# Channel equalization for MSK

Started by March 11, 2004
```Hello,

I am trying to set up an adaptive LMS adaptive equalizer to apply the
equalizer on a phase modulated signal eg: MSK.
For modulation schemes such as PSK/QAM, the effect of a channel filter
leads to severe ISI and hence channel equalizers are very important.
Further, they have been extensively documented and well-studied.

How severe is the effect of a channel filter on a MSK type signal?

Representing an MSK signal as:

inf
s(t)=exp{-j*pi/2*Integral{sum    [a(i)*g(t-i*T)]}
i=0

where a(i) belongs to {-1,+1} and the support of g(t) lies in [0,T].
If for convenience, we choose g(t)=1/T, then the phase of s(t) changes
by pi/2 or -pi/2 per symbol interval. So, the information is in the
signal phase.

If such a signal is passed through a channel with a FIR impulse
response limited to N taps, the effect of the channel is to add DC
noise effectively to the information part of the signal. The reason
being that arg(z1*z2)=arg(z1)+arg(z2), for any two complex numbers z1
and z2. This makes me wonder, if the effect of FIR channels on MSK is
as severe as it would be on a QAM-type signal.

How does this translate to attempting to equalize an MSK type signal.
To put it in another way, is there a need to equalize such signals
since the information is in the signal phase.

Vikram
```
```cvikram@mac.com (Vikram Chandrasekhar) wrote in message news:<f43924b.0403102017.1648ecd@posting.google.com>...
> Hello,
>
> I am trying to set up an adaptive LMS adaptive equalizer to apply the
> equalizer on a phase modulated signal eg: MSK.
> For modulation schemes such as PSK/QAM, the effect of a channel filter
> leads to severe ISI and hence channel equalizers are very important.
> Further, they have been extensively documented and well-studied.
>
> How severe is the effect of a channel filter on a MSK type signal?
>
> Representing an MSK signal as:
>
>                                         inf
> s(t)=exp{-j*pi/2*Integral{sum    [a(i)*g(t-i*T)]}
>                                        i=0
>
> where a(i) belongs to {-1,+1} and the support of g(t) lies in [0,T].
> If for convenience, we choose g(t)=1/T, then the phase of s(t) changes
> by pi/2 or -pi/2 per symbol interval. So, the information is in the
> signal phase.
>
> If such a signal is passed through a channel with a FIR impulse
> response limited to N taps, the effect of the channel is to add DC
> noise effectively to the information part of the signal. The reason
> being that arg(z1*z2)=arg(z1)+arg(z2), for any two complex numbers z1
> and z2. This makes me wonder, if the effect of FIR channels on MSK is
> as severe as it would be on a QAM-type signal.

MSK Signals can also be thought of as QAM-type signal. In classical
QAM you would mutliply the I and Q parts of the constellation by
quadrature carriers whereas in MSK, the phase of the constellation
points is continuosly varying. Look at Digital Communications, Proakis
for a very good theoretical treatment of MSK.

So a FIR channel would also affect the MSK signal as it does a QAM
signal. Even in case of QAM signal, the channel does spoil both the
amplitude information as well as phase information. The severity of
the effect can be evaluated from the BER functions.

> How does this translate to attempting to equalize an MSK type signal.
> To put it in another way, is there a need to equalize such signals
> since the information is in the signal phase.

Equalization is usually a must if you want to build a reliable system.
Some systems like which use CDMA signals do away with equalization,
but then they don't use MSK modulation. 2G/GSM uses Gaussian MSK and
equalization used is Maximum Likelihood Sequence Estimation (again

HTH,
Sachin
```
```scngupta@yahoo.com (Sachin Gupta) wrote in message news:<d2308724.0403112057.397202f1@posting.google.com>...
> cvikram@mac.com (Vikram Chandrasekhar) wrote in message news:<f43924b.0403102017.1648ecd@posting.google.com>...
> > Hello,
> >
> > I am trying to set up an adaptive LMS adaptive equalizer to apply the
> > equalizer on a phase modulated signal eg: MSK.
> > For modulation schemes such as PSK/QAM, the effect of a channel filter
> > leads to severe ISI and hence channel equalizers are very important.
> > Further, they have been extensively documented and well-studied.
> >
> > How severe is the effect of a channel filter on a MSK type signal?

2)CIR of propagation media 3) receive filter?  For e.g QPSK modulation
scheme uses Root raised cosine filters at both ends(transmit and
receive)and mitigates some ISI. The propagation media in the form
multipath fading gives rise to severe ISI also. So in addition, both
MSK and PSK systems have to compensate this media ISI. Standard
procedure for GSM system(2G) uses GMSK(Gaussian filter at the transmit
front end) modulation for channel like Speech/CSD/RACH/CS1-CS4 etc.
and Viterbi equalizer is the standard equalizer. For EDGE system(2.5G)
uses 8PSK modulation for channels like MCS5-9 - equalizer normally
used is based on Maxlog MAP. I assume your channel estimation is based
on training sequence(Preamble) information available in received
signal.

I wonder why do you go for adaptive LMS equalizer - is there a
specific purpose?

Santosh

> >
> > Representing an MSK signal as:
> >
> >                                         inf
> > s(t)=exp{-j*pi/2*Integral{sum    [a(i)*g(t-i*T)]}
> >                                        i=0
> >
> > where a(i) belongs to {-1,+1} and the support of g(t) lies in [0,T].
> > If for convenience, we choose g(t)=1/T, then the phase of s(t) changes
> > by pi/2 or -pi/2 per symbol interval. So, the information is in the
> > signal phase.
> >
> > If such a signal is passed through a channel with a FIR impulse
> > response limited to N taps, the effect of the channel is to add DC
> > noise effectively to the information part of the signal. The reason
> > being that arg(z1*z2)=arg(z1)+arg(z2), for any two complex numbers z1
> > and z2. This makes me wonder, if the effect of FIR channels on MSK is
> > as severe as it would be on a QAM-type signal.
>
> MSK Signals can also be thought of as QAM-type signal. In classical
> QAM you would mutliply the I and Q parts of the constellation by
> quadrature carriers whereas in MSK, the phase of the constellation
> points is continuosly varying. Look at Digital Communications, Proakis
> for a very good theoretical treatment of MSK.
>
> So a FIR channel would also affect the MSK signal as it does a QAM
> signal. Even in case of QAM signal, the channel does spoil both the
> amplitude information as well as phase information. The severity of
> the effect can be evaluated from the BER functions.
>
> > How does this translate to attempting to equalize an MSK type signal.
> > To put it in another way, is there a need to equalize such signals
> > since the information is in the signal phase.
>
> Equalization is usually a must if you want to build a reliable system.
> Some systems like which use CDMA signals do away with equalization,
> but then they don't use MSK modulation. 2G/GSM uses Gaussian MSK and
> equalization used is Maximum Likelihood Sequence Estimation (again
>
> HTH,
> Sachin
```
```Hello Santosh and Sachin

My question is addressed more from the theoretical standpoint. I am
not really concerned by the fact that GSM/EDGE etc use Viterbi based
equalizer. I do know that they are the ML technique for MSK detection.
But they are not the <only> way to equalize the MSK signal. Instead, I
wish to understand the practical points that need to be considered
while equalizing the MSK signal using adaptive algorithms[from my
experiences so far.]

Here is my point:

The derivative of phase of the MSK signal is essentially a BPSK type
signal
[i.e sigma{a(i)*g(t-i*T)}]. I am using Gaussian filters/no filtering
for transmit and receive filters. This is matched-filtered, and
decimated down to symbol rate. Thereon, The receiver can *in theory *
receive a training sequence, adapt the LMS taps to track the symbol
spaced phase derivative of the MSK signal and allow the taps to
converge. Therefore, it can be done in theory to the signal phase.
Once the taps converge, the equalizer output can be used to generate
hard symbol decisions.

Vikram

santosh.nath@ntlworld.com (santosh nath) wrote in message news:<6afd943a.0403121128.7dccea96@posting.google.com>...
> scngupta@yahoo.com (Sachin Gupta) wrote in message news:<d2308724.0403112057.397202f1@posting.google.com>...
> > cvikram@mac.com (Vikram Chandrasekhar) wrote in message news:<f43924b.0403102017.1648ecd@posting.google.com>...
> > > Hello,
> > >
> > > I am trying to set up an adaptive LMS adaptive equalizer to apply the
> > > equalizer on a phase modulated signal eg: MSK.
> > > For modulation schemes such as PSK/QAM, the effect of a channel filter
> > > leads to severe ISI and hence channel equalizers are very important.
> > > Further, they have been extensively documented and well-studied.
> > >
> > > How severe is the effect of a channel filter on a MSK type signal?
>
> 2)CIR of propagation media 3) receive filter?  For e.g QPSK modulation
> scheme uses Root raised cosine filters at both ends(transmit and
> receive)and mitigates some ISI. The propagation media in the form
> multipath fading gives rise to severe ISI also. So in addition, both
> MSK and PSK systems have to compensate this media ISI. Standard
> procedure for GSM system(2G) uses GMSK(Gaussian filter at the transmit
> front end) modulation for channel like Speech/CSD/RACH/CS1-CS4 etc.
> and Viterbi equalizer is the standard equalizer. For EDGE system(2.5G)
> uses 8PSK modulation for channels like MCS5-9 - equalizer normally
> used is based on Maxlog MAP. I assume your channel estimation is based
> on training sequence(Preamble) information available in received
> signal.
>
> I wonder why do you go for adaptive LMS equalizer - is there a
> specific purpose?
>
> Santosh
>
>
> > >
> > > Representing an MSK signal as:
> > >
> > >                                         inf
> > > s(t)=exp{-j*pi/2*Integral{sum    [a(i)*g(t-i*T)]}
> > >                                        i=0
> > >
> > > where a(i) belongs to {-1,+1} and the support of g(t) lies in [0,T].
> > > If for convenience, we choose g(t)=1/T, then the phase of s(t) changes
> > > by pi/2 or -pi/2 per symbol interval. So, the information is in the
> > > signal phase.
> > >
> > > If such a signal is passed through a channel with a FIR impulse
> > > response limited to N taps, the effect of the channel is to add DC
> > > noise effectively to the information part of the signal. The reason
> > > being that arg(z1*z2)=arg(z1)+arg(z2), for any two complex numbers z1
> > > and z2. This makes me wonder, if the effect of FIR channels on MSK is
> > > as severe as it would be on a QAM-type signal.
> >
> > MSK Signals can also be thought of as QAM-type signal. In classical
> > QAM you would mutliply the I and Q parts of the constellation by
> > quadrature carriers whereas in MSK, the phase of the constellation
> > points is continuosly varying. Look at Digital Communications, Proakis
> > for a very good theoretical treatment of MSK.
> >
> > So a FIR channel would also affect the MSK signal as it does a QAM
> > signal. Even in case of QAM signal, the channel does spoil both the
> > amplitude information as well as phase information. The severity of
> > the effect can be evaluated from the BER functions.
> >
> > > How does this translate to attempting to equalize an MSK type signal.
> > > To put it in another way, is there a need to equalize such signals
> > > since the information is in the signal phase.
> >
> > Equalization is usually a must if you want to build a reliable system.
> > Some systems like which use CDMA signals do away with equalization,
> > but then they don't use MSK modulation. 2G/GSM uses Gaussian MSK and
> > equalization used is Maximum Likelihood Sequence Estimation (again
> >
> > HTH,
> > Sachin
```
```cvikram@mac.com (Vikram Chandrasekhar) wrote in message news:<f43924b.0403121535.345e4322@posting.google.com>...
> Hello Santosh and Sachin
>
> My question is addressed more from the theoretical standpoint. I am
> not really concerned by the fact that GSM/EDGE etc use Viterbi based
> equalizer. I do know that they are the ML technique for MSK detection.
> But they are not the <only> way to equalize the MSK signal. Instead, I
> wish to understand the practical points that need to be considered
> while equalizing the MSK signal using adaptive algorithms[from my
> experiences so far.]

I am lost here - what significant benifit you get using adaptive
algorithm like LMS. You have mentined your signal is training sequence
driven and hence we know that channel estimation will be known before
kernel equalization. I only see the benifit of adaptation if your
channel is time varying to large extent - but is it the case for you ?
>
> Here is my point:
>
> The derivative of phase of the MSK signal is essentially a BPSK type
> signal
> [i.e sigma{a(i)*g(t-i*T)}].

Let me make some statement here. MSK is a nonlinear modulation but in
actual system we make linear appoximation  of its phase function to
simplify equalization,
phi(t) = sigma(s(k)*j^k*c0(t-k*T)
where s(k) is information bits which is differentially encoded.j^k
represents
phase rotation by phi/2 per symbol,j=squareroot(-1). c0(t) is the main
pulse derived from the nonlinear function q(t)representing actual
phase function before appoximation.
Passband signal, x(t)=const*cos(2*phi*f0 +phi(t)+w0), w0 is random
phase and can be taken constant over a burst.

BPSK signal is linear modulated.  I would like to know the definition
of the function g(t-i*T). May be - you can highlight more details of
" The derivative of phase of the MSK signal is essentially a BPSK type
signal". Later in your article you strongly highlight usage of phase
derivative for LMS convergence - I guess it will help us understanding

I am using Gaussian filters/no filtering
> for transmit and receive filters. This is matched-filtered, and
> decimated down to symbol rate. Thereon, The receiver can *in theory *
> receive a training sequence, adapt the LMS taps to track the symbol
> spaced phase derivative of the MSK signal and allow the taps to
> converge. Therefore, it can be done in theory to the signal phase.
> Once the taps converge, the equalizer output can be used to generate
> hard symbol decisions.

I am not very sure about the reliability of these hard decisions.
Question comes how intelligent your slicer is. Normally Equalizer
provides soft decision to channel decoder which helps Viterbi decoder
to make final hard decisions.

Other questions come for LMS Tap adaptation
1. No of LMS taps
2. No of iterations for convergence
3. Robustness against rapid channel variation
4. Step size control mechanism

Santosh

>
>
> Vikram
>
>
> santosh.nath@ntlworld.com (santosh nath) wrote in message news:<6afd943a.0403121128.7dccea96@posting.google.com>...
> > scngupta@yahoo.com (Sachin Gupta) wrote in message news:<d2308724.0403112057.397202f1@posting.google.com>...
> > > cvikram@mac.com (Vikram Chandrasekhar) wrote in message news:<f43924b.0403102017.1648ecd@posting.google.com>...
> > > > Hello,
> > > >
> > > > I am trying to set up an adaptive LMS adaptive equalizer to apply the
> > > > equalizer on a phase modulated signal eg: MSK.
> > > > For modulation schemes such as PSK/QAM, the effect of a channel filter
> > > > leads to severe ISI and hence channel equalizers are very important.
> > > > Further, they have been extensively documented and well-studied.
> > > >
> > > > How severe is the effect of a channel filter on a MSK type signal?
> >
> > Does your channel filter consider cascading of 1) transmit filter
> > 2)CIR of propagation media 3) receive filter?  For e.g QPSK modulation
> > scheme uses Root raised cosine filters at both ends(transmit and
> > receive)and mitigates some ISI. The propagation media in the form
> > multipath fading gives rise to severe ISI also. So in addition, both
> > MSK and PSK systems have to compensate this media ISI. Standard
> > procedure for GSM system(2G) uses GMSK(Gaussian filter at the transmit
> > front end) modulation for channel like Speech/CSD/RACH/CS1-CS4 etc.
> > and Viterbi equalizer is the standard equalizer. For EDGE system(2.5G)
> > uses 8PSK modulation for channels like MCS5-9 - equalizer normally
> > used is based on Maxlog MAP. I assume your channel estimation is based
> > on training sequence(Preamble) information available in received
> > signal.
> >
> > I wonder why do you go for adaptive LMS equalizer - is there a
> > specific purpose?
> >
> > Santosh
> >
> >
> > > >
> > > > Representing an MSK signal as:
> > > >
> > > >                                         inf
> > > > s(t)=exp{-j*pi/2*Integral{sum    [a(i)*g(t-i*T)]}
> > > >                                        i=0
> > > >
> > > > where a(i) belongs to {-1,+1} and the support of g(t) lies in [0,T].
> > > > If for convenience, we choose g(t)=1/T, then the phase of s(t) changes
> > > > by pi/2 or -pi/2 per symbol interval. So, the information is in the
> > > > signal phase.
> > > >
> > > > If such a signal is passed through a channel with a FIR impulse
> > > > response limited to N taps, the effect of the channel is to add DC
> > > > noise effectively to the information part of the signal. The reason
> > > > being that arg(z1*z2)=arg(z1)+arg(z2), for any two complex numbers z1
> > > > and z2. This makes me wonder, if the effect of FIR channels on MSK is
> > > > as severe as it would be on a QAM-type signal.
> > >
> > > MSK Signals can also be thought of as QAM-type signal. In classical
> > > QAM you would mutliply the I and Q parts of the constellation by
> > > quadrature carriers whereas in MSK, the phase of the constellation
> > > points is continuosly varying. Look at Digital Communications, Proakis
> > > for a very good theoretical treatment of MSK.
> > >
> > > So a FIR channel would also affect the MSK signal as it does a QAM
> > > signal. Even in case of QAM signal, the channel does spoil both the
> > > amplitude information as well as phase information. The severity of
> > > the effect can be evaluated from the BER functions.
> > >
> > > > How does this translate to attempting to equalize an MSK type signal.
> > > > To put it in another way, is there a need to equalize such signals
> > > > since the information is in the signal phase.
> > >
> > > Equalization is usually a must if you want to build a reliable system.
> > > Some systems like which use CDMA signals do away with equalization,
> > > but then they don't use MSK modulation. 2G/GSM uses Gaussian MSK and
> > > equalization used is Maximum Likelihood Sequence Estimation (again