1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
|
/*
* 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 */
double log2(double); /* declaration seems to be missing from some math.h's */
#if !defined(HAVE_LOG2)
#define log2(x) (log(x)*M_LOG2E)
#endif
/* 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] = log2(2*p0/(p1+p0)) - bias;
metrics[1][0] = 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] = log2(2*p0/(p1+p0)) - bias;
metrics[1][s] = 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] = log2(2*p0/(p1+p0)) - bias;
metrics[1][255] = 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
}
}
}
|
