verilog实现qpsk最大似然检测软判决，并输出对数似然比

QPSK最大似然检测软判决可以通过以下几个步骤来实现：

1. 接收到的QPSK信号进行采样，并将采样后的信号分别与I路和Q路的正交基进行内积，得到I路和Q路的实数值。

2. 计算接收到的信号与两个可能的符号值之间的欧几里得距离，然后选择距离最小的符号作为接收到的符号。

3. 计算对数似然比。对数似然比是指接收到的符号对应的概率与未接收到的符号对应的概率的比值的对数。计算公式为：$L = \ln\frac{P(s=1|r)}{P(s=-1|r)}$，其中$s$表示发送的符号，$r$表示接收到的符号。

4. 输出得到的符号以及对数似然比。

下面是使用Verilog实现QPSK最大似然检测软判决的示例代码：

module qpsk_detection_soft_decision(
  input clk,
  input rst,
  input signed [15:0] i_sample,
  input signed [15:0] q_sample,
  output wire [1:0] symbol,
  output wire signed [15:0] log_likelihood_ratio
);

  // 定义常量
  parameter SYMBOL_00 = 2'b00;
  parameter SYMBOL_01 = 2'b01;
  parameter SYMBOL_10 = 2'b10;
  parameter SYMBOL_11 = 2'b11;

  // 定义符号值对应的载波相位
  parameter PHASE_00 = 0;
  parameter PHASE_01 = 90;
  parameter PHASE_10 = 180;
  parameter PHASE_11 = 270;

  // 定义符号值对应的复数值
  parameter COMPLEX_00 = 16'h4000;
  parameter COMPLEX_01 = 16'hC000;
  parameter COMPLEX_10 = 16'h8000;
  parameter COMPLEX_11 = 16'h0000;

  // 定义符号对应的概率
  parameter PROBABILITY_00 = 0.25;
  parameter PROBABILITY_01 = 0.25;
  parameter PROBABILITY_10 = 0.25;
  parameter PROBABILITY_11 = 0.25;

  // 定义符号值和载波相位的映射关系
  reg [1:0] symbol_map;
  always @(*) begin
    if (i_sample >= 0) begin
      if (q_sample >= 0) begin
        symbol_map = SYMBOL_00;
      end else begin
        symbol_map = SYMBOL_01;
      end
    end else begin
      if (q_sample >= 0) begin
        symbol_map = SYMBOL_10;
      end else begin
        symbol_map = SYMBOL_11;
      end
    end
  end

  // 计算接收到的符号对应的载波相位
  reg [7:0] phase;
  always @(*) begin
    case (symbol_map)
      SYMBOL_00: phase = PHASE_00;
      SYMBOL_01: phase = PHASE_01;
      SYMBOL_10: phase = PHASE_10;
      SYMBOL_11: phase = PHASE_11;
      default: phase = 0;
    endcase
  end

  // 计算接收到的符号对应的复数值
  reg signed [15:0] complex_i;
  reg signed [15:0] complex_q;
  always @(*) begin
    case (symbol_map)
      SYMBOL_00: begin
        complex_i = COMPLEX_00 * $cos(phase);
        complex_q = COMPLEX_00 * $sin(phase);
      end
      SYMBOL_01: begin
        complex_i = COMPLEX_01 * $cos(phase);
        complex_q = COMPLEX_01 * $sin(phase);
      end
      SYMBOL_10: begin
        complex_i = COMPLEX_10 * $cos(phase);
        complex_q = COMPLEX_10 * $sin(phase);
      end
      SYMBOL_11: begin
        complex_i = COMPLEX_11 * $cos(phase);
        complex_q = COMPLEX_11 * $sin(phase);
      end
      default: begin
        complex_i = 0;
        complex_q = 0;
      end
    endcase
  end

  // 计算欧几里得距离
  reg signed [31:0] distance_00;
  reg signed [31:0] distance_01;
  reg signed [31:0] distance_10;
  reg signed [31:0] distance_11;
  always @(posedge clk) begin
    distance_00 <= (i_sample - complex_i) * (i_sample - complex_i) + (q_sample - complex_q) * (q_sample - complex_q);
    distance_01 <= (i_sample + complex_q) * (i_sample + complex_q) + (q_sample - complex_i) * (q_sample - complex_i);
    distance_10 <= (i_sample - complex_q) * (i_sample - complex_q) + (q_sample + complex_i) * (q_sample + complex_i);
    distance_11 <= (i_sample + complex_i) * (i_sample + complex_i) + (q_sample + complex_q) * (q_sample + complex_q);
  end

  // 选择距离最小的符号
  reg [1:0] detected_symbol;
  always @(posedge clk) begin
    if (distance_00 < distance_01 && distance_00 < distance_10 && distance_00 < distance_11) begin
      detected_symbol <= SYMBOL_00;
    end else if (distance_01 < distance_00 && distance_01 < distance_10 && distance_01 < distance_11) begin
      detected_symbol <= SYMBOL_01;
    end else if (distance_10 < distance_00 && distance_10 < distance_01 && distance_10 < distance_11) begin
      detected_symbol <= SYMBOL_10;
    end else begin
      detected_symbol <= SYMBOL_11;
    end
  end

  // 计算对数似然比
  wire [31:0] distance_0 = {distance_00, distance_10};
  wire [31:0] distance_1 = {distance_01, distance_11};
  reg signed [15:0] log_likelihood_ratio_raw;
  always @(*) begin
    log_likelihood_ratio_raw = $log10(PROBABILITY_0 * $exp(-distance_0) / PROBABILITY_1 * $exp(-distance_1));
  end
  assign log_likelihood_ratio = {16'h0000, log_likelihood_ratio_raw};

  // 输出检测结果
  assign symbol = detected_symbol;

endmodule

在上面的代码中，我们使用了Verilog的内置函数来计算正弦和余弦值，以及取对数和指数。注意，对数似然比的计算需要使用浮点数运算，这在硬件实现中可能会带来一定的困难。因此，实际的实现可能需要采用一些近似方法来计算对数似然比，或者使用专门的硬件模块来进行浮点数运算。