1 //
2 // eqlms_cccf_test.c
3 //
4 // Tests least mean-squares (LMS) equalizer (EQ).
5 //
6 
7 #include <stdio.h>
8 #include <stdlib.h>
9 #include <string.h>
10 #include <math.h>
11 #include <complex.h>
12 #include "liquid.h"
13 
14 #define OUTPUT_FILENAME "eqlms_cccf_test.m"
15 
main()16 int main() {
17     // options
18     unsigned int k=2;       // samples/symbol
19     unsigned int m=3;
20     float beta = 0.3f;
21     //float dt = 0.4f;        // timing offset
22     unsigned int num_symbols = 256;
23     unsigned int hc_len=1;  // channel impulse response length
24     unsigned int p=13;      // equalizer filter length
25     float mu = 0.05f;
26 
27     // TODO : validate input
28 
29     // derived values
30     unsigned int num_samples = k*num_symbols;
31 
32     // data arrays
33     float complex s[num_symbols];   // original QPSK symbols
34     float complex x[num_samples];   // interpolated samples
35     float complex y[num_samples];   // received samples
36     float complex z[num_samples];   // recovered samples
37 
38     // generate data sequence
39     unsigned int i;
40     for (i=0; i<num_symbols; i++) {
41         s[i] = (rand() % 2 ? 1.0f : -1.0f) +
42                (rand() % 2 ? 1.0f : -1.0f) * _Complex_I;
43     }
44 
45     // interpolate
46     unsigned int h_len = 2*k*m+1;
47     float hm[h_len];
48 #if 1
49     // design GMSK
50     float c0 = 1.0f / sqrtf(logf(2.0f));
51     for (i=0; i<h_len; i++) {
52         float t = (float)(i) / (float)(k) - (float)(m);
53         //float sig = 0.7f;
54         //hm[i] = expf(-t*t / (2*sig*sig) );
55 
56         hm[i] = liquid_Qf(2*M_PI*beta*(t-0.5f)*c0) -
57                 liquid_Qf(2*M_PI*beta*(t+0.5f)*c0);
58         printf("h(%3u) = %12.8f\n", i+1, hm[i]);
59     }
60 #else
61     design_rrc_filter(k,m,beta,dt,hm);
62 #endif
63     firinterp_crcf interp = firinterp_crcf_create(k,hm,h_len);
64     for (i=0; i<num_symbols; i++)
65         firinterp_crcf_execute(interp, s[i], &x[i*k]);
66     firinterp_crcf_destroy(interp);
67 
68     // generate channel filter
69     float complex hc[hc_len];
70     for (i=0; i<hc_len; i++)
71         hc[i] = (i==0) ? 1.0f : 0.1f*randnf()*cexpf(_Complex_I*2*M_PI*randf());
72 
73     // push signal through channel...
74     firfilt_cccf fchannel = firfilt_cccf_create(hc,hc_len);
75     for (i=0; i<num_samples; i++) {
76         firfilt_cccf_push(fchannel, x[i]);
77         firfilt_cccf_execute(fchannel, &y[i]);
78     }
79     firfilt_cccf_destroy(fchannel);
80 
81     // initialize equalizer
82 #if 1
83     // initialize with delta at center
84     float complex h[p]; // coefficients
85     unsigned int p0 = (p-1)/2;  // center index
86     for (i=0; i<p; i++)
87         h[i] = (i==p0) ? 1.0f : 0.0f;
88 #else
89     // initialize with square-root raised cosine
90     p = 2*k*m+1;
91     float h_tmp[p];
92     float complex h[p];
93     design_rrc_filter(k,m,beta,0.0f,h_tmp);
94     for (i=0; i<p; i++)
95         h[i] = h_tmp[i] / k;
96 #endif
97 
98     // run equalizer
99     float complex w0[p];
100     float complex w1[p];
101     memmove(w0, h, p*sizeof(float complex));
102     windowcf buffer = windowcf_create(p);
103     for (i=0; i<num_samples; i++) {
104         // push value into buffer
105         windowcf_push(buffer, y[i]);
106 
107         // compute d_hat
108         float complex d_hat = 0.0f;
109         float complex * r;
110         windowcf_read(buffer, &r);
111         unsigned int j;
112         for (j=0; j<p; j++)
113             d_hat += conjf(w0[j]) * r[j];
114 
115         // store in output
116         z[i] = d_hat;
117 
118         // check to see if buffer is full, return if not
119         if (i <= p) continue;
120 
121         // decimate by k
122         if ( (i%k) != 0 ) continue;
123 
124         // estimate transmitted QPSK symbol
125         float complex d_prime = (crealf(d_hat) > 0.0f ? 1.0f : -1.0f) +
126                                 (cimagf(d_hat) > 0.0f ? 1.0f : -1.0f) * _Complex_I;
127 
128         // compute error
129         float complex alpha = d_prime - d_hat;
130 
131         // compute signal energy
132         float ex2 = 1.414f;
133 
134         // update weighting vector
135         for (j=0; j<p; j++)
136             w1[j] = w0[j] + mu*conjf(alpha)*r[j]/ex2;
137 
138         // copy new filter values
139         memmove(w0, w1, p*sizeof(complex float));
140     }
141 
142     // destroy additional objects
143     windowcf_destroy(buffer);
144 
145     // print results to file
146     FILE * fid = fopen(OUTPUT_FILENAME,"w");
147     fprintf(fid,"%% %s : auto-generated file\n\n", OUTPUT_FILENAME);
148     fprintf(fid,"clear all\n");
149     fprintf(fid,"close all\n");
150 
151     fprintf(fid,"k = %u;\n", k);
152     fprintf(fid,"m = %u;\n", m);
153     fprintf(fid,"num_symbols = %u;\n", num_symbols);
154     fprintf(fid,"num_samples = num_symbols*k;\n");
155 
156     // save samples
157     fprintf(fid,"x = zeros(1,num_samples);\n");
158     fprintf(fid,"y = zeros(1,num_samples);\n");
159     fprintf(fid,"z = zeros(1,num_samples);\n");
160     for (i=0; i<num_samples; i++) {
161         fprintf(fid,"x(%3u) = %12.4e + j*%12.4e;\n", i+1, crealf(x[i]), cimagf(x[i]));
162         fprintf(fid,"y(%3u) = %12.4e + j*%12.4e;\n", i+1, crealf(y[i]), cimagf(y[i]));
163         fprintf(fid,"z(%3u) = %12.4e + j*%12.4e;\n", i+1, crealf(z[i]), cimagf(z[i]));
164     }
165     fprintf(fid,"t = 1:num_samples;\n");
166     fprintf(fid,"tsym = 1:k:num_samples;\n");
167     fprintf(fid,"figure;\n");
168     fprintf(fid,"subplot(2,1,1), plot(t, real(z), tsym, real(z(tsym)),'x');\n");
169     fprintf(fid,"subplot(2,1,2), plot(t, imag(z), tsym, imag(z(tsym)),'x');\n");
170 
171     // plot symbols
172     fprintf(fid,"tsym0 = tsym([1:length(tsym)/2]);\n");
173     fprintf(fid,"tsym1 = tsym((length(tsym)/2):end);\n");
174     fprintf(fid,"figure;\n");
175     fprintf(fid,"plot(real(z(tsym0)),imag(z(tsym0)),'x','Color',[0.7 0.7 0.7],...\n");
176     fprintf(fid,"     real(z(tsym1)),imag(z(tsym1)),'x','Color',[0.0 0.0 0.0]);\n");
177     fprintf(fid,"xlabel('In-phase');\n");
178     fprintf(fid,"ylabel('Quadrature');\n");
179     fprintf(fid,"axis([-1 1 -1 1]*1.5);\n");
180     fprintf(fid,"axis square;\n");
181     fprintf(fid,"grid on;\n");
182 
183     // save filter coefficients
184     for (i=0; i<h_len; i++) fprintf(fid,"hm(%3u) = %12.4e;\n", i+1, hm[i]);
185     for (i=0; i<p; i++)     fprintf(fid,"hp(%3u) = %12.4e + j*%12.4e;\n", i+1, crealf(w0[i]), cimagf(w0[i]));
186     for (i=0; i<hc_len; i++)fprintf(fid,"hc(%3u) = %12.4e + j*%12.4e;\n", i+1, crealf(hc[i]), cimagf(hc[i]));
187 
188     fprintf(fid,"nfft = 1024;\n");
189     fprintf(fid,"f = [0:(nfft-1)]/nfft - 0.5;\n");
190     fprintf(fid,"Hm = 20*log10(abs(fftshift(fft(hm/k,nfft))));\n");
191     fprintf(fid,"Hc = 20*log10(abs(fftshift(fft(hc,nfft))));\n");
192     fprintf(fid,"Hp = 20*log10(abs(fftshift(fft(hp,nfft))));\n");
193     fprintf(fid,"G = Hm + Hp + Hc;\n");
194     fprintf(fid,"figure;\n");
195     fprintf(fid,"plot(f,Hm, f,Hc, f,Hp, f,G,'-k','LineWidth',2);\n");
196     fprintf(fid,"xlabel('Normalized Frequency');\n");
197     fprintf(fid,"ylabel('Power Spectral Density');\n");
198     fprintf(fid,"legend('transmit','channel','equalizer','total');\n");
199     fprintf(fid,"axis([-0.5 0.5 -10 10]);\n");
200     fprintf(fid,"grid on;\n");
201 
202     fclose(fid);
203 
204     printf("results written to '%s'\n", OUTPUT_FILENAME);
205 
206     printf("done.\n");
207     return 0;
208 }
209