FPGA Central

My simple question is that whether or not the capacity of MU-MISO is
better than the capacity of SU-MIMO conditioning on the same
configuration as that in MU-MISO.

In my analysis, the answer is obviously *NO*. To support my answer, I
provide the analysis results of two cases in terms of outage capacity
on [1]. Assume that in the considering system we have one transmitter
and several different configurations of receivers such as 1 receiver
with 4 antennas, 4 receivers with 1 antenna for each, and 2 receivers
each with 2 antennas. Then, first the outage capacity of each
configuration are

\begin{equation}
C_{1Rx-4} = \sum_{m=1}^{4} c_f \left( \lambda_m^{4 \times 4}
\frac{SNR}{4} \right) \leq \sum_{k=1}^{4} c_f \left( \chi^2_2(k)
SNR \right)
\end{equation}

\begin{equation}
C_{4Rx-1} = \sum_{k=1}^{4} c_f \left( \chi^2_2(k) \frac{SNR}{4}
\right)
\end{equation}

\begin{equation}
C_{1Rx-4} = \sum_{k=1}^{2} \sum_{m=1}^{2} c_f \left( \lambda_m^{2
\times 2}(k) \frac{SNR}{4} \right) \leq \sum_{k=1}^{4} c_f \left(
\chi^2_2(k) \frac{SNR}{2} \right)
\end{equation}

In short, from these results I have concluded that the capacity of
MU-MISO may not be better that the capacity of Su-MISO.

References
[1] Ruly Lai U Choi, Michel T. Ivrlac, Ross Murch, and Josef A.
Nossek. Joint transmit and receive multi-user mimo decomposition
approach for the downlink of multi-user mimo systems. In Submitted to
IEEE Vehicular Technology Conference, Orlando, Florida, October Fall
2003
[2] Hyundong Shin and Jae Hong Lee, "Closed-form formulas for ergodic
capacity of MIMO Rayleigh fading channels, " in Proc. of the IEEE ICC
2003. pp. 2996-3000. May 2003.
---
Sung Jin Kim
A member of MCL in SNU: [email protected],
A MTS of i-Networking Lab in SAIT: [email protected]

James K. wrote:

...

Learning new things is one of the prime pleasures I derive from
comp.dsp. Unfortunately, not only do I know too little to estimate
the correctness of your post, I can't learn from it because I don't
understand its underlying assumptions. Knowing what some of the
acronyms mean might help.

A motorist once stopped on a country road to ask the way to a particular
farm. The fellow he asked knew the farm well, and directed the motorist
to turn onto a dirt road about a quarter mile before the little stone
bridge, adding, "You know the stone bridge, don't you?" When the
motorist said no, the fellow chose a different landmark. "Take the
second left after the road to Hanson's place." When the motorist said
that he had no knowledge of Hanson or his place, the fellow responded,
"Mister, you don't know enough for me to tell you anything."
I don't know enough for you to tell me anything, but thanks for trying.

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

On Sat, 17 Apr 2004 12:52:21 -0400, Jerry Avins <[email protected]> wrote:

> Knowing what some of the acronyms mean might help.

So, I revised my article involving the explanation to help showing
what the acronyms mean, as follows; however, you may not yet fully
satisfied with this, please forgive me for my poor writing:

My simple question is that whether or not the capacity of MU-MISO over
wireless communication environments is better than the capacity of
SU-MIMO conditioning on the same number of total receiving antennas as
that in MU-MISO, where MU-MISO and SU-MIMO are acronyms for multiuser
multi-input single-output antenna system and single-user multi-input
multi-output system.

In my analysis, the answer is obviously *NO*. To support my answer, I
provide the analysis results of two cases in terms of outage capacity,
based on [1] and [2]. Assume that in the considering system we have
one transmitter and several different configurations of receivers such
as 1 receiver with 4 antennas, 4 receivers with 1 antenna for each,
and 2 receivers each with 2 antennas. Then, first the outage capacity
of each configuration are

\begin{equation}
C_{1Rx-4} = \sum_{m=1}^{4} c_f \left( \lambda_m^{4 \times 4}
\frac{SNR}{4} \right) \leq \sum_{k=1}^{4} c_f \left( \chi^2_2(k)
SNR \right)
\end{equation}

\begin{equation}
C_{4Rx-1} = \sum_{k=1}^{4} c_f \left( \chi^2_2(k) \frac{SNR}{4}
\right)
\end{equation}

\begin{equation}
C_{1Rx-4} = \sum_{k=1}^{2} \sum_{m=1}^{2} c_f \left( \lambda_m^{2
\times 2}(k) \frac{SNR}{4} \right) \leq \sum_{k=1}^{4} c_f \left(
\chi^2_2(k) \frac{SNR}{2} \right)
\end{equation}

where Latex format has been used, and t is the number of transmit
antennas and other notations are fully followed from [2].

In short, from these results I have concluded that the capacity of
MU-MISO may not be better that the capacity of SU-MIMO as long as they
have the same number of total receive antennas.

References
[1] Ruly Lai U Choi, Michel T. Ivrlac, Ross Murch, and Josef A.
Nossek. Joint transmit and receive multi-user mimo decomposition
approach for the downlink of multi-user mimo systems. In Submitted to
IEEE Vehicular Technology Conference, Orlando, Florida, October Fall
2003
[2] Hyundong Shin and Jae Hong Lee, "Closed-form formulas for ergodic
capacity of MIMO Rayleigh fading channels, " in Proc. of the IEEE ICC
2003. pp. 2996-3000. May 2003.
---
Sung Jin Kim
A member of MCL in SNU: [email protected],
A MTS of i-Networking Lab in SAIT: [email protected]
- Any remarks, proposal and/or indicator would be respected.
- Private opinions: These are not the opinions from my affiliation.
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