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-Digital Predistortion Computation Engine for ODR-DabMod
-=======================================================
-
-This folder contains a digital predistortion prototype.
-It was only tested in a laboratory system, and is not ready
-for production usage.
-
-Concept
--------
-
-ODR-DabMod makes outgoing TX samples and feedback RX samples available to an
-external tool. This external tool can request a buffer of samples for analysis,
-can calculate coefficients for the predistorter in ODR-DabMod and load the new
-coefficients using the remote control.
-
-The external tool is called the Digital Predistortion Computation Engine (DPDCE).
-The DPDCE is written in python, and makes use of the numpy library for
-efficient computation. Its sources reside in the *dpd* folder.
-
-The predistorter in ODR-DabMod supports two modes: polynomial and lookup table.
-In the DPDCE, only the polynomial model is implemented at the moment.
-
-The *dpd/main.py* script is the entry point for the *DPD Computation Engine*
-into which these features will be implemented. The tool uses modules from the
-*dpd/src/* folder:
-
-- Sample transfer and time alignment with subsample accuracy is done by *Measure.py*
-- Estimating the effects of the PA using some model and calculation of the updated
-  polynomial coefficients is done in *Model.py* and other specific *Model_XXX.py* files
-- Finally, *Adapt.py* updates the ODR-DabMod predistortion setting and digital gain
-
-These modules themselves use additional helper scripts in the *dpd/src/* folder.
-
-Requirements
-------------
-
-- USRP B200.
-- Power amplifier.
-- A feedback connection from the power amplifier output, such that the average power level at
-  the USRP RX port is at -45dBm or lower.
-  Usually this is done with a directional coupler and additional attenuators.
-- ODR-DabMod with enabled *dpd_port*, and with a samplerate of 8192000 samples per second.
-- Synchronous=1 so that the USRP has the timestamping set properly, internal refclk and pps
-  are sufficient (not GPSDO necessary).
-- A live mux source with TIST enabled.
-
-See dpd/dpd.ini for an example.
-
-The DPD server port can be tested with the *dpd/show_spectrum.py* helper tool, which can also display
-a constellation diagram.
-
-Hardware Setup
---------------
-
-![setup diagram](img/setup_diagram.svg)
-![setup photo](img/setup_photo.svg)
-
-Our setup is depicted in the Figure above. We used components with the following properties:
- 1. USRP TX (max +20dBm)
- 2. Band III Filter (Mini-Circuits RBP-220W+, 190-250MHz, -3.5dB)
- 3. Power amplifier (Mini-Circuits, max +15dBm output, +10 dB gain at 200MHz)
- 4. Directional coupler (approx. -25dB @ 223MHz)
- 5. Attenuator (-20 dB)
- 6. Attenuator (-30 dB)
- 7. USRP RX (max -15dBm input allowed, max -45dBm desired)
- 8. Spectrum analyzer (max +30dBm allowed)
-
-It is important to make sure that the USRP RX port does not receive too much
-power. Otherwise the USRP will break. Here is an example of how we calculated
-the maximal USRP RX input power for our case. As this is only a rough
-calculation to protect the port, the predistortion software will later
-automatically apply a normalization for the RX input by adapting the USRP RX
-gain.
-
-    TX Power + PA Gain - Coupling Factor - Attenuation = 20dBm + 10dB -25dB -50dB = -45dBm
-
-Thus we have a margin of about 30dB for the input power of the USRP RX port.
-Keep in mind we need to calculate using peak power, not average power, and it is
-essential that there is no nonlinearity in the RX path!
-
-Software Setup
---------------
-
-We assume that you already installed *ODR-DabMux* and *ODR-DabMod*.
-You should install the required python dependencies for the DPDCE using
-distribution packages. You will need at least scipy, matplotlib and
-python-zeromq.
-
-Use the predistortion
-----------------------
-
-Make sure you have a ODR-DabMux running with a TCP output on port 9200.
-
-Then run the modulator, with the example dpd configuration file.
-
-```
-./odr-dabmod dpd/dpd.ini
-```
-
-This configuration file is different from usual defaults in several respects:
-
- * logging to /tmp/dabmod.log
- * 4x oversampling: 8192000 sample rate
- * a very small digital gain, which will be overridden by the DPDCE
- * predistorter enabled
-
-The TX gain should be chosen so that you can drive your amplifier into
-saturation with a digital gain of 0.1, so that there is margin for the DPD to
-operate.
-
-You should *not modify txgain, rxgain, digital gain or coefficient settings manually!*
-When the DPDCE is used, it controls these settings, and there are command line
-options for you to define initial values.
-
-To verify that the communication between the DPDCE and ODR-DabMod is ok,
-you can use the status and reset options:
-
-```
-cd dpd
-python main.py --status
-python main.py --reset
-```
-
-The reset option sets all DPD-related settings to the defaults (as shown in the
-`--help` usage screen) and stops.
-
-When neither `--status` nor `--reset` is given, the DPDCE will run the predistortion
-algorithm. As a first test you should run the DPDCE with the `--plot`
-parameter. It preserves the output power and generates all available
-visualisation plots in the newly created logging directory
-`/tmp/dpd_<time_stamp>`. As the predistortion should increase the peak to
-shoulder ratio, you should select a *txgain* in the ODR-DabMod configuration
-file such that the initial peak-to-soulder ratio visible on your spectrum
-analyser. This way, you will be able to see a the
-change.
-
-```
-cd dpd
-python main.py --plot
-```
-
-The DPDCE now does 10 iterations, and tries to improve the predistortion effectiveness.
-In each step the learning rate is decreased. The learning rate is the factor
-with which new coefficients are weighted in a weighted mean with the old
-coefficients. Moreover the nuber of measurements increases in each iteration.
-You find more information about that in *Heuristic.py*.
-
-Each plot is stored to the logging directory under a filename containing its
-time stamp and its label. Following plots are generated chronologically:
-
- - ExtractStatistic: Extracted information from one or multiple measurements.
- - Model\_AM: Fitted function for the amplitudes of the power amplifier against the TX amplitude.
- - Model\_PM: Fitted function for the phase difference of the power amplifier against the TX amplitude.
- - adapt.pkl: Contains all settings for the predistortion.
-   You can load them again without doing measurements with the `apply_adapt_dumps.py` script.
- - MER: Constellation diagram used to calculate the modulation error rate.
-
-After the run you should be able to observe that the peak-to-shoulder
-difference has increased on your spectrum analyzer, similar to the figure below.
-
-Without digital predistortion:
-
-![shoulder_measurement_before](img/shoulder_measurement_before.png)
-
-With digital predistortion, computed by the DPDCE:
-
-![shoulder_measurement_after](img/shoulder_measurement_after.png)
-
-Now see what happens if you apply the predistortions for different TX gains.
-You can either set the TX gain before you start the predistortion or using the
-command line option `--txgain gain`. You can also try to adjust other
-parameters. To see their documentation run `python main.py --help`.
-
-File format for coefficients
-----------------------------
-The coef file contains the polynomial coefficients used in the predistorter.
-The file format is very similar to the filtertaps file used in the FIR filter.
-It is a text-based format that can easily be inspected and edited in a text
-editor.
-
-The first line contains an integer that defines the predistorter to be used:
-1 for polynomial, 2 for lookup table.
-
-For the polynomial, the subsequent line contains the number of coefficients
-as an integer. The second and third lines contain the real, respectively the
-imaginary parts of the first coefficient. Fourth and fifth lines give the
-second coefficient, and so on. The file therefore contains 1 + 1 + 2xN lines if
-it contains N coefficients.
-
-For the lookup table, the subsequent line contains a float scalefactor that is
-applied to the samples in order to bring them into the range of 32-bit unsigned
-integer. Then, the next pair of lines contains real and imaginary part of the first
-lookup-table entry, which is multiplied to samples in first range. Then it's
-followed by 31 other pairs. The entries are complex values close to 1 + 0j.
-The file therefore contains 1 + 1 + 2xN lines if it contains N coefficients.
-
-TODO
-----
-
- - Understand and fix occasional ODR-DabMod crashes when using DPDCE.
- - Make the predistortion more robust. At the moment the shoulders sometimes
-   increase instead of decrease after applying newly calculated predistortion
-   parameters. Can this behaviour be predicted from the measurement? This would
-   make it possible to filter out bad predistortion settings.
- - Find a better measurement for the quality of the predistortion. The USRP
-   might not be good enough to measure large peak-to-shoulder ratios, because
-   the ADC has 12 bits and DAB signals have a large crest factor.
- - Implement a Volterra polynomial to model the PA. Compared to the current
-   model this would also capture the time dependent behaviour of the PA (memory
-   effects).
- - Continuously observe DAB signal in frequency domain and make sure the power
-   stays the same. At the moment only the power in the time domain is kept the
-   same.
- - At the moment we assume that the USRP RX gain has to be larger than 30dB and
-   the received signal should have a median absolute value of 0.05 in order to
-   have a high quality quantization. Do measurements to support or improve
-   this heuristic.
- - Check if we need to measure MER differently (average over more symbols?)
- - Is -45dBm the best RX feedback power level?
-
-REFERENCES
-----------
-
-Some papers:
-
-The paper Raich, Qian, Zhou, "Orthogonal Polynomials for Power Amplifier
-Modeling and Predistorter Design" proposes other base polynomials that have
-less numerical instability.
-
-Aladrén, Garcia, Carro, de Mingo, and Sanchez-Perez, "Digital Predistortion
-Based on Zernike Polynomial Functions for RF Nonlinear Power Amplifiers".
-
-Jiang and Wilford, "Digital predistortion for power amplifiers using separable functions"
-
-Changsoo Eun and Edward J. Powers, "A New Volterra Predistorter Based on the Indirect Learning Architecture"
-
-Raviv Raich, Hua Qian, and G. Tong Zhou, "Orthogonal Polynomials for Power Amplifier Modeling and Predistorter Design"
-
-
-Models without memory:
-
-Complex polynomial: y[i] = a1 x[i] + a2 x[i]^2 + a3 x[i]^3 + ...
-
-The complex polynomial corresponds to the input/output relationship that
-applies to the PA in passband (real-valued signal). According to several
-sources, this gets transformed to another representation if we consider complex
-baseband instead. In the following, all variables are complex.
-
-Odd-order baseband: y[i] = (b1 + b2 abs(x[i])^2 + b3 abs(x[i])^4) + ...) x[i]
-
-Complete baseband: y[i] = (b1 + b2 abs(x[i]) + b3 abs(x[i])^2) + ...) x[i]
-
-with
-    b_k = 2^{1-k} \binom{k}{(k-1)/2} a_k
-
-
-Models with memory:
-
- - Hammerstein model: Nonlinearity followed by LTI filter
- - Wiener model: LTI filter followed by NL
- - Parallel Wiener: input goes to N delays, each delay goes to a NL, all NL outputs summed.
-
-Taken from slide 36 of [ECE218C Lecture 15](http://www.ece.ucsb.edu/Faculty/rodwell/Classes/ece218c/notes/Lecture15_Digital%20Predistortion_and_Future%20Challenges.pdf)
-