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Need for I-Q modulator and demodulator

Posted by Krishna Pillai
April 5, 2008

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Some time back, a friend mentioned that he is yet to understand the need for having both in-phase (I) and quadrature-phase (Q) signals in typical wireless systems.

In this post, the attempt is to bring out the motivation for having I-Q modulation and present the block diagram of a simple I-Q modulator (and demodulator).

I am using the text provided in Sec 5.2.1 of [DIG-COMM-BARRY-LEE-MESSERSCHMITT] as reference.

Baseband PAM transmission

Consider a simple baseband transmission where the information is sent by modulating a pulse. This can be represented as

, where

is the symbol period,

is the symbol to transmit,

is the transmit filter,

is thesymbol index and

is the output waveform.

Pictorially the same can be represented as,

transmission of baseband PAM signal

Figure: Baseband PAM transmission (Refer: Figure 5.1 [DIG-COMM-BARRY-LEE-MESSERSCHMITT]]

To transmit undistorted through the channel, the minimum bandwidth required is half the symbol rate (per the Nyquist criterion).

Spectrum of baseband PAM

Figure: Minimum bandwidth required for transmitting baseband PAM with symbol rate

Assuming that there are alphabets in , the spectral efficiency for basedband PAM is,

bits/second/Hertz.

BB-PAM : Baseband PAM

Passband PAM transmission

Now, consider that the baseband PAM signal is upconverted to a carrier frequency by multiplication by a carrier, i.e.

.

The spectrum of the passband PAM is as shown below,

spectrum of passband PAM

Figure: Spectrum of passband PAM

To avoid transmit undistorted through the channel, we require a passband filter having bandwidth .

Assuming that there are alphabets in , the spectral efficiency for passband PAM is,

bits/second/Hertz.

PB-PAM : PassBand PAM

Can see that spectral efficiency of passband PAM is half of baseband PAM.

Note:

Passband PAM is composed of real signals and real signals have symmetric spectra. So, half the bandwidth is not carrying any ‘extra’ information.

Moving to passband QAM

It is known that if a sine wave and a cosine wave is periodic over time , then they are orthogonal i.e.
.

Given so, a popular way which people came across to improve the efficiency of the passband PAM is to send information on the sine wave also in parallel, i.e.

.

This forms the passband QAM modulation. This signal requires the same bandwidth as passband PAM, however carries twice the informtion. For notational convineance, the above signal can be represented mathematically as,

, where

and

.

This forms the I-Q modulator circuit. :)

IQ modulator

Figure: IQ modulator

The IQ demodulator can be visualized as shown in the figure below

IQ demodulator

Figure: IQ demodulator

On the combined signal, downconvert the cosine (inphase, I) and the sine (quadrature Q) arms, then proceed to do independent demodulation on each arm.

Summarizing,

(a) It is the need for improved spectral efficiency that resulted in I-Q modulation (and de-modulation).

(b) Another approach for improving the spectral efficiency of passband PAM is to filter away half the bandwidth (which is not carrying any ‘extra’ information). This is called Single Sideband Modulation (SSB).

Anyhow, it seems that using I-Q modulation is simpler to implement than circuit for filtering away half the spectrum. So, I-Q modulation stays. :)

Reference

[DIG-COMM-BARRY-LEE-MESSERSCHMITT] Digital Communication: Third Edition, by John R. Barry, Edward A. Lee, David G. Messerschmitt

Thanks,
Krishna

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    • Comments
    Comment by Jhony on April 18, 2008 @ 8:09 pm

    Hi,
    I have been reading your topics they are very good and helping me alot. I request you not to stop this good work. I am new to this field so i might ask you alot of foolish questions bt thts how i will learn… in the above derviation can you please tell me what this ‘R’ symbol (in the equation very after this line …notational convineance, the above signal can be represented mathematically as,) means? why are we using it? I didnt understand it please explain thanking in advance…
    tc

    Comment by Krishna on April 18, 2008 @ 8:39 pm

    @ Johny: Thanks. Ofcourse, you can shoot in your queries. I will try answer to the best of my knowledge.
    The symbol R stands for real, which means the output takes only the real part of s(t) e^{j2*pi*f_c*t).
    Helps?

    Krishna

    Comment by jhony on April 20, 2008 @ 1:14 am

    Hi
    thanks… but why do we want to consider only the real part?
    thankyou very much for your reply please clear this query. I shall be very thank to you …

    Comment by Krishna on April 20, 2008 @ 7:05 am

    @johny:
    What we want to transmit is
    s(t) = aI cos(2*pi*f_ct) - aQsin(2*pi*f_ct)

    It is reasonably intuitive to see that above equation is equal to
    real part of (aI + jaQ)*(cos(2*pi*f_c*t) + j*sin(2*pi*f_c*t)). Do you agree?

    Comment by jhony on April 20, 2008 @ 10:27 pm

    Hi
    yeah thank you very much now its clear… i hope u dont get disturbed by my questions but i really want to clear things up

    Comment by Krishna on April 21, 2008 @ 7:46 am

    @Johny: No worries. I typically do not get disturbed by questions. :)

    Comment by Yahia on April 21, 2008 @ 10:44 pm

    Great job! this website is very impressive. I am working on digital commincations for SDR and I have added this website to my top favorites. Keep it up and thank you for all your efforts.

    Comment by Krishna on April 22, 2008 @ 7:45 am

    @Yahia: Thanks. :)
    Do you have a website where information about your work is presented? I would be keen to have a look and get a feel about the work on SDR.

    Comment by Yahia on April 22, 2008 @ 8:51 am

    Unfortunately not Krishna :(

    My work on SDR is part of my research for PhD. But I will be happy to share my work with you. I am using an SDR platform from Lyrtech. At any case I will be happy to discuss any issue about SDR with you. There is a coming standard called 802.22 which will be a cognitive radio based standard. If you are interested, we can exchange ideas and information about these topics.
    Thank you for your interest and for answering my questions

    Comment by Krishna on April 23, 2008 @ 4:45 am

    @Yahia: Yes, it would be interesting to share thoughts.
    Quick q: When we say SDR, is it
    (a) the RF center frequency which is getting dynamically programmed ?
    (b) the baseband processing adapting to various modulation schemes?
    OR is it the SDR concept too vast to encapsulate in the above bullets?

    Comment by Yahia on April 23, 2008 @ 6:17 am

    Here are two definitions of SDR:
    1- a radio that is substantially defined in software and whose physical layer behavior can be significantly altered through changes to its software
    2- The software radio is a radio which employs one wideband analog to digital converter (ADC) with a resource of programmable digital signal processors (DSPs) to service an entire spectrum allocation in a single integrated module

    Now the first one is taken from Jifferey Reed book of Software Radio which I recommend for interested readers. it is titled “Software Radio: A Modern Approach to Radio Engineering ”

    To make it clear, SDR is a configurable wireless platform that can change its personality using software “channel frequency, modulation, data rate, transmission power and many others”

    Now the ability to sense and “make decisions” to change personality to an appropriate format is called cognitive radio. So in simple words, cognitive radio =SDR+intellegence
    I have the following link that has a nice collection of links about SDR:

    http://www-sop.inria.fr/planete/SoftwareRadio/

    Comment by Krishna on April 23, 2008 @ 7:44 am

    @Yahia. Thanks for the information.
    I just happened to see an SDR Overview article in DSPDesignline.com
    http://www.dspdesignline.com/207401351?cid=RSSfeed_dspdesignline_dspdlRSS

    Comment by Yahia on April 24, 2008 @ 5:16 am

    Nice link Krishna. You can see that the book I have recommended is being cited in a number of articles in this link. But as you can concluse from these articles, SDR is about building a configurable transceiver using software.

    Thanks again for the link.

    Comment by Didi on May 17, 2008 @ 4:46 am

    I’m using GNURADIO plattaform to implement SDR for OFDM transceiver.

    http://www.gnu.org/software/gnuradio/

    Comment by Krishna Pillai on May 17, 2008 @ 4:00 pm

    @Didi: Thanks for the link :)

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