier signal, a single receiving antenna receives the multi-carrier signal transmitted synchronously by two transmitting antennas. By utilizing the carrier frequency and phase information of the transmitted signal and the received signal of the single receiving antenna, the purpose of high-precision and rapid determination of the off-wave direction is achieved.

Claims

1. A multi-carrier off-wave direction finding method based on Fast Fourier Transform, defined as using one antenna to receive multi-carrier signals simultaneously transmitted by two transmitting antennas, the distance between the two transmitting antennas being d, the number of carriers in the transmitted signal being N, and the frequency of the nth carrier being f. n The amplitude of the nth carrier wave of the signal transmitted by the first transmitting antenna is The number of digital signal samples input to the digital-to-analog converters of the two transmitting antennas is K, and the digital-to-analog conversion rate is f. DAC The analog-to-digital conversion rate of the signal received by the receiving antenna is f. ADC The number of wave-departure directions searched is M, θ m Let m be the wave-leaving direction for the m-th search, where m = 1, 2, ..., M, and the search sequence for wave-leaving directions is {θ1, θ2, ..., θ...}. M }; characterized in that, The direction finding method includes the following steps: S1. Define the digitally transmitted signal of the first transmitting antenna as: Where k = 0, 1, 2, ..., K-1; the digital transmission signal of the second transmitting antenna is: S2. Define the digital received signal of the receiving antenna as x(t); S3, the received digital signal x(t) and the analog-to-digital conversion rate f of the received signal. ADC and the frequency f of the nth carrier signal n Phase Construct the first carrier complex amplitude sequence: And the second carrier complex amplitude sequence: S4. Using the Fast Fourier Transform, the Fourier transform of the first carrier complex amplitude sequence is obtained as follows: The Fourier transform of the second carrier complex amplitude sequence is: S5, the m-th wave-departing direction θ from the search m The Fourier transforms of the first carrier complex amplitude sequence and the second carrier complex amplitude sequence are used to determine the m-th off-wave direction θ to be searched. m The corresponding spectral values ​​are: S6. Determine the sequence of off-wave direction spectral values ​​to be searched {g(θ1), g(θ2), ..., g(θ)}. M The maximum value in )} is g(θ) p This allows us to determine the out-of-wave direction finding as the corresponding θ. p .

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