From 4f313f3ef978e44c2394ee081c26007fc9253a8f Mon Sep 17 00:00:00 2001 From: Jinghao Shi Date: Fri, 14 Apr 2017 10:59:40 -0400 Subject: [PATCH] doc --- docs/source/decode.rst | 104 ++++++++++++++ docs/source/eq.rst | 134 +++++++++++++++++- docs/source/files/802.11_interleaver.pdf | Bin 0 -> 2015136 bytes docs/source/freq_offset.rst | 4 +- docs/source/images/cons.png | Bin 22662 -> 33594 bytes docs/source/images/cons_w_coarse.png | Bin 28503 -> 37023 bytes docs/source/images/cons_w_coarse_fine.png | Bin 28764 -> 23142 bytes .../images/cons_w_coarse_fine_pilot.png | Bin 26513 -> 21647 bytes docs/source/images/mod.png | Bin 0 -> 44742 bytes docs/source/images/norm_fft.png | Bin 0 -> 37023 bytes docs/source/images/pilot_fft.png | Bin 0 -> 21541 bytes docs/source/images/raw_fft.png | Bin 0 -> 42990 bytes docs/source/index.rst | 5 +- 13 files changed, 239 insertions(+), 8 deletions(-) create mode 100644 docs/source/decode.rst create mode 100644 docs/source/files/802.11_interleaver.pdf create mode 100644 docs/source/images/mod.png create mode 100644 docs/source/images/norm_fft.png create mode 100644 docs/source/images/pilot_fft.png create mode 100644 docs/source/images/raw_fft.png diff --git a/docs/source/decode.rst b/docs/source/decode.rst new file mode 100644 index 0000000..3236753 --- /dev/null +++ b/docs/source/decode.rst @@ -0,0 +1,104 @@ +Decoding +======== + +Now we have corrected the residual CFO and also have corrected the channel gain, +the next step is to map the FFT output to actual data bits. This is the reverse +process of encoding a packet. + +1. demodulation: complex number to bits +#. deinterleaving: shuffle the bits inside each OFDM symbol +#. Convolution decoding: remove redundancy and correct potential bit errors +#. Descramble. + +Step 1 and 3 depend on the modulation and coding scheme, which can be obtained +from the SIGNAL field. The SIGNAL field is encoded in the first OFDM symbol +after the long preamble and is always BPSK modulated regardless of the actual +modulation. Recall that in +802.11a/g, one OFDM symbol contains 48 data sub-carriers, which corresponds to +48 data bits in BPSK scheme. The SIGNAL field is also convolutional encoded at +1/2 rate so there are 24 actual data bits in the SIGNAL field. + +Next, we first go through the decoding process and then explain the format of +both legacy (802.11a/g) and the HT (802.11n) SIGNAL format. + +Demodulation +------------ + +- **Module**: :file:`demodulate.v` +- **Input**: ``rate (7), cons_i (16), cons_q (16)`` +- **Output**: ``bits (6)`` + +This step maps the complex number in the FFT plane into bits. :numref:`fig_mod` +shows the constellation encoding schemes for BPSK, QPSK, 16-QAM and 64-QAM. +also supported in |project|. + +.. _fig_mod: +.. figure:: /images/mod.png + :align: center + :scale: 80% + + BPSK, QPSK, 16-QAM and 64-QAM Constellation Bit Encoding + +Inside each OFDM symbol, each sub-carrier is mapped into 1, 2, 4 or 6 bits +depending on the modulation. + +Deinterleaving +-------------- + +Inside each OFDM symbol, the encoded bits are interleaved to map adjacent bits +into non-adjacent sub-carriers and also alternatively into less or more +significant bits in the constellation bits. + +To understand how the block interleaver works, first we need to define a few +parameters. Here we only consider 802.11a/g and 802.11n single spatial stream +mode. + +.. table:: Modulation Dependent Parameters (802.11a/g) + :align: center + + +------------+-------------+----------+------------------+------------------+------------------+ + | Modulation | Coding Rate | Bit-Rate | :math:`N_{BPSC}` | :math:`N_{CBPS}` | :math:`N_{DBPS}` | + +------------+-------------+----------+------------------+------------------+------------------+ + | BPSK | 1/2 | 6 | 1 | 48 | 24 | + +------------+-------------+----------+------------------+------------------+------------------+ + | BPSK | 3/4 | 9 | 1 | 48 | 36 | + +------------+-------------+----------+------------------+------------------+------------------+ + | QPSK | 1/2 | 12 | 2 | 96 | 48 | + +------------+-------------+----------+------------------+------------------+------------------+ + | QPSK | 3/4 | 18 | 2 | 96 | 72 | + +------------+-------------+----------+------------------+------------------+------------------+ + | 16-QAM | 1/2 | 24 | 4 | 192 | 96 | + +------------+-------------+----------+------------------+------------------+------------------+ + | 16-QAM | 3/4 | 36 | 4 | 192 | 144 | + +------------+-------------+----------+------------------+------------------+------------------+ + | 64-QAM | 2/3 | 48 | 6 | 288 | 192 | + +------------+-------------+----------+------------------+------------------+------------------+ + | 64-QAM | 3/4 | 54 | 6 | 288 | 216 | + +------------+-------------+----------+------------------+------------------+------------------+ + +where: + +- :math:`N_{BPSC}`: number of bits per sub-carrier +- :math:`N_{CBPS}`: number of coded bits per OFDM symbol +- :math:`N_{DBPS}`: number of data bits per OFDM symbol + +Let :math:`s=max(N_{BPSC}/2, + +The interleaving process involves two permutations. Accordingly, the +de-interleaving process also contains two permutation to reverse the +interleaving. + +The first permutation of de-interleaving is: + +.. math:: + + i = s\times\lfloor\frac{j}{s}\rfloor + (j+\lfloor16\times\frac{j}{N_{CBPS}}\rfloor)\%s, j\in[0, N_{CBPS}-1] + +where :math:`s=max(N_{BPSC}/2, 1)` + +The second permutation is defined as: + +.. math:: + + k = 16\times i - (N_{CBPS}-1)\times\lfloor\frac{16\times i}{N_{CBPS}}\rfloor + diff --git a/docs/source/eq.rst b/docs/source/eq.rst index ab09438..fe65d59 100644 --- a/docs/source/eq.rst +++ b/docs/source/eq.rst @@ -31,6 +31,9 @@ Each sub-carrier carries I/Q modulated information, corresponding to the output of 64 point FFT from :file:`sync_long.v` module. +Sub-Carrier Equalization +------------------------ + .. _fig_lts_fft: .. figure:: /images/lts_fft.png :align: center @@ -72,20 +75,141 @@ LTS. In particular, the mean of the two LTS is used as channel gain (:math:`H`): .. math:: H[i] = \frac{1}{2}(LTS_1[i] + LTS_2[i])\times L[i], i \in - [-26,\ldots, -1, 1, \ldots, 26] + [-26, 26] where :math:`L[i]` is the sign of the LTS sequence: .. math:: L_{-26,26} = \{ - &1, 1, –1, –1, 1, 1, –1, 1, –1, 1, 1, 1, 1, 1, 1, –1, –1, 1,\\ - &1, –1, 1, –1, 1, 1, 1, 1, 0, 1, –1, –1, 1, 1, –1, 1, –1, 1,\\ - &–1, –1, –1, –1, –1, 1, 1, –1, –1, 1, –1, 1, –1, 1, 1, 1, 1\} + &1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1,\\ + &1, -1, 1, -1, 1, 1, 1, 1, 0, 1, -1, -1, 1, 1, -1, 1, -1, 1,\\ + &-1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1\} And the FFT output at sub-carrier :math:`i` is normalized as: .. math:: - S'[i] = \frac{S[i]}{H[i]} + Y[i] = \frac{X[i]}{H[i]}, i \in [-26, 26] +where :math:`X[i]` is the FFT output at sub-carrier :math:`i`. + + +.. _fig_raw_fft: +.. figure:: /images/raw_fft.png + :align: center + :scale: 80% + + FFT Without Normalization + +.. _fig_norm_fft: +.. figure:: /images/norm_fft.png + :align: center + :scale: 80% + + FFT With Normalization + +:numref:`fig_raw_fft` and :numref:`fig_norm_fft` shows the FFT before and after +normalization using channel gain. + + +Residual Frequency Offset Correction +------------------------------------ + +We can see from :numref:`fig_norm_fft` that the FFT output is tilted slightly. +This is caused by residual frequency offset that was not compensated during the +coarse CFO correction step. + +This residual CFO can be corrected either by :ref:`sec_fine_cfo`, or/and by the +pilot sub-carriers. Ideally we want to do both, but since the fine CFO is +usually beyond the resolution of the phase look up table, we skip it in the +:file:`sync_long.v` module and only rely on the pilot sub-carriers. + +Regardless of the data sub-carrier modulation, the four pilot sub-carriers (-21, +-7, 7, 21) always contains BPSK modulated pseudo-random binary sequence. + + +The polarity of the pilot sub-carriers varies symbol to symbol. For 802.11a/g, +the pilot pattern is: + +.. math:: + + p_{0,\ldots,126} = \{ + &1, 1, 1, 1,-1,-1,-1, 1,-1,-1,-1,-1, 1, 1,-1, 1,-1,-1, 1, 1,-1, 1, 1,-1, 1,\\ + &1, 1, 1, 1, 1,-1, 1, 1, 1,-1, 1, 1,-1,-1, 1, 1, 1,-1, 1,-1,-1,-1, 1,-1,\\ + &1,-1,-1, 1,-1,-1, 1, 1, 1, 1, 1,-1,-1, 1, 1,-1,-1, 1,-1, 1,-1, 1,\\ + &1,-1,-1,-1, 1, 1,-1,-1,-1,-1, 1,-1,-1, 1,-1, 1, 1, 1, 1,-1, 1,-1, 1,-1,\\ + &1,-1,-1,-1,-1,-1, 1,-1, 1, 1,-1, 1,-1, 1, 1, 1,-1,-1, 1,-1,-1,-1, 1, 1,\\ + &1,-1,-1,-1,-1,-1,-1,-1\} + +And the pilot sub-carriers at OFDM symbol :math:`n` (starting at 0 from the first +symbol after the long preamble) is then: + +.. math:: + + P^{(n)}_{-21, -7, 7, 21} = \{p_{n\%127}, p_{n\%127}, p_{n\%127}, -p_{n\%127}\} + + +For 802.11n at 20MHz bandwidth with single spatial stream, the n'th pilot +sub-carriers are: + +.. math:: + P^{(n)}_{-21, -7, 7, 21} = \{\Psi_{n\%4}, \Psi_{(n+1)\%4}, \Psi_{(n+2)\%4}, + \Psi_{(n+3)\%4}\} + +And: + +.. math:: + \Psi_{0, 1, 2, 3} = \{1, 1, 1, -1\} + + +In other words, the pilot sub-carries of the first few symbols are: + + +.. math:: + + P^{(0)}_{-21, -7, 7, 21} = \{1, 1, 1, -1\}\\ + P^{(1)}_{-21, -7, 7, 21} = \{1, 1, -1, 1\}\\ + P^{(2)}_{-21, -7, 7, 21} = \{1, -1, 1, 1\}\\ + P^{(3)}_{-21, -7, 7, 21} = \{-1, 1, 1, 1\}\\ + P^{(4)}_{-21, -7, 7, 21} = \{1, 1, 1, -1\}\\ + \cdots + +For other configurations (e.g., spatial stream, bandwidth), the pilot +sub-carrier pattern can be found in Section 20.3.11.10 in +:download:`802.11-2012 std <./files/802.11-2012.pdf>`. + + +The residual phase offset at symbol :math:`n` can then be estimated as: + +.. math:: + + \theta_n = \angle(\sum_{i\in\{-21, -7, 7, 21\}}\overline{X^{(n)}[i]}\times P^{(n)}[i]\times H[i]) + + +Combine this phase offset and the previous channel gain correction together, the +adjustment to symbol :math:`n` is: + +.. math:: + + Y^{(n)}[i] = \frac{X^{(n)}[i]}{H[i]}e^{j\theta_n} + + +.. _fig_pilot_fft: +.. figure:: /images/pilot_fft.png + :align: center + :scale: 80% + + Residual CFO Correction Using Pilot Sub-Carriers + +:numref:`fig_pilot_fft` shows the effect of correcting the residual CFO using +pilot sub-carriers. Each sub-carrier can then be mapped to constellation points +easily. + +In |project|, the above tasks are implemented by the :file:`equalizer.v` module. +It first stores the first LTS, and then calculates the mean of the two LTS and +store it as channel gain. + +For each incoming OFDM symbol, it first obtains the polarity of the pilot +sub-carriers in current symbol, then calculates the residual CFO using the pilot +sub-carriers and also performs the channel gain correction. diff --git a/docs/source/files/802.11_interleaver.pdf b/docs/source/files/802.11_interleaver.pdf new file mode 100644 index 0000000000000000000000000000000000000000..a34cb3ea31c0fe58d6498f31e2383862c7496be9 GIT binary patch literal 2015136 zcmc$_b8uzf)+m~!W82uVy<^+9Z5tiiMh6|+w#|+^PRF+0FTZoXbH97vy|3#1@v2_U z8f$8B%{At(U1JP#MNx5jW(FWE`R?A#0xS!F3E*IC4a>{RC~IbK;c5wBXX9jM6t}W< zHFIVZw>5G#6E!n&Fg4@ncX4$#GqQt~j7-s3ciw12@mgbv`a)i;)L|E=TR zfI+=FBu!XGT%DgT@+%78=0IRV;Xr4;6faMFzJf-lVm<+U*7w!DqyBRtl&d>KeoHr} 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Implementation of 802.11 OFDM Decoder +======================================================== .. toctree:: :maxdepth: 2 @@ -15,6 +15,7 @@ Welcome to |project|'s documentation! freq_offset sync_long eq + decode setting verilog

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