5625_project1

7/29/2019 5625_project1

1/15

ECE 5625 Spring 2012 Project 1Multicarrier SSB Transceiver

1 Introduction

In this team project you will be implementing the Weaver SSB modulator as part of a multicarrier

transmission scheme. Coherent demodulation will be implemented for a single carrier that lies

between two adjacent carriers. Test message signals consisting of bandlimited noise will be used

to check crosstalk levels. Recorded speech waveforms will be used to provide a final test of the

complete system after it has been turned in. The entire simulation will be constructed in MATLAB

m-code. A code framework will be provided along with interface requirements, so that the code

submitted with the report project can be easily tested using the speech waveform message signals.

The m-code functions are documented in Appendix A and the source code itself is on the course

web site as a ZIP file package.

Honor Code: The project teams will be limited to at most two members. Teams are to workindependent of one another. Bring questions about the project to me. I encourage you to work in

teams of two. Since each team member receives the same project grade, a group of two should

attempt to give each team member equal responsibility. The due date for the completed project

will be 12:00 pm, Friday, March 23, 2012.

2 System Description

A block diagram of the complete multicarrier single sideband system (SSB) is shown in Figure 1.

This is more of a conceptual block diagram, as the actual system that will be implemented will use

discrete-time signal processing. Specifically the input message signals will be either bandlimitedwhite noise or speech waveforms, both at a sampling rate of 8 ksp/s (ksamples per second). Using

SSB we are able to pack three message signals very close to each other. This provides bandwidth

efficiency for sending many message signals over a narrow band of frequencies. The frequency

plan shows that three W D 4 kHz message signals when SSB modulated can easily fit a channel

spanning 16 to 32 kHz. Packing the signals right next to each other may not be the most desirable

since adjacent channel interference may occur. Placing a small guard band, say f, between each

channel may give improved performance.

Each of the SSB modulator blocks will be implemented as a reusable function block in MATLAB.

The message signal input to each modulator is a signal sampled at 8 ksps. From basic sampling

theory, when we sample at fs samples per second, the usable lowpass bandwidth runs from 0

fs=2 Hz. If a continuous-time signal has bandwidth exceeding fs=2 Hz, aliasing will occur, effec-tively folding spectral energy at frequencies greater than fs=2 back down into the 0fs=2 band.

In particular for fs D 8 ksps the usable signal bandwidth must be less than 4 kHz. Signals with

bandwidth exceeding 4 kHz will be aliased when sampled at 8 ksps. Telephony grade speech is

sampled at 8 ksps. Band limiting of a speech waveform must be done prior to sampling at 8 ksps to

avoid aliasing. The passband of telephone grade speech is about 300 3300 Hz, thus an antialising

filter can be designed to avoid aliasing when sampled at 8 kHz, yet avoid disturbing the 3003300

Hz signal spectrum.

7/29/2019 5625_project1

2/15

SSBModulator

m1 t( )

USSB fc1

SSBModulator

SSBModulator

USSB fc2

USSB fc3

m2 t( )

m3 t( )

BPFCoherent SSBDemodulator

mj t( )

Ideal Channel withusable Bandwidthfrom 16 32 kHz.Each SSB channeloccupies ~4 kHz.

f(kHz)

16 320

m1 m2 m3

Transmission Bandwidth

j 1 2 3, ,=

Sing

le-S

ided

Spectrum

fc1 fc2 fc3

xc1 t( )

xc2 t( )

xc3 t( )

x t( ) x t( ) y t( )

Figure 1: Multicarrier SSB transmission system top level block diagram.

In the SSB modulators of Figure 1 the message signal is assumed to be sampled at 8 ksps. In

discrete-time form the message signal is denoted by the sequences mjn D mj.n=ds/, j D 1 ;2 ;3.

These discrete-time signals enter a bank of three SSB modulators, each of which processes its inputsignal with filters and multiplications by reference sinusoids to produce nominally three upper

SSB (USSB) signals. The signal carrier frequencies are denoted fc1, fc2 , and fc3. In order to

accommodate a useful range of carrier frequencies, yet still remain in the discrete-time domain,

the sampling rate is increased from 8 ksps up to 96 ksps, fs1 D 8 ! fs2 D 96, which corresponds

to an upsampling factor ofL D 12. This factor was chosen to be convenient for use in this project.

A real system would likely consider a different value for L.

With the sampling rate increased to 96 ksps, the usable bandwidth, from sampling theory, is

now 096=2 D 48 kHz. In Figure 1 we further see that for the purposes of this project, the trans-

mission bandwidth or channel is defined to be 16 to 32 kHz. In practice this band of frequencies

could be located at any assignable frequency band. Note that the discrete-time signals might firstbe digital-to-analog converted and then frequency translated using analog mixing.

The received signal x.t/, which is composed of three adjacent USSB signals, is ready for

demodulation of just one of the message signals mjn, j D 1 ;2 ;3. In this project a coherent

demodulator is proposed as the means to recover an estimate of the transmitted message signal

(sequence). A coherent demodulator needs a coherent reference, but we will assume for this project

that such a reference is available. It might be that one or more pilot signals are sent such that

through frequency mixing operations, following a nonlinearity, all three coherent carriers, fc1,

ECE 5/4625 Project 1: Multicarrier SSB Transceiver 2

7/29/2019 5625_project1

3/15

fc2, and fc3, can be obtained from the received signal.

The various filters, frequency mixing, and digital signal processing , will result in some crosstalk

between the three adjacent channels, as well as undesired band limiting of the desired signal. The

Project Tasks section of this project description document, will detail measurements to assess some

of these distortions.

The top level simulation file, which implements all of Figure 1 is contained in the m-fileSSB_transceiver.m and is listed below. The functions weaver() and SSB_demod() will be

written by each project team.

function m_recovered = SSB_transceiver(fc,message_type,demod_channel)

% m_recovered = SSB_transceiver(fc,message_type,demod_channel)

%

%=============== Inputs ======================

% fc = Carrier frequencies in Hz of signal to be demodulated

% message_type = String value either noise or speech; the speech input

% requires that that the .wav files be present.

% demod_channel = An integer, 1, 2, or 3, to specify which message channel

% will be demodulated and output from the function

%

%=============== Outputs =====================

% m_recovered = The recovered modulation downsampled to 8 ksps

%

% Mark Wickert, March 2007

L = 12; % Upsampling factor

fs = 8000; % sampling rate = 8000 Hz

%////////////// BEGIN TRANSMITTER ////////////////////////////

% Create transmitter message signals from either bandlimited white noise or

% from available sampled speech test vectors

switch lower(message_type)

case noise

% Design a 9th-order bandpass noise shaping filter with 3 dB

% cutoffs at 300 & 3300 Hz relative to a 8000 Hz sampling rate.

[bn,an] = butter(9,2*([300 3300]/8000));

% Create 3 zero mean noise vectors

m1 = randn(1,100000);

m2 = randn(1,100000);

m3 = randn(1,100000);

% Filter the noise vectors.

m1 = filter(bn,an,m1);

m2 = filter(bn,an,m2);m3 = filter(bn,an,m3);

case speech

N = 100000;

m1 = wavread(OSR_uk_000_0050_8k.wav,[1,N]);

m1 = m1; %transpose to row vector

m2 = wavread(OSR_us_000_0018_8k.wav,[1,N]);


m3 = wavread(OSR_us_000_0030_8k.wav,[1,N]);



7/29/2019 5625_project1

4/15

7/29/2019 5625_project1

5/15

2.1 SSB Modulator Design

Ideal

LPF

B=W/2

Ideal

LPF

B=W/2

m t! " xc t! "

2 2! W2!!!!!" #

$ %tcos

2

! fcW

2!!!!!

#" #$ %

tcos

+

+_

90" $ 90" $

Figure 2: Weaver SSB modulator as an analog signal processing function.

or bandpass filter has transfer function

H.s/ Dc0 C c1s C c2s

2 C C cMsM

d0 C d1s C d2s2 C C dNsN: (1)

A study of digital signal processing, in particular digital filter design, reveals that analog filter pro-

totypes, e.g., Butterworth, Chebyshev, Elliptic, etc., can be converted to digital filter equivalents

with knowledge of the sampling rate, fs, and the analog filter coefficients fck; dkg. The corre-

sponding digital filter in the discrete-time domain will havea transfer function in the z-domaingiven by

H.z/ Db0 C b1z

1 C b2z2 C C bMz

M

a0 C a1z1 C a2z2 C C aNzN(2)

A z-domain expression results by taking the z-transform of a discrete-time sequence, much like an

s-domain expression results by taking the Laplace transform of a continuous-time signal. A course

in DSP is needed to obtain the details. The new ECE 2610 course serves as the starting point for

this study. The significance of having z-domain filter coefficients is that we can implement the

filter as an algorithm of the form

yn D

N

XkD1

akyn k C

M

XkD0

bkxn k; (3)

assuming we have normalized the denominator coefficients so that a0 D 1. Note that (3) is known

as a linear constant coefficient difference equation (LCCDE).

The MATLAB signal processing toolbox has a collection of functions for designing digital fil-

ters. For our purposes the output of a particular digital filter design is simply a pair of coefficient

vectors (b,a). The MATLAB GUI tool fdatool (launched by typing fdatool at the command

prompt) can be useful in designing filters and placing a and b coefficient vectors into the MATLAB


7/29/2019 5625_project1

6/15


Lowpass

Digital

B=W/2

Lowpass

Digital

B=W/2

m n[ ] xc n[ ]2 2! W

2-----" #$ %

nfs1------cos 2! fc

W

2-----" #

$ % nfs2------cos +

+_

Interpolate

12 LPF

Interpolate

12 LPF

2 2! W2-----" #

$ % nfs1------sin 2! fc

W

2-----" #

$ % nfs2------sin

Sampling Rate fs2 96 kHz= =Sampling Rate fs1 8 kHz= =

Figure 3: Weaver SSB modulator discrete-time implementation.

workspace. This may be useful for some design teams more comfortable with DSP. For the pur-

poses of this project however, it is sufficient to obtain all of your needed filter designs, both lowpass

and bandpass, from the Butterworth family.

2.1.1 Butterworth Filter DesignButterworth digital filters can be designed from MATLAB s command prompt using the function

butter() (for more information type help butter). Suppose we desire a 5th-order lowpassfilter with cutoff frequency of 2 kHz and fs D 8 ksps. This can be synthesized at the MATLABcommand prompt as follows:

>> n = 5; % filter order

>> fc = 2000; % cutoff frequency in Hz

>> fs = 8000; % sampling frequency in Hz

>> [b,a] = butter(n,2*(fc/fs));

The filter coefficients are returned in the vector variables b and a. If we wanted to characterize thefilter we just designed, we can use the function fvtool as follows:

>> fvtool(b,a,fs,8000); % scale the frequency axis to fs = 8000 Hz

The resulting plot, following vertical axis scaling using the cursors, is shown in Figure 4. The

fvtool window allows you to show a variety of frequency response format, e.g., magnitude in

dB, phase, group delay, pole-zero, etc. The cursors can be used to scale the plot to reasonable

dynamic range values, i.e., filter gains down to say only -80 to -60 dB. Without re-scaling the


7/29/2019 5625_project1

7/15


display will show the filter gain down to -150 dB, which is beyond reason for any real hardware

implementation. Dont make plots like this. Note that MATLAB is uses double precision floating-

point arithmetic for all calculations by default.

x and y axisscaling cursorbuttons

Figure 4: Studying filter characteristics using fvtool.

With a filter now designed, we can put it to work using the MATLAB filter() function, whichimplements (3) for vector input/output. If we have a sequence of signal samples stored in the vectorm we can produce the filtered output m_filt via:

>> N = 10000; % Length of input vector

>> n = 0:N-1; % create a time index vector

>> m = cos(2*pi*1000/fs*n);

>> m_filt = filter(b,a,m);

If we need a bandpass filter, we can again use the butter function to obtain a and b coefficientvectors. A bandpass design requires both a lower and upper cutoff frequency in its specification.As an example, a filter having lower and upper cutoff frequencies of f1 and f2 respectively, iscreated as follows:

>> % order 5, lower and upper cutoff at f1 and f2 relative to fs

>> [b_bpf, a_bpf] = butter(5, 2*[f1, f2]/fs);


7/29/2019 5625_project1

8/15

2.2 SSB Coherent Demodulator with Downsampling

Note that you must make sure that f1 and f2 are well between 0 and fs=2 Hz. Recall again that

from lowpass sampling theory, the usable bandwidth lies between 0 and fs=2 Hz. For a bandpass

filter to make sense in a DSP system, the passband must be well inside this frequency range. For

example, 1632 kHz with respect to a 96 kHz sampling rate makes sense.

2.1.2 Upsampling and Interpolation

The Weaver modulator requires that we implement a sampling rate change from fs1 D 8 kHz

to fs2 D 96 kHz. Without getting into the DSP math details, this requires the cascade of an

upsampler with L D 12 followed by a lowpass interpolation filter. The upsample function inserts

L 1 zero samples between every input sample, and the lowpass filter interpolates signal sample

values to replace the zero sample values inserted by the upsampler. The bandwidth of the lowpass

interpolation filter should be the bandwidth of the signal being upsampled, in this case about 4

kHz. The MATLAB function interp(x,L) automatically implements both operations (type

help interp for more information). The discussion thus far should allow the SSB modulator

function to be constructed.

2.2 SSB Coherent Demodulator with Downsampling

Coherent demodulation of SSB is described in [3]. A DSP implementation follows this exact ap-

proach. The transmitter carrier frequency is generated from knowledge of the sampling frequency,

so a coherent demodulation reference can be generated in like fashion. A real receiver would not

have this knowledge, but as mentioned earlier, might be able to take advantage of a pilot signal

from which to derive a demodulation carrier reference.One question you need to consider is whether or not you need to place a bandpass filter in

front of the coherent demodulator? Secondly, once the signal is demodulated, the sampling rate

can be reduced back to fs1 D 8 kHz. The DSP function used for sampling rate reduction is knownas a decimator. A decimator is composed of a lowpass filter in cascade with a downsampler.

Downsampling by the factor M keeps every Mth sample of the input sequence. The M1 samplesin between are discarded. Since downsampling reduces the effective sampling rate, and we knowthat the usable frequency band is always 0fs=2, the signal input to a downsampler must be strictlybandlimited to .fs=2/=M Hz to insure that aliasing does not occur. When a signal sampled atfs2 D 96 kHz is down sampled by M D 12 to fs1 D 8 kHz, the input signal to the decimator mustbe lowpass filtered down to a nominal bandwidth of no more than W D .96000=2=12/ D 4000 Hz.Recall that telephone grade audio only needs 3003300 Hz. Note that this is the same bandwidth

as required in the coherent demodulator, so the coherent demodulator and decimator can share

the same lowpass filter? The MATLAB function decimate() implements the functionality of thelowpass filter and downsampler in a single function call, i.e.,

>> M = 12; % sampling rate reduction factor

>> y = decimate(x,M);

The MATLAB default decimation lowpass filter is a Chebyshev design. To discover the exact

implementation details type help decimate.


7/29/2019 5625_project1

9/15

2.3 System Performance via Spectral Analysis

2.3 System Performance via Spectral Analysis

As you are building up your system it will be helpful to view signals in the frequency domain.

Since random signals are involved in the testing process, both the noise input the speech input, we

need to use the power spectral density (PSD) as opposed to just the Fourier transform of the signal.Recall that Chapter 2 of [3] introduced the PSD as a tool for spectral analysis of deterministic and

random signals. The MATLAB function simpleSA() estimates the power spectrum of a randomsignal (sequence). To demonstrate this function in action we will execute the full SSB transceiver

system using filtered noise as the message signals. The carrier frequencies have been chosen to be

20, 24, and 28 kHz. There are no guard bands between the channels with this configuration. An

in-class demonstration will demonstrate this configuration using the sample speech files available

in the project zip package. Figure 5 shows the PSD of bandlimited white noise entering the SSBmodulators. The sampling rate at this point is 8 ksps. Note that the bandpass shaping filter has

given the spectrum a passband running from 3003300 Hz as expected.

>> m_rec = SSB_transceiver([20000,24000,28000],noise,2);

49 x = xc2; % a breakpoint was set at line 49 in SSB_transceiver.m

K>> simpleSA(m2,2^10,fs,-60,5,b)K>> axis([0 4000 -60 5])

K>> title(PSD of Band Limited White Noise Input to SSB Modulator)

K>> print -tiff -depsc mess.eps

K>> simpleSA(xc2,2^10,L*fs,-80,20,b)

K>> axis([10000 40000 -80 20])

K>> title(PSD of the f_c1 SSB Modulator Output (fs = 96 ksps))

K>> print -tiff -depsc fc1.eps

K>> simpleSA(xc1+xc2+xc3,2^10,L*fs,-80,20,b)

K>> axis([10000 40000 -80 20])

K>> title(PSD of the Composite SSB Modulator Output (fs = 96 ksps))

K>> print -tiff -depsc fc123.eps

In Figure 6 we see the spectrum of the SSB signal at fc1 D 20 kHz. Notice that the spectrum

is far from perfect. The filters in the Weaver modulator, especially the upsampling operation from

8 ksps to 96 ksps, has introduced spectral images which are not completely removed by the default

interpolation filter of the function interp. The composite spectrum, as sent through the channel

is shown in Figure 7.

3 Project Tasks

1. Implement and test the SSB modulator function weaver using the function interface de-

scribed below. During normal operation, i.e., as exercised by SSB_transceiver, the inputsampling rate will be 8 ksps and the output sampling rate will be 96 ksps, i.e., L D 12.

function [y,fs2] = weaver(x,W,fc,fs,L,mode)

% [y,fs2] = weaver(x,W,fc,fs,L,mode)

%

%================== Inputs ======================

% x = Input message signal


7/29/2019 5625_project1

10/15

0 "00 #000 #"00 $000 $"00 3000 3"00 &000!'0

!"0

!&0

!30

!$0

!#0

0

()*+,*-./

012*)45*.6),738

9:-;6,9-

7/29/2019 5625_project1

11/15

! !"# $ $"# 3 3"# &

'(!0&

!*0

!+0

!,0

!#0

!&0

!30

!$0

!!0

0

!0

$0

-./1/24

567/.89/3:.1;(2?:1@/@B)

58D(6E(:F/(E!

(G($0(Hz(88B(&

7/29/2019 5625_project1

12/15

! !"# $ $"# 3 3"# &

'(!0&

!*0

!+0

!,0

!#0

!&0

!30

!$0

!!0

0

!0

$0

-./1/24

567/.89/3:.1;(2?:1@/@B)

58D(6E(:F/(G6;96H?:/(88B(

7/29/2019 5625_project1

13/15

Comment on any observed performance improvements obtained by including guard bands

between the carriers.

5. Returning once again to carrier frequencies at 20, 24, and 28 kHz, switch the modulator

inputs to the sample speech files provided in the zip package. With all three signals present at

the transmitter output (x = xc1 + xc2 + xc3), demodulate message signal m2n. Listento this signal using the PC sound system via sound(m_rec,8000).

(a) Listen carefully for any interference heard in the background of the desired message

signal. You may want to listen to all three speech files straight from the ZIP package

so that you know what they are supposed to sound like. Comment on what you hear.

(b) Calculate the SIR for demodulation of the center signal using the superposition tech-

nique of Task 3b.

6. Comment on your overall experience with this team project.

7. In addition to a project report, please package you completed simulation software into a ZIP

package and Email this package to me. I will be verifying your projects by listening to the

demodulated output of the speech files.

4 Appendix

The power spectral density of signals within the system model can be displayed using the supplied

function simpleSA.m. This function will work with either real or complex signals and has a

number of parameters to best plot signal power spectra. The function listing is given below:

function [Px,F] = simpleSA(x,N,fs,min_dB,max_dB,color)

% [Px,F] = simpleSA(x,N,fs,min_dB,max_dB,color)% Plot the estimated power spectrum of real and complex baseband signals

% using the toolbox function psd(). This replaces the use of psd().

%

% x = complex baseband data record, at least N samples in length

% N = FFT length

% fs = Sampling frequency in Hz

% min_dB = floor of spectral plot in dB

% max_dB = ceiling of spectral plot in dB

% color = line color and type as a string, e.g., r or r--

%

%////////// Optional output variables ///////////////////////////////////

% Px = power spectrum estimate values on two-sided frequency axis

% F = the corresponding frequency axis values

%

% Mark Wickert, October 2008

% while length(x) < N

% N = N/2;

% end

warning off


7/29/2019 5625_project1

14/15

if isreal(x)

[Px,F] = psd(x,N,fs);

else

[Px,F] = psd(x,[],[],N,fs);

N = fix(length(F)/2);

F = [F(end-N+1:end)-fs; F(1:N)];

Px = [Px(end-N+1:end); Px(1:N)];end

warning on

if nargout == 2

return

end

if nargin == 3 || nargin == 5,

plot(F,10*log10(Px))

else

plot(F,10*log10(Px),color)

end

if nargin >= 5

axis([F(1) F(end) min_dB max_dB]);

end

xlabel(Frequency (Hz))

ylabel(Power Spectrum in dB)

grid on

Let us consider a sinusoid in noise followed by a lowpass filter. The signal input to the filter is

xn D A cos.2f0=fs n/ C wn

where fs is the sampling frequency, f0 < fs=2, and wn is white Gaussian noise. We design an

Elliptical lowpass filter using the MATLAB function

[b,a] = ellip(5,R_pass_dB,R_stop_dB,2*fcutoff/fs):

A good starting value for N is 1024. This places 1024 points in the power spectrum estimate. For

the estimate of the true spectrum to free of estimation noise averaging is needed the total number of

signal samples input to the function needs to exceed N by a factor of 10 or so. A higher resolution

spectral estimate can be obtained by increasing N, but at the expense of increased estimation error,

unless of course the number of signals samples is increased accordingly.

>> n = 0:100000;

>> fs = 20000;

>> x = 2*cos(2*pi*4000/fs*n) + 0.1*randn(size(n));

>> [b,a] = ellip(5,0.1,60,2*5000/fs);

>> y = filter(b,a,x);

>> simpleSA(y,2 10,fs,-90,30,b);

>> print -tiff -depsc test_PSD.eps

The results are shown below in Figure 8. We clearly see a spectral line at 4000 Hz and then


7/29/2019 5625_project1

15/15

REFERENCES

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

80

60

40

20

0

20

Frequency (Hz)

PowerSpectrumi

ndB

Figure 8: Spectra of the composite SSB noise modulated carrier.

a noise background that has been shaped by the Elliptic lowpass filter. The noise level is at -20

dB due to the scale factor of 0.1 included in front of randn(). By default randn() produces unit

variance random numbers and scaling by 0.1 means the variance is reduced by 0:12

D 0:01. In dBthis is 10 log10.0:01/ D 20 dB.

References

[1] Donald K. Weaver, A Third Method of Generation and Detection of Single-Sideband Signals,

IRE Proceedings, 1956, pp. 1703-1705.

[2] Nico Palermo, A 9 MHz Digital SSB Modulator, available on the internet at

www.microtelecom.it/ssbdex/ssbdex-e.htm .

[3] R. Ziemer and W. Tranter, Principles of Communications, fifth edition, John Wiley, 2002.


5625_project1

Documents