Matlab exercises ELEC-E5410 Signal processing for communications

Transcription

1 Matlab exercises 2017 ELEC-E5410 Signal processing for communications

2 RTL-SDR Specifications MHz tuning range 3.57 MHz intermediate frequency 2.4 MHz maximum sampling rate 8-bit in-phase and quadrature signals in the output Dongle originally made for DVB-T reception. Driver bypasses the DVB-T decoder Dongles have Realtek chip but may use different tuners

3 Rx with RTL-SDR 3

4 Guidelines min 50% points of the exercises required in the scale 0-100% Groups of 1-2 persons Sign up in MyCourses If several groups return the same code (or similar code, changing names of the variables etc. doesn t count), the max. number of points/group becomes 100%/ #similar submissions See deadlines of the exercises in MyCourses

5 Possible issues Ensure you observe the FM signal. If the received signal is just noise, the performance is difficult/impossible to assess Do not compensate carrier frequency offset when receiving the FM signal in comm.sdrrtlreceiver() unless otherwise specified The offset (sinusoidal) signal is used to test the algorithms Show the output of the algorithms i.e. don t just design filters but filter as well Return the.pdf made by Matlab s publish() or Matlab live script.mlx with the results Not.html + several.pngs or some other awkward format Live script requires Matlab 2016/2017 5

6 Exercise 1 setup 6

7 Exercise 1 1. Make Matlab and RTL-SDR work - Get a dongle and install Matlab RTL-SDR toolbox on your computer. Requires Aalto address and Mathworks user account 2. Run frequency offset calibration example in RTL-SDR toolbox 1. The calibration example comes with the toolbox Tune to a FM frequency to find an unused frequency slot Iswithc on the FM transmitter and tune it to the unused frequency you found 3. Find out the estimated carrier frequency offset (CFO) - Frequency offset stabilizes once warmed up - In comparison, LTE specification allows max. 0.1 ppm CFO. Dongles may go up to 100 ppm 4. Determine the CFO That is, put the estimated CFO into comm.sdrrtlreceiver until you get zero CFO

8 Exercise 1 5. Find out maximum and minimum sampling rates the RTL- SDR dongle can support 6. Run FM receiver example in RTL-SDR toolbox to check it works Use some radio station, e.g., YLE 7. Write a short document (a separate file or type in MyCourses) containing your findings: CFO, max/min sampling rate and max/min tuning range (carrier frequency). No need to return code this time 8

9 Installation Download Matlab from download.aalto.fi Make a Mathworks account Install RTL-SDR hardware support package from Add-Ons in the Matlab menu bar Optionally, install rtl command line tools as well See 9

10 Known issues in installation Admin rights needed to install driver On Windows, installation of the toolbox changes the rights of Matlab to admin and the path to toolbox is hidden from regular users Always use the same USB port for RTL-SDR on Windows Kernel drive active on Linux sudo echo blacklist dvb_usb_rtl28xxu >/etc/modprobe.d/rtlsdr.conf and reboot Mac requires Xcode, which takes 7GB of disk space Install command line tools (130MB) only osxdaily.com/2014/02/12/install-command-line-tools-mac-os-x/ Matlab 2016a, 2017a and RTL-SDR toolbox work for sure 10

11 Exercise 2 Decimation 11

12 Down-sample and listen 1. Download the Matlab script template from MyCourses 2. Switch on your FM transmitter 3. Down-sample the signal and listen to it with audiodevicewriter() Choose sampling rate for the dongle Tune the carrier frequency offset in the script so that you see a frequency peak (unmodulated FM carrier) on the audio range Down-sample the signal (i.e. without low-pass filtering) Play the downsampled signal. You should hear a tone but the signal is very noisy. Since we did not do FM demodulation, you can only here the noisy carrier, not a modulated FM transmission Keep the loop as simple (read and listen) as possible so that audio doesn t loose samples between the function calls. If that doesn t help try to increase down-sampling factor

13 Decimate with one-stage FIR 2. Decimate the signal using one-stage low-pass FIR filter H(z) Determine you filter parameters (attenuation in stop-band, oscillation is pass-band, pass-band edge and stop-band edge) and down-sampling factor Design H(z) using one of Matlab s filter design functions in slide 18. Display the magnitude response of the filter with fvtool() and check it matches to the specifications. Describe briefly the algorithm used in the filter design function Decimate the signal using H(z) Listen to the decimated signal. Quality should be better than with down-sampling only. 13

14 Decimating using interpolated FIR filter 3. Decimate the signal using interpolated FIR filter Design the two filters G(z) and F(z) such that G(z L ) F(z)~ H(z) and decimate. Display the spectra (use two spectrum analyzer objects) of the received signal and the decimated signals obtained by 1-stage filter and IFIR. Display the real or imaginary part of the decimated time-domain signal. It should look like a sinusoidal signal - Tune dongle s CFO, or change the scale of the x axes if needed 14

15 Decimating using interpolated FIR filter 4. Calculate and compare the number of required multiplications in one-stage and IFIR implementations. For linear-phase FIR filters #multiplications = ceil(length/2) 5. Return your Matlab code (.m) and a pdf made by Matlab s publish function (or.mlx with the results from Live Script). The document must contain figures on 1) magnitude responses of the designed filters, 2) output spectra, 3) time domain output signal, 4) #multiplications. Write a short document containing your findings. Note: You can use Matlab commands ifir(), decimate() to check your algorithms but they don t give you points. Design your filters instead! 15

16 IFIR design example by Matlab s ifir() Magnitude Response (db) Magnitude Response (db) 0 0 Overall filter Magnitude (db) -40 Magnitude (db) Normalized Frequency ( rad/sample) Image suppression filter with don t care bands Normalized Frequency ( rad/sample) Cascade of the sparse filter and image suppression filter 16

17 Own designs, 1-stage and IFIR Magnitude Response (db) 0 Direct realization Magnitude (db) Normalized Frequency ( rad/sample) One-stage filter Image suppression filter without don t care bands 17

18 Linear-phase FIR filter design commands command fir1 fir2 fircls fircls1 firls firpm firpmord operation Window-based FIR filter design Frequency sampling-based FIR filter design Constrained-least-squares FIR multiband filter design Constrained-least-squares linear-phase FIR lowpass and highpass filter design Least-squares linear-phase FIR filter design Parks-McClellan optimal FIR filter design Parks-McClellan optimal FIR filter order estimation 18

19 Exercise 3 Spectrum estimation

20 Goal Identify the 19 KHz (+CFO) indicating stereo FM transmission using the spectrum estimation methods presented in the lecture magnitude 45% mono 10% 22.5% 22.5% stereo stereo RDS KHz

21 Problem The received FM signal may not resemble the sketch at all The source signal (music) is wide band and the strong FM modulated source signal masks the stereo carrier 21

22 Problem The carriers may appear, though, when the level of the input signal is low Speech is better than music 22

23 Task Choose the algorithm, the length of the signal vector used for the estimator, number of subsequencies in Bartlett and/or Welch methods, time/spectral window, sampling rate, etc., so that you are able to see a clear 19 KHz (+CFO) A clear peak No good 23

24 Workflow Tune to a FM station (YLE Puhe recommended) and record a snapshot of the signal Run the spectrum estimation algorithms on the recorded signal and tune the parameters to see the stereo carrier CFO compensation and decimation are not necessary Use as short signal vector as possible i.e. as few samples for the estimation as possible Once the estimation works, apply your algorithm to the received signal in (almost) real time as shown in the Matlab template 24

25 Matlab functions barthannwin bartlett blackman blackmanharris bohmanwin chebwin enbw flattopwin gausswin hamming hann kaiser nuttallwin parzenwin rectwin taylorwin triang tukeywin Modified Bartlett-Hann window Bartlett window Blackman window Minimum 4-term Blackman-Harris window Bohman window Chebyshev window Equivalent noise bandwidth Flat top weighted window Gaussian window Hamming window Hann (Hanning) window Kaiser window Nuttall-defined minimum 4-term Blackman-Harris window Parzen (de la Vallée Poussin) window Rectangular window Taylor window Triangular window Tukey (tapered cosine) window Use fft xcorr Don t use pwelch periodogram pcov There are Matlab functions for several different PSD estimators, but using those ready-made functions does not give points R.W. 25

26 Report Return your Matlab code (.m) and a pdf made by Matlab s publish function (or.mlx with the results from Live Script). The document must contain the algorithms and the parameters sampling frequency, the size of the signal vector used for estimation and the corresponding time in (milli)seconds, number of subsequences in the estimation, temporal/spectral window, FFT length And the figure of the result showing a clear peak at 19KHz (+CFO) 26

27 Exercise 4 Fractional delay using polyphase 27

28 Goal Extract the carrier of an FM transmission and apply fractional delay to the in-phase or quadrature component of the received signal such that the components are aligned in time This has no real use, the goal is just to understand polyphase filtering To align the I and Q components, interpolate using polyphase structure Matlab template in MyCourses

29 Extract a signal vector 1. Receive the FM signal (e.g. Yle Puhe 103.7MHz) like in Exercise 3. Use your spectrum analyzer in Ex. 3 and select a signal with a clear peak. One signal vector is enough for experiments The figure displays a clear peak but since CFO is not compensated the carrier is not close to zero frequency

30 Extract a signal vector Either compensate the CFO or modulate the signal vector to place the carrier close to zero frequency

31 Low-pass filter Low-pass filter the signal to reduce noise level Filtered I&Q I Q Choose the filter design functions as in Exercise Choose the cut-off frequency such that only the main carrier is present in the output

32 Down-sample Down-sample the signal such that you have about 10 samples/cycle Downsampled I&Q I Q Note that the cut-off frequency of the low-pass filter has to be less than π/down-samplingfactor

33 Interpolation and fractional delay Interpolate the real/imaginary (I or Q) part of the downsampled signal Use the usual filter design commands to design the interpolation filter Choose the delay of the interpolated signal such that the I and Q part are aligned as well as possible FractIonal delay by interpolation 0.04 I 0.03 Q

34 Interpolation with a polyphase filter Finally implement the fractional delay with a polyphase structure, see Slide 14 in Lecture Use the polyphase decomposition of your interpolation filter, commutator form This implements a fractional delay, 0,,(L-1)/L. In addition you need to add an integer-valued delay as in the previous case 34

35 Report Return your Matlab code (.m) and a pdf made by Matlab s publish function (or.mlx with the results from Live Script). The document must contain the algorithms, the parameters and the figures The same structure as in the template 35

36 Exercise 5 FM transmission and reception

37 Tasks 1. Due to popular demand, implement a simple FM receiver in Matlab Template in MyCourses No stereo, no de-emphasis filter Subtract mean to compensate residual CFO 2. Modulate binary data by on-off-keying and transmit it through the FM transmitter 3. Receive the FM transmission and calculate bit-error rate (BER) Use the receiver designed in 1) You should be able to receive frames where BER << 0.5 Template in MyCourses

38 Practical issues Generate a.wav file containing the data signal in Matlab. Connect the FM transmitter to computer or mobile phone When using the same computer for Rx and Tx, it is not possible to listen to the signal Let RTL-SDR and FM Tx to warm-up to stabilize carrier frequency offsets Search for a frequency (e.g MHz) without FM radio station Compensate the carrier frequency offset Keep enough distance between Rx and Tx such that Rx does not saturate See Ex &12.18 in RTL-SDR book, slides in Lecture 5

39 Generate binary information signal Generate information bits Add preamble to the Tx data Decoder has to know the start of the message Rx matched filter searches for the preamble Barker code of length 13 is one option for preamble Barker 13 autocorrelation

40 Generate Tx signal Generate Tx signal using onoff-keying Bit 0: no signal, bit 1: cos(2f o t) Parameters Sampling rate in.wav: Fs Bit rate: Fb Bit 1 frequency: Fo Oversampling factor: L=Fs/Fb Cycles/bit (repetition coding): Fo/Fb OOK example

41 Generate Tx signal Pulse shaping is not necessary It changes only the edges between modulated bits 0 and 1 FM transmitter does lowpass filtering anyway OOK after pulse shaping

42 Decode the OOK modulated signal 1. Decimate the Rx signal to Fs 2. Apply FM demodulation 3. Apply low-pass filter to squared signal Subtract the mean to do sign detection 4. Search for the optimum sampling time as in the template, decode and calculate BER Better implementations are welcome After envelope detection (simulation)

43 Report Return your Matlab code (.m) and a pdf made by Matlab s publish function (or.mlx with the results from Live Script). The document must contain the algorithms, the parameters and the figures Bit-error rate should be way less than 0.5 at least for some frames Justify your solutions. This increases grade points 43

44 Exercise 6 Estimation of CFO 44

45 CFO estimation from FM transmitter 1. Receive the carrier of the FM transmitter and display its spectrum Check the spectrum to select a coarse frequency offset, and the max. frequency offset -> the number of lags in autocorrelation in Fitz and L&R 2. Low-pass filter and down-sample the received signal Check that the carrier with CFO fits to the decimated band (sampling rate >> CFO) 3. Implement the three algorithms in lecture slides to estimate CFO: Kay, Fitz, and Luise and Regiannini 4. Compensate the CFO of the received signal by the CFO. Display the spectrum of the compensated signal Compensation = de-rotate the signal (at front-end sampling rate) by the estimate If the algorithms work, the CFO estimate should be now very small Convert the CFO estimate to PPM Coarse frequency offset RTL-SDR Compensate CFO Filter and downsample Estimate CFO Display spectrum Display spectrum

46 FM signal after CFO compensation Original sampling rate Carriers indicating stereo FM are strong but they are filtered out when the signal is decimated for CFO estimation CFO estimation algorithms use the decimated signal 46

47 Report Return your Matlab code (.m) and a pdf made by Matlab s publish function (or.mlx with the results from Live Script). Write a short document containing your findings Which algorithm of the three works best? Did you notice any differences in performance? Can you use these algorithms after FM discriminator? 47

48 Example of Kay s algorithm Mikes signal Uniform weighting simply calculates the mean of the angles Kay s weighting is more stable w.r.t. the number of samples than the uniform weighting Sign of CFO is inverted, because the estimator used z(k)z*(k+1) instead of z(k)z*(k-1) 48

49 Example of Fitz and L&R Fitz Luise&Regiannini 49

50 Exercise 7: FM Receiver using PLL 50

51 Background on PLL The error signal of the loop filter is proportional to the FM modulated information signal v(t), θ fm (t) = k 0 v(t) dt cos(w c t + θ fm (t)) when phase locked loop (PLL) is locked to the FM signal, Δω is the residual CFO exp(j(δω[n] + Θfm[n]) / A0exp(-j(Δω^[n] + Θ^[n]) Kph exp(-j ) arg( ) Voltage controlled oscillator 1/(1-z -1 ) Loop filter ~Θ fm[n] See Section 9.8 in SDR using Matlab, Simulink and RTL-SDR

52 Receive using PLL Calculate the loop-filter (1 st -order IIR) coefficients K p and K i (see the slide set) for the loop filter given the front-end sampling rate and the bandwidth of the FM signal Use one of the three phase detectors in the slides Tune to a FM radio station Apply a coarse carrier frequency offset compensation. The offset should be small enough for the PLL to lock Receive. Low-pass filter after PLL to remove noise at high frequencies Make the loop as simple as possible to be able to operate it in real time 52

53 Finally Return your Matlab code (.m) and a pdf made by Matlab s publish function (or.mlx with the results from Live Script). Write a short document containing your findings 53

54 Exercise 8: Timing estimation 54

55 Timing estimation BPSK modulation FM transmitter Flow chart of the timing estimation exercise Barker Preamble 1:L Frame generation Up-sampling RTL-SDR FM demod. Coarse freq. offset Frame synch. Pulseshaping Decimate to.wav freq. no Detection Repeate Eye open BER calculation yes.wav TED no BER<<0.5 L:1 yes Done

56 Timing estimation 1. Generate BPSK data, add Barker preamble, up-sample and pulse shape Select matching numbers for data rate, up-sampling factor and.wav sampling frequency. rcosdesign() makes the pulse shaping filter 2. Write signal to.wav and transmit using your computer or phone and FM transmitter 3. Demodulate the FM signal and low-pass filter to remove high-frequency noise. Down-sample to.wav frequency. 4. Filter the FM-demodulated signal with matched filter (MF) and derivative matched filter (DMF) Calculate DMF from MF numerically using a digital differentiator (see Lecture 6) Set MF and DMF to the same length so that their outputs are in the same phase Filtering and timing estimation could be done using polyphase representation of DMF and MF and a loop, but applying filter() first is faster 56

57 Timing estimation Check that the eye is open before moving to the next step The amplitude depends on the gain of Rx signal strength and the gain of the MF These also affect to the error signal to the loop filter 57

58 Timing estimation Implement the timing estimator feedback loop Determine the filter coefficients of the first-order IIR. The same filter structure applies as with PLL but parameters differ. Timing changes slowly so the bandwidth of the filter should be very narrow Implement the generation of the error signal using one of the non-data aided methods Rate of change of the timing error estimate depends on the magnitude of the error signal and the gain of the loop filter. Choose the parameters such that the change matches to that in the eye diagram

59 Finally Return your Matlab code (.m) and a pdf made by Matlab s publish function (or.mlx with the results from Live Script). Write a short document containing your findings Bit-error rate should be way below