FFT（快速傅里叶变换）和滤波在相控阵雷达波束控制中的应用

yummy 阅读：189 2024-02-26 15:07:26 评论：0

1. FFT的工作原理

FFT是一种高效计算离散傅里叶变换（DFT）的算法。DFT将时域信号转换为频域信号，揭示信号的频率成分。FFT通过分治法将DFT的计算复杂度从O(N^2)降低到O(N log N)。

2. 滤波的工作原理

滤波器用于信号处理中的频率选择。常见的滤波器包括低通滤波器、高通滤波器和带通滤波器。滤波器可以去除噪声或提取特定频率成分。

具体实现过程

下面的Verilog代码展示了如何在相控阵雷达波束控制中引入FFT和滤波算法。

1. Butterfly单元

Butterfly单元是FFT的基本运算单元，用于合并子问题的结果。

module butterfly(
    input wire signed [15:0] a_real,
    input wire signed [15:0] a_imag,
    input wire signed [15:0] b_real,
    input wire signed [15:0] b_imag,
    input wire signed [15:0] w_real,
    input wire signed [15:0] w_imag,
    output wire signed [15:0] y0_real,
    output wire signed [15:0] y0_imag,
    output wire signed [15:0] y1_real,
    output wire signed [15:0] y1_imag
);

    wire signed [15:0] bw_real;
    wire signed [15:0] bw_imag;

    // 复数乘法
    assign bw_real = (b_real * w_real - b_imag * w_imag) >>> 15;
    assign bw_imag = (b_real * w_imag + b_imag * w_real) >>> 15;

    // Butterfly运算
    assign y0_real = a_real + bw_real;
    assign y0_imag = a_imag + bw_imag;
    assign y1_real = a_real - bw_real;
    assign y1_imag = a_imag - bw_imag;

endmodule

2. FFT模块

FFT模块实现了基于Butterfly运算的递归计算和结果合并。

module fft(
    input wire clk,
    input wire rst,
    input wire signed [15:0] data_in_real [0:7],
    input wire signed [15:0] data_in_imag [0:7],
    output wire signed [15:0] data_out_real [0:7],
    output wire signed [15:0] data_out_imag [0:7]
);

    reg signed [15:0] stage_real [0:7][0:2];
    reg signed [15:0] stage_imag [0:7][0:2];

    wire signed [15:0] w_real [0:3];
    wire signed [15:0] w_imag [0:3];

    // Twiddle factors (预计算的旋转因子)
    assign w_real[0] = 16'd32767; // 1
    assign w_imag[0] = 16'd0;     // 0
    assign w_real[1] = 16'd23170; // cos(pi/4)
    assign w_imag[1] = -16'd23170; // -sin(pi/4)
    assign w_real[2] = 16'd0;     // cos(pi/2)
    assign w_imag[2] = -16'd32767; // -sin(pi/2)
    assign w_real[3] = -16'd23170; // cos(3pi/4)
    assign w_imag[3] = -16'd23170; // -sin(3pi/4)

    // 初始输入
    always @(posedge clk or posedge rst) begin
        if (rst) begin
            integer i;
            for (i = 0; i < 8; i = i + 1) begin
                stage_real[i][0] <= 16'd0;
                stage_imag[i][0] <= 16'd0;
            end
        end else begin
            integer i;
            for (i = 0; i < 8; i = i + 1) begin
                stage_real[i][0] <= data_in_real[i];
                stage_imag[i][0] <= data_in_imag[i];
            end
        end
    end

    // 第一阶段
    butterfly bf0 (
        .a_real(stage_real[0][0]), .a_imag(stage_imag[0][0]),
        .b_real(stage_real[4][0]), .b_imag(stage_imag[4][0]),
        .w_real(w_real[0]), .w_imag(w_imag[0]),
        .y0_real(stage_real[0][1]), .y0_imag(stage_imag[0][1]),
        .y1_real(stage_real[4][1]), .y1_imag(stage_imag[4][1])
    );

    butterfly bf1 (
        .a_real(stage_real[1][0]), .a_imag(stage_imag[1][0]),
        .b_real(stage_real[5][0]), .b_imag(stage_imag[5][0]),
        .w_real(w_real[1]), .w_imag(w_imag[1]),
        .y0_real(stage_real[1][1]), .y0_imag(stage_imag[1][1]),
        .y1_real(stage_real[5][1]), .y1_imag(stage_imag[5][1])
    );

    butterfly bf2 (
        .a_real(stage_real[2][0]), .a_imag(stage_imag[2][0]),
        .b_real(stage_real[6][0]), .b_imag(stage_imag[6][0]),
        .w_real(w_real[2]), .w_imag(w_imag[2]),
        .y0_real(stage_real[2][1]), .y0_imag(stage_imag[2][1]),
        .y1_real(stage_real[6][1]), .y1_imag(stage_imag[6][1])
    );

    butterfly bf3 (
        .a_real(stage_real[3][0]), .a_imag(stage_imag[3][0]),
        .b_real(stage_real[7][0]), .b_imag(stage_imag[7][0]),
        .w_real(w_real[3]), .w_imag(w_imag[3]),
        .y0_real(stage_real[3][1]), .y0_imag(stage_imag[3][1]),
        .y1_real(stage_real[7][1]), .y1_imag(stage_imag[7][1])
    );

    // 第二阶段
    butterfly bf4 (
        .a_real(stage_real[0][1]), .a_imag(stage_imag[0][1]),
        .b_real(stage_real[2][1]), .b_imag(stage_imag[2][1]),
        .w_real(w_real[0]), .w_imag(w_imag[0]),
        .y0_real(stage_real[0][2]), .y0_imag(stage_imag[0][2]),
        .y1_real(stage_real[2][2]), .y1_imag(stage_imag[2][2])
    );

    butterfly bf5 (
        .a_real(stage_real[1][1]), .a_imag(stage_imag[1][1]),
        .b_real(stage_real[3][1]), .b_imag(stage_imag[3][1]),
        .w_real(w_real[2]), .w_imag(w_imag[2]),
        .y0_real(stage_real[1][2]), .y0_imag(stage_imag[1][2]),
        .y1_real(stage_real[3][2]), .y1_imag(stage_imag[3][2])
    );

    butterfly bf6 (
        .a_real(stage_real[4][1]), .a_imag(stage_imag[4][1]),
        .b_real(stage_real[6][1]), .b_imag(stage_imag[6][1]),
        .w_real(w_real[0]), .w_imag(w_imag[0]),
        .y0_real(stage_real[4][2]), .y0_imag(stage_imag[4][2]),
        .y1_real(stage_real[6][2]), .y1_imag(stage_imag[6][2])
    );

    butterfly bf7 (
        .a_real(stage_real[5][1]), .a_imag(stage_imag[5][1]),
        .b_real(stage_real[7][1]), .b_imag(stage_imag[7][1]),
        .w_real(w_real[2]), .w_imag(w_imag[2]),
        .y0_real(stage_real[5][2]), .y0_imag(stage_imag[5][2]),
        .y1_real(stage_real[7][2]), .y1_imag(stage_imag[7][2])
    );

        // 输出
    assign data_out_real[0] = stage_real[0][2];
    assign data_out_imag[0] = stage_imag[0][2];
    assign data_out_real[1] = stage_real[1][2];
    assign data_out_imag[1] = stage_imag[1][2];
    assign data_out_real[2] = stage_real[2][2];
    assign data_out_imag[2] = stage_imag[2][2];
    assign data_out_real[3] = stage_real[3][2];
    assign data_out_imag[3] = stage_imag[3][2];
    assign data_out_real[4] = stage_real[4][2];
    assign data_out_imag[4] = stage_imag[4][2];
    assign data_out_real[5] = stage_real[5][2];
    assign data_out_imag[5] = stage_imag[5][2];
    assign data_out_real[6] = stage_real[6][2];
    assign data_out_imag[6] = stage_imag[6][2];
    assign data_out_real[7] = stage_real[7][2];
    assign data_out_imag[7] = stage_imag[7][2];

endmodule

滤波模块实现

滤波模块实现了一个简单的FIR滤波器，用于信号预处理。

module filter(
    input wire clk,
    input wire rst,
    input wire signed [15:0] data_in,
    output wire signed [15:0] data_out
);

    reg signed [15:0] buffer [0:3];

    // 简单的FIR滤波器实现
    always @(posedge clk or posedge rst) begin
        if (rst) begin
            integer i;
            for (i = 0; i < 4; i = i + 1) begin
                buffer[i] <= 16'd0;
            end
        end else begin
            buffer[3] <= buffer[2];
            buffer[2] <= buffer[1];
            buffer[1] <= buffer[0];
            buffer[0] <= data_in;
        end
    end

    assign data_out = (buffer[0] + buffer[1] + buffer[2] + buffer[3]) >>> 2;

endmodule

顶层模块集成

将FFT和滤波模块集成到相控阵雷达波束控制系统中。

module phased_array_radar(
    input wire clk,
    input wire rst,
    input wire sync_pulse,
    input wire signed [15:0] rf_in_real [0:7],
    input wire signed [15:0] rf_in_imag [0:7],
    input wire [7:0] scan_control,
    output wire signed [15:0] rf_out_real,
    output wire signed [15:0] rf_out_imag
);

    wire signed [15:0] fft_out_real [0:7];
    wire signed [15:0] fft_out_imag [0:7];
    wire signed [15:0] filtered_signal_real [0:7];
    wire signed [15:0] filtered_signal_imag [0:7];
    wire [7:0] phase_control [0:7];
    wire sync_signal;

    // 实例化时间同步模块
    time_sync sync_inst (
        .clk(clk),
        .rst(rst),
        .sync_pulse(sync_pulse),
        .sync_signal(sync_signal)
    );

    // 实例化FFT模块
    fft fft_inst (
        .clk(clk),
        .rst(rst),
        .data_in_real(rf_in_real),
        .data_in_imag(rf_in_imag),
        .data_out_real(fft_out_real),
        .data_out_imag(fft_out_imag)
    );

    // 实例化滤波模块
    genvar i;
    generate
        for (i = 0; i < 8; i = i + 1) begin : filter_gen
            filter filter_real_inst (
                .clk(clk),
                .rst(rst),
                .data_in(fft_out_real[i]),
                .data_out(filtered_signal_real[i])
            );
            filter filter_imag_inst (
                .clk(clk),
                .rst(rst),
                .data_in(fft_out_imag[i]),
                .data_out(filtered_signal_imag[i])
            );
        end
    endgenerate

    // 实例化波束扫描控制模块
    beam_scanning_control scan_control_inst (
        .clk(clk),
        .rst(rst),
        .scan_control(scan_control),
        .phase_control(phase_control)
    );

    // 实例化数字波束形成模块
    digital_beamforming beamforming_inst (
        .clk(clk),
        .rst(rst),
        .data_in_real(filtered_signal_real),
        .data_in_imag(filtered_signal_imag),
        .phase_control(phase_control),
        .data_out_real(rf_out_real),
        .data_out_imag(rf_out_imag)
    );

endmodule

测试平台

用于验证优化后的相控阵雷达系统的功能。

module testbench;

    reg clk;
    reg rst;
    reg sync_pulse;
    reg signed [15:0] rf_in_real [0:7];
    reg signed [15:0] rf_in_imag [0:7];
    reg [7:0] scan_control;
    wire signed [15:0] rf_out_real;
    wire signed [15:0] rf_out_imag;

    // 实例化顶层模块
    phased_array_radar radar_inst (
        .clk(clk),
        .rst(rst),
        .sync_pulse(sync_pulse),
        .rf_in_real(rf_in_real),
        .rf_in_imag(rf_in_imag),
        .scan_control(scan_control),
        .rf_out_real(rf_out_real),
        .rf_out_imag(rf_out_imag)
    );

    // 时钟生成
    initial begin
        clk = 0;
        forever #5 clk = ~clk;
    end

    // 测试向量
    initial begin
        rst = 1;
        sync_pulse = 0;
        scan_control = 8'd0;
        rf_in_real[0] = 16'd100;
        rf_in_imag[0] = 16'd0;
        rf_in_real[1] = 16'd100;
        rf_in_imag[1] = 16'd0;
        rf_in_real[2] = 16'd100;
        rf_in_imag[2] = 16'd0;
        rf_in_real[3] = 16'd100;
        rf_in_imag[3] = 16'd0;
        rf_in_real[4] = 16'd100;
        rf_in_imag[4] = 16'd0;
        rf_in_real[5] = 16'd100;
        rf_in_imag[5] = 16'd0;
        rf_in_real[6] = 16'd100;
        rf_in_imag[6] = 16'd0;
        rf_in_real[7] = 16'd100;
        rf_in_imag[7] = 16'd0;
        #10 rst = 0;
        #10 sync_pulse = 1;
        #10 sync_pulse = 0;
        #100 scan_control = 8'd10;
        #100 scan_control = 8'd20;
        #100 scan_control = 8'd30;
        #100 $stop;
    end

    // 输出监控
    initial begin
        $monitor("Time: %0d, rf_out_real: %d, rf_out_imag: %d", $time, rf_out_real, rf_out_imag);
    end

endmodule

代码解释

Butterfly单元：实现FFT的基本运算单元。

FFT模块：实现基于Butterfly单元的递归计算和结果合并。

滤波模块：实现一个简单的FIR滤波器，用于信号预处理。

顶层模块：将FFT和滤波模块集成到相控阵雷达波束控制系统中。

测试平台：用于验证系统功能的测试平台。