# Questions about QR-RLS algorithm and antenna beamforming

Started by January 6, 2004
```Hi,
I want to simulate an adaptive beamforming algorithm (using QR-RLS).
From what I learned, I have the following thoughts and questions.
Because I am not sure whether they are right or not (and the question
From &#2013266091;Adaptive Filter Theory&#2013266107; of Simon Haykin, 4th edition, Page 115,
"The essence of a Wiener filter is that it minimizes the mean-square
value of an estimation error, defined as the difference between a
desired response and the actual filter out." The LS based algorithms
are optimized in the least square sense (?). QR-RLS is one of LS
algorithm, which has some adavantage in structure, accuracy,
convergent speed, etc..
From some of the papers of QR-RLS I read, they are evaluated in a
situation of known direction of the desired signal and the
interferences. QR-RLS algorithm can adaptively suppress the
interference signals at the same time enforce the desired signals from
different antennas. The reference signal for the QR-RLS is the pilot
PN binary sequences, i.e., in the time domain. I want to do a similar
simulation with the desired and interference signals known their
directions (There are 4 antennas to receive these signals). My
question is: how can I design the signal source model with the
intended directions? I have been thinking for quite a while. Could you
help me?

Any suggestion is highly appreciated.
```
```"Jeff" <freelait2000@yahoo.com> wrote in message
> Hi,
> I want to simulate an adaptive beamforming algorithm (using QR-RLS).
> From what I learned, I have the following thoughts and questions.
> Because I am not sure whether they are right or not (and the question
> is still unsolved), I want to get your answer to these.
> From &#2013266091;Adaptive Filter Theory&#2013266107; of Simon Haykin, 4th edition, Page 115,
> "The essence of a Wiener filter is that it minimizes the mean-square
> value of an estimation error, defined as the difference between a
> desired response and the actual filter out." The LS based algorithms
> are optimized in the least square sense (?). QR-RLS is one of LS
> algorithm, which has some adavantage in structure, accuracy,
> convergent speed, etc..
> From some of the papers of QR-RLS I read, they are evaluated in a
> situation of known direction of the desired signal and the
> interferences. QR-RLS algorithm can adaptively suppress the
> interference signals at the same time enforce the desired signals from
> different antennas. The reference signal for the QR-RLS is the pilot
> PN binary sequences, i.e., in the time domain. I want to do a similar
> simulation with the desired and interference signals known their
> directions (There are 4 antennas to receive these signals). My
> question is: how can I design the signal source model with the
> intended directions? I have been thinking for quite a while. Could you
> help me?

If you already know the directions then the problem is deterministic and you
can design an optimum array weighting to zero out the interfering sources -
as long as there aren't too many of them.  In this case, you appear to have
amplitude and phase that can be adjusted for each antenna, is that right?
I'd look for papers that adjust complex coefficients (i.e. amplitude and
phase) to get optimum array patterns.

The adaptive algorithms are good for situations where you don't know the
direction of the interfering sources.

Fred

```
```Fred Marshall wrote:
> "Jeff" <freelait2000@yahoo.com> wrote in message
>
>>Hi,
>>I want to simulate an adaptive beamforming algorithm (using QR-RLS).
>>From what I learned, I have the following thoughts and questions.
>>Because I am not sure whether they are right or not (and the question
>>From &#2013266091;Adaptive Filter Theory&#2013266107; of Simon Haykin, 4th edition, Page 115,
>>"The essence of a Wiener filter is that it minimizes the mean-square
>>value of an estimation error, defined as the difference between a
>>desired response and the actual filter out." The LS based algorithms
>>are optimized in the least square sense (?). QR-RLS is one of LS
>>algorithm, which has some adavantage in structure, accuracy,
>>convergent speed, etc..
>>From some of the papers of QR-RLS I read, they are evaluated in a
>>situation of known direction of the desired signal and the
>>interferences. QR-RLS algorithm can adaptively suppress the
>>interference signals at the same time enforce the desired signals from
>>different antennas. The reference signal for the QR-RLS is the pilot
>>PN binary sequences, i.e., in the time domain. I want to do a similar
>>simulation with the desired and interference signals known their
>>directions (There are 4 antennas to receive these signals). My
>>question is: how can I design the signal source model with the
>>intended directions? I have been thinking for quite a while. Could you
>>help me?
>
>
> If you already know the directions then the problem is deterministic and you
> can design an optimum array weighting to zero out the interfering sources -
> as long as there aren't too many of them.  In this case, you appear to have
> amplitude and phase that can be adjusted for each antenna, is that right?
> I'd look for papers that adjust complex coefficients (i.e. amplitude and
> phase) to get optimum array patterns.
>
> The adaptive algorithms are good for situations where you don't know the
> direction of the interfering sources.

But they suck if you don't know the directions of the desired signals.
>
> Fred
>
>

```
```"Stan Pawlukiewicz" <stanp@nospam_mitre.org> wrote in message
news:btet0l\$eid\$1@newslocal.mitre.org...
> Fred Marshall wrote:
> > "Jeff" <freelait2000@yahoo.com> wrote in message
> >
> >>Hi,
> >>I want to simulate an adaptive beamforming algorithm (using QR-RLS).
> >>From what I learned, I have the following thoughts and questions.
> >>Because I am not sure whether they are right or not (and the question
> >>is still unsolved), I want to get your answer to these.
> >>From &#2013266091;Adaptive Filter Theory&#2013266107; of Simon Haykin, 4th edition, Page 115,
> >>"The essence of a Wiener filter is that it minimizes the mean-square
> >>value of an estimation error, defined as the difference between a
> >>desired response and the actual filter out." The LS based algorithms
> >>are optimized in the least square sense (?). QR-RLS is one of LS
> >>algorithm, which has some adavantage in structure, accuracy,
> >>convergent speed, etc..
> >>From some of the papers of QR-RLS I read, they are evaluated in a
> >>situation of known direction of the desired signal and the
> >>interferences. QR-RLS algorithm can adaptively suppress the
> >>interference signals at the same time enforce the desired signals from
> >>different antennas. The reference signal for the QR-RLS is the pilot
> >>PN binary sequences, i.e., in the time domain. I want to do a similar
> >>simulation with the desired and interference signals known their
> >>directions (There are 4 antennas to receive these signals). My
> >>question is: how can I design the signal source model with the
> >>intended directions? I have been thinking for quite a while. Could you
> >>help me?
> >
> >
> > If you already know the directions then the problem is deterministic and
you
> > can design an optimum array weighting to zero out the interfering
sources -
> > as long as there aren't too many of them.  In this case, you appear to
have
> > amplitude and phase that can be adjusted for each antenna, is that
right?
> > I'd look for papers that adjust complex coefficients (i.e. amplitude and
> > phase) to get optimum array patterns.
> >
> > The adaptive algorithms are good for situations where you don't know the
> > direction of the interfering sources.
>
> But they suck if you don't know the directions of the desired signals.

Good point Stan.  That was an unstated assumption.  I guess if the antenna
array is always physically aimed (rotated) at the desired source always then
this is a contraint on the main lobe as is often the case.

Fred

```