metrics.c

这是用python语言写的一个数字广播的信号处理工具包。利用它

/*
 * Copyright 1995 Phil Karn, KA9Q
 * Copyright 2008 Free Software Foundation, Inc.
 * 
 * This file is part of GNU Radio
 * 
 * GNU Radio is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 3, or (at your option)
 * any later version.
 * 
 * GNU Radio is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 * 
 * You should have received a copy of the GNU General Public License
 * along with GNU Radio; see the file COPYING.  If not, write to
 * the Free Software Foundation, Inc., 51 Franklin Street,
 * Boston, MA 02110-1301, USA.
 */

/* 
 * Generate metric tables for a soft-decision convolutional decoder
 * assuming gaussian noise on a PSK channel.
 *
 * Works from "first principles" by evaluating the normal probability
 * function and then computing the log-likelihood function
 * for every possible received symbol value
 *
 */

#ifdef HAVE_CONFIG_H
#include <config.h>
#endif

/* Symbols are offset-binary, with 128 corresponding to an erased (no
 * information) symbol
 */
#define	OFFSET	128

#include <stdlib.h>
#include <math.h>

/* Normal function integrated from -Inf to x. Range: 0-1 */
#define	normal(x)	(0.5 + 0.5*erf((x)/M_SQRT2))

/* Logarithm base 2 */ 
#define gr_log2(x) (log(x)*M_LOG2E)

/* Generate log-likelihood metrics for 8-bit soft quantized channel
 * assuming AWGN and BPSK
 */
void
gen_met(int mettab[2][256],	/* Metric table, [sent sym][rx symbol] */
	int amp,		/* Signal amplitude, units */
	double esn0,		/* Es/N0 ratio in dB */
	double bias,		/* Metric bias; 0 for viterbi, rate for sequential */
	int scale)		/* Scale factor */
{
  double noise;
  int s,bit;
  double metrics[2][256];
  double p0,p1;
  
  /* Es/N0 as power ratio */
  esn0 = pow(10.,esn0/10);
  
  noise = 0.5/esn0;	/* only half the noise for BPSK */
  noise = sqrt(noise);	/* noise/signal Voltage ratio */
  
  /* Zero is a special value, since this sample includes all
   * lower samples that were clipped to this value, i.e., it
   * takes the whole lower tail of the curve 
   */
  p1 = normal(((0-OFFSET+0.5)/amp - 1)/noise);	/* P(s|1) */
  
  /* Prob of this value occurring for a 0-bit */	/* P(s|0) */
  p0 = normal(((0-OFFSET+0.5)/amp + 1)/noise);
  metrics[0][0] = gr_log2(2*p0/(p1+p0)) - bias;
  metrics[1][0] = gr_log2(2*p1/(p1+p0)) - bias;
  
  for(s=1;s<255;s++){
    /* P(s|1), prob of receiving s given 1 transmitted */
    p1 = normal(((s-OFFSET+0.5)/amp - 1)/noise) -
      normal(((s-OFFSET-0.5)/amp - 1)/noise);
    
    /* P(s|0), prob of receiving s given 0 transmitted */
    p0 = normal(((s-OFFSET+0.5)/amp + 1)/noise) -
      normal(((s-OFFSET-0.5)/amp + 1)/noise);
    
#ifdef notdef
    printf("P(%d|1) = %lg, P(%d|0) = %lg\n",s,p1,s,p0);
#endif
    metrics[0][s] = gr_log2(2*p0/(p1+p0)) - bias;
    metrics[1][s] = gr_log2(2*p1/(p1+p0)) - bias;
  }
  /* 255 is also a special value */
  /* P(s|1) */
  p1 = 1 - normal(((255-OFFSET-0.5)/amp - 1)/noise);
  /* P(s|0) */
  p0 = 1 - normal(((255-OFFSET-0.5)/amp + 1)/noise);
  
  metrics[0][255] = gr_log2(2*p0/(p1+p0)) - bias;
  metrics[1][255] = gr_log2(2*p1/(p1+p0)) - bias;
#ifdef	notdef
  /* The probability of a raw symbol error is the probability
   * that a 1-bit would be received as a sample with value
   * 0-128. This is the offset normal curve integrated from -Inf to 0.
   */
  printf("symbol Pe = %lg\n",normal(-1/noise));
#endif
  for(bit=0;bit<2;bit++){
    for(s=0;s<256;s++){
      /* Scale and round to nearest integer */
      mettab[bit][s] = floor(metrics[bit][s] * scale + 0.5);
#ifdef	notdef
      printf("metrics[%d][%d] = %lg, mettab = %d\n",
	     bit,s,metrics[bit][s],mettab[bit][s]);
#endif
    }
  }
}