As we know we can make use of adaptive technology  in MIMO
multiplexing when
we know the full CSI. we also can switch between SM and SD in MIMO
according the decemal condition number. All these adaptive are in
Uncorrelated channel condition ,But anyone can tell me how to swich
between Correlate and uncorrelated? Since channle are varying with
time.How can we qurratee the handset are always in the rich
scatterring ebvironment.Assume LOS appears in MIMO. More correlation
will come up.How to adapt it?

y...@sina.com (Yan Zhi Jie) wrote in message news:<8...@posting.google.com>...

> But anyone can tell me how to swich
> between Correlate and uncorrelated?

It is much simpler than switching between SM and SD 
except we have a additional possibility to consider
the beamforming gain at the trasmitter.

In uncorrelated case, we exploit the instananeous 
correlation channel matrix R(k) = H(k)*H(k)' to switch SM and SD,
where H(k) is MIMO channel matrix at time k. As you said,
we find out the condition value from the eigen vaules of R
and the condition value is used to decide whether SM
or SD is appropriate. 

Very simply, we exploit instead the moving average value of R to 
switch the operation for between correlated and uncorrelated 
in correlated senarios. The optimal window size 
for the moving average filter is designed in terms of 
the channel coherence times. Note that the duration T for windowing
should be larger than the fast fading duration but smaller 
than longterm fading duration.  Assume R_LT = sum(R, l=k-K/2..k+K/2),
the moving average value of R. Then, the number of the SM stream 
is upper bounded by the rank of R_LT, since 
the average channel matrix H has no more rank than the rank of R_LT.
Thus, we can detect the status of the correlation of the 
MIMO system by using R_LT.

Futhermore, we can apply the beamforming to the case where 
the signals among the transmitter antennas are correlated each
other. Since the average rank is reduced by correlation, the
diversity gain is reduced but suprizingly the beamforming is to be
easier implemantable by a kind of feedback solution. 
The long term channel is changed slowly as its difinition shows 
so that the feedback solutions are more practically implementable
than the uncorrelated case.

In short, I noticed three points for the corrlated case of MIMO:
the difference between the short term and the long term MIMO channel as
well as how to define the longterm channel information, the 
criterion using for switching between correlated and uncorrelated, 
and finally, the beamforming gain in terms of the correlated channel
information. 

-- 
Best regards,
James K. (t...@hotmail.com)
- Private opinions: These are not the opinions from my affiliation.

"Yan Zhi Jie" <y...@sina.com> wrote in message
news:8...@posting.google.com...

I'd like to introduce two different point of views
when we are considering such SM and SD in MIMO systems
as in your question.

> We also can switch between SM [Multiplexing] and SD [Diversity] in MIMO
> according the [Demmel] condition number.

  First, one of those views [1] is regarding to
the Demmel condition number of MIMO channel matrix.
In there, it is interesting that SM is better method for MIMO
channel that has low Demmel condition number and
necessarily SD is better method otherwise. Thus,
feedback signaling to switch between them is proposed.

  Another view [2] is that SD and SM are considered
to have fundamental trade-off. For example, SISO(1x1) system
has trade-off relationship as

  SD = 1 - SM.

Furthermore, 2x2 MIMO system has

  SD = (1-SM1) + 3*(1-SM2), such that
  SM = SM1 + SM2,

where 0<=SM1<=SM2<=1. In this case, it emphasis that
the data transmission with lower rate (SM --> 0) provides
fundamentally more diversity order (SD --> 2x2=4).

In short, I told that we have two different views
regarding to SM and SD: 1) the idea of swathing by feedback signaling
2) the concept about the fundamental trade-off between twos.

[1] Robert W. Heath Jr and Arogyaswami J. Paulraj, Diversity Versus
Multiplexing in Narrowband MIMO Channels: A Tradeoff Based on Euclidean
Distance, Submitted to IEEE Transactions on Communications April 2001,
revised December 2002.
(http://www.ece.utexas.edu/~rheath/papers/2001/muxdiv/paper.pdf)

[2] L. Zheng and D. Tse, ``Diversity and Multiplexing: A Fundamental
Tradeoff in Multiple Antenna Channels'', IEEE Transactions on Information
Theory, vol. 49(5), May 2003.
(http://www.eecs.berkeley.edu/~dtse/tradeoff.pdf)

-- 
Best regards,
James K. (t...@hotmail.com)
- Any remarks, proposal and/or indicator to text would be greatly respected.
- Private opinions: These are not the opinions from my affiliation.