add wifi constellation objects

utils/constellations.py

@@ -0,0 +1,96 @@
+#!/usr/bin/env python
+
+import sys
+import numpy as np
+import matplotlib as mpl
+import matplotlib.pyplot as plt
+
+import ieee802_11
+
+###############################################
+#                 16-QAM
+###############################################
+
+c = ieee802_11.constellation_16qam()
+a = np.array(c.points())
+p = np.average(np.abs(a)**2)
+level = .1**.5
+
+print "16-QAM, average power: {0:.4f}".format(p)
+
+plt.scatter(a.real, a.imag)
+for i, x in enumerate(a):
+    s = "{0:04b}".format(i)[::-1]
+    plt.text(x.real, x.imag+0.1, s, ha='center')
+
+plt.show()
+
+#######################
+# test decison maker
+#######################
+
+N = 1000
+data = np.random.randint(0, 16, N)
+orig_const = a[data]
+noisy_const = orig_const + np.random.sample(N) * 2 * level - level +\
+                           np.random.sample(N) * 2j * level - level * 1j
+
+rx = np.array(map(lambda x: c.decision_maker_v([x]), noisy_const))
+rx_const = a[rx]
+
+if any(rx != data):
+    print "16-QAM: data does not match."
+else:
+    print "16-QAM: points decoded successfully."
+
+plt.scatter(a.real, a.imag)
+plt.scatter(noisy_const.real, noisy_const.imag, marker='x')
+for d, a, b in zip(rx, rx_const, noisy_const):
+    plt.plot([a.real, b.real], [a.imag, b.imag], color=mpl.cm.hsv(d/16.0))
+
+plt.show()
+
+
+
+###############################################
+#                 64-QAM
+###############################################
+
+c = ieee802_11.constellation_64qam()
+a = np.array(c.points())
+p = np.average(np.abs(a)**2)
+level = (1.0/42)**.5
+
+print "64-QAM, average power: {0:.4f}".format(p)
+
+plt.scatter(a.real, a.imag)
+for i, x in enumerate(a):
+    s = "{0:06b}".format(i)[::-1]
+    plt.text(x.real, x.imag+0.06, s, ha='center')
+
+plt.show()
+
+#######################
+# test decison maker
+#######################
+
+N = 1000
+data = np.random.randint(0, 64, N)
+orig_const = a[data]
+noisy_const = orig_const + np.random.sample(N) * 2 * level - level +\
+                           np.random.sample(N) * 2j * level - level * 1j
+
+rx = np.array(map(lambda x: c.decision_maker_v([x]), noisy_const))
+rx_const = a[rx]
+
+if any(rx != data):
+    print "16-QAM: data does not match."
+else:
+    print "16-QAM: points decoded successfully."
+
+plt.scatter(a.real, a.imag)
+plt.scatter(noisy_const.real, noisy_const.imag, marker='x')
+for d, a, b in zip(rx, rx_const, noisy_const):
+    plt.plot([a.real, b.real], [a.imag, b.imag], color=mpl.cm.hsv(d/64.0))
+
+plt.show()