Transceiver52M: Add 4 samples-per-symbol Laurent pulse shape

When 4 samples-per-symbol operation is selected, replace the
existing pulse approximation, which becomes inaccurate with
non-unit oversampling, with the primary pulse, C0, from the
Laurent linear pulse approximation.

Pierre Laurent, "Exact and Approximate Construction of Digital Phase
  Modulations by Superposition of Amplitude Modulated Pulses", IEEE
  Transactions of Communications, Vol. 34, No. 2, Feb 1986.

Octave pulse generation code for the first three pulses of the
linear approximation are included.

Signed-off-by: Thomas Tsou <tom@tsou.cc>

1 files changed, 40 insertions, 9 deletions

diff --git a/Transceiver52M/sigProcLib.cpp b/Transceiver52M/sigProcLib.cpp
index b0ef21a..51584b7 100644
--- a/Transceiver52M/sigProcLib.cpp
+++ b/Transceiver52M/sigProcLib.cpp
@@ -422,11 +422,22 @@ void generateGSMPulse(int sps, int symbolLength)
   GSMPulse->empty->isRealOnly(true);
   *(GSMPulse->empty->begin()) = 1.0f;
 
-  len = sps * symbolLength;
-  if (len < 4)
-    len = 4;
+  /*
+   * For 4 samples-per-symbol use a precomputed single pulse Laurent
+   * approximation. This should yields below 2 degrees of phase error at
+   * the modulator output. Use the existing pulse approximation for all
+   * other oversampling factors.
+   */
+  switch (sps) {
+  case 4:
+    len = 16;
+    break;
+  default:
+    len = sps * symbolLength;
+    if (len < 4)
+      len = 4;
+  }
 
-  /* GSM pulse approximation */
   GSMPulse->buffer = convolve_h_alloc(len);
   GSMPulse->gaussian = new signalVector((complex *)
                                         GSMPulse->buffer, 0, len);
@@ -435,12 +446,32 @@ void generateGSMPulse(int sps, int symbolLength)
 
   signalVector::iterator xP = GSMPulse->gaussian->begin();
 
-  center = (float) (len - 1.0) / 2.0;
+  if (sps == 4) {
+    *xP++ = 4.46348606e-03;
+    *xP++ = 2.84385729e-02;
+    *xP++ = 1.03184855e-01;
+    *xP++ = 2.56065552e-01;
+    *xP++ = 4.76375085e-01;
+    *xP++ = 7.05961177e-01;
+    *xP++ = 8.71291644e-01;
+    *xP++ = 9.29453645e-01;
+    *xP++ = 8.71291644e-01;
+    *xP++ = 7.05961177e-01;
+    *xP++ = 4.76375085e-01;
+    *xP++ = 2.56065552e-01;
+    *xP++ = 1.03184855e-01;
+    *xP++ = 2.84385729e-02;
+    *xP++ = 4.46348606e-03;
+    *xP++ = 0.0;
+  } else {
+    center = (float) (len - 1.0) / 2.0;
 
-  for (int i = 0; i < len; i++) {
-    arg = ((float) i - center) / (float) sps;
-    *xP++ = 0.96 * exp(-1.1380 * arg * arg -
-                        0.527 * arg * arg * arg * arg);
+    /* GSM pulse approximation */
+    for (int i = 0; i < len; i++) {
+      arg = ((float) i - center) / (float) sps;
+      *xP++ = 0.96 * exp(-1.1380 * arg * arg -
+			 0.527 * arg * arg * arg * arg);
+    }
   }
 
   float avgAbsval = sqrtf(vectorNorm2(*GSMPulse->gaussian)/sps);