Bandwidth compression method based on quadrinomial weighted score Fourier transformation
A fractional Fourier transform and bandwidth compression technology, applied in the direction of multi-frequency code system, etc., can solve the problems of wide communication bandwidth, transmission power consumption, occupation, etc., and achieve the effect of reduced occupation and improved spectrum utilization
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specific Embodiment approach 1
[0022] Specific implementation mode 1. Combination figure 1 Describe this embodiment, the specific implementation method of the bandwidth compression method based on the four-item weighted fractional Fourier transform described in this embodiment is as follows:
[0023] Step 1. At the sending end of the communication system, for a signal X of length N, use an N×N weighting matrix W α Perform four weighted fractional Fourier transform 4-WFRFT to obtain a weighted domain signal Y with a length of N;
[0024] Step 2: The sender sends a signal Y h , the signal Y h is the first half of the weighted signal Y, the signal Y h The length of is N / 2;
[0025] Step 3: The receiving end receives the weighted domain signal Y h , for signal Y h Find the generalized inverse of the matrix to obtain the estimated signal At the same time, use the signal-to-noise ratio formula SNR=10log 10 (P x / P n ) to estimate the signal-to-noise ratio of the channel, where P n is the average power...
specific Embodiment approach 2
[0053] Specific embodiment 2. This embodiment is a further description of the specific implementation method of the bandwidth compression technology based on the four-item weighted fractional Fourier transform described in the specific embodiment 1. The estimated signal is obtained as described in step 3. The specific process is: first extract the first N rows of the weighted matrix to form a new matrix as and then find The generalized inverse matrix of , denoted as W h α + = ( W h α ) H [ W h α ( W h α ) ...
specific Embodiment approach 3
[0054] Specific Embodiment 3. This embodiment is a further description of the specific implementation method of the bandwidth compression technology based on the four-item weighted fractional Fourier transform described in Specific Embodiment 1. The threshold ξ described in step 6 1 By sure, where n i Indicates the i-th noise signal point, N indicates the signal length, Among them, P n Derived from the signal-to-noise ratio formula in step 3 to obtain P n =P x / 10 SNR / 10 .
[0055] Simulate the signal length N=16, the angle α=0.15 of the weighting matrix, ξ 1 According to the estimated value of noise, ξ 2 =10 -4 , using BPSK modulation, the signal-to-noise ratio--bit error rate curve 2 is obtained, such as figure 2 shown. Follow steps 1 to 8 to get the signal-to-noise ratio-bit error rate curve 1 of the weighted fractional Fourier transform that only transmits half the bandwidth. When the signal-to-noise ratio is 9dB, the bit error rate of the symbol full search a...
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