phase lut

docs/source/verilog.rst

@@ -42,34 +42,63 @@ Phase Estimation
 **Module**:: ``phase.v``
 
 When correcting the frequency offset, we need to estimate the phase of a complex
-number, which can be calculated using the :math:`arctan` function. 
+number. The *right* way of doing this is probably using the `CORDIC
+<https://dspguru.com/dsp/faqs/cordic/>`_ algorithm. In OpenOFDM, we use look up
+table.
+
+More specifically, we calculate the phase using the :math:`arctan` function. 
 
 
 .. math::
 
-    \angle(\langle I, Q\rangle) = arctan(\frac{Q}{I})
+    \theta = \angle(\langle I, Q\rangle) = arctan(\frac{Q}{I})
 
 The overall steps are:
 
-1. Project the complex number to the :math:`[0, \pi/4]` range.
+1. Project the complex number to the :math:`[0, \pi/4]` range, so that the
+   :math:`tan(\theta)` range is :math:`[0, 1]`.
 #. Calculate :math:`arctan` (division required)
 #. Looking up the quantized :math:`arctan` table
 #. Project the phase back to the :math:`[-\pi, \pi)` range
 
 Here we use both quantization and look up table techniques.
 
-The first step can be achieved by this transformation:
+Step 1 can be achieved by this transformation:
 
 .. math::
 
     \langle I, Q\rangle \rightarrow \langle max(|I|, |Q|), min(|I|, |Q|)\rangle
 
 
-The *right* way to calculate :math:`arctan` is probably using the `CORDIC
-<https://dspguru.com/dsp/faqs/cordic/>`_ algorithm. However, this function is
-implemented using look up tables in OpenOFDM.
+In the lookup table used in step 3, we use :math:`int(tan(\theta)*256)` as the
+key, which effectively maps the :math:`[0.0, 1.0]` range of :math:`tan` function
+to the integer range of :math:`[0, 256]`. In other words, we quantize the
+:math:`[0, \pi/4]` quadrant into 256 slices.
 
-In the table, we use :math:`int(tan(\angle)*256)` as the key, which effective
-map the :math:`[0.0, 1.0]` range of :math:`tan` function to the integer range of
-:math:`[0, 256]`. In other words, we quantize the :math:`[0, \pi/4]` quadrant
-into 256 slices.
+This :math:`arctan` look up table is generated using the
+``scripts/gen_atan_lut.py`` script. The core logic is as follows:
+
+.. code-block:: python
+    :linenos:
+
+    SIZE = 2**8
+    SCALE = SIZE*2
+    data = []
+    for i in range(SIZE):
+        key = float(i)/SIZE
+        val = int(round(math.atan(key)*SCALE))
+        data.append(val)
+
+
+Note that we also scale up the :math:`arctan` values to distinguish adjacent
+values. This also systematically scale up :math:`\pi` in OpenOFDM. In fact,
+:math:`\pi` is defined as :math:`1608=int(\pi*512)` in
+``verilog/common_params.v``.
+
+The generated lookup table is stored in the ``verilog/atan_lut.coe``
+file (see `COE File Syntax
+<https://www.xilinx.com/support/documentation/sw_manuals/xilinx11/cgn_r_coe_file_syntax.htm>`_).
+Refer to `this guide
+<https://www.xilinx.com/itp/xilinx10/isehelp/cgn_p_memed_single_block.htm>`_ on
+how to create a look up table in Xilinx ISE. The generated module is stored in
+``verilog/coregen/atan_lut.v``.

scripts/decode.py

@@ -225,6 +225,7 @@ class ChannelEstimator(object):
             prod_sum += prod
         beta = cmath.phase(prod_sum)
         print "[PILOT OFFSET] %f (%d)" % (beta, int(beta*PHASE_SCALE))
+        # beta = 0
         carriers = []
         for c in self.subcarriers:
             if c in PILOT_SUBCARRIES:
@@ -269,8 +270,8 @@ class ChannelEstimator(object):
 
         coarse_offset = cmath.phase(sum([sts[i]*sts[i+16].conjugate()
                                          for i in range(len(sts)-16)]))/16
-        coarse_offset = int(coarse_offset*256)/256.0
         print '[COARSE OFFSET] %f (%d)' % (coarse_offset, int(coarse_offset*PHASE_SCALE))
+        # coarse_offset = 0
 
         # coarse correction
         lts = [c*cmath.exp(complex(0, n*coarse_offset))
@@ -279,7 +280,7 @@ class ChannelEstimator(object):
         fine_offset = cmath.phase(sum([lts[i]*lts[i+64].conjugate()
                                        for i in range(len(lts)-64)]))/64
         print '[FINE OFFSET] %f (%d)' % (fine_offset, int(fine_offset*PHASE_SCALE))
-        fine_offset = 0
+        # fine_offset = 0
 
         self.lts_samples = [c*cmath.exp(complex(0, n*fine_offset))
                for n, c in enumerate(lts)]
@@ -430,6 +431,7 @@ class Decoder(object):
     def decode_next(self, *args, **kwargs):
         trigger = False
         samples = []
+        glbl_index = 0
         while True:
             chunk = array.array('h', self.fh.read(self.window))
             chunk = [complex(i, q) for i, q in zip(chunk[::2], chunk[1::2])]
@@ -437,6 +439,7 @@ class Decoder(object):
                 trigger = True
                 samples = []
                 print "Power trigger at %d" % (self.count)
+                glbl_index = self.count
 
             self.count += self.window
 
@@ -448,6 +451,8 @@ class Decoder(object):
                 if start is None:
                     trigger = False
                 else:
+                    print "Decoding packet starting from sample %d" %\
+                        (glbl_index + start)
                     return self.decode(samples[start:], *args, **kwargs)
 
     def find_pkt(self, samples):