Dear all, I have the following doubt. Consider a 2x1 MIMO system, 2 antennas in the Tx and 1 antenna in the receiver. Which scheme should work better 2x1 TX beamforming (with perfect knwoledge in the transmitter) or 2x1 Alamouti ? Where I understand by beamforming the following: The MIMO channel matrix is in this case H = [h_0 h_1]. Then the transmitter would perform the SVD of the channel matrix obtaining a 2x2 transmit processing matrix V that would represent the transmit beamforming. What the transmitter would then transmit is: x = V*s, where s = [a 0]', a vertical vector containing the modulation symbol "a" and a zero. In my understanding what the transmitter is doing in this case is analyzing the two spatial channels between himself and the receiver and putting all the energy through the best spatial channel. Instead Alamouti is doing MRC (maximal ratio combining) among the two spatial channels. Is it then correct to say that in this case Alamouti should be better than beamforming ? Regards Daniel

# 2x1 TX beamforming vs 2x1 Alamouti

Started by ●June 10, 2008

Reply by ●June 12, 20082008-06-12

> The MIMO channel matrix is in this case H = [h_0 h_1]. Then the > transmitter would perform the SVD of the channel matrix obtaining a > 2x2 transmit processing matrix V that would represent the transmit > beamforming. What the transmitter would then transmit is: > > x = V*s, where s = [a 0]', a vertical vector containing the modulation > symbol "a" and a zero.for MISO case, the optimal beamforming vector is simply the conjugate of H, as the eigenspace of the channel is only 1 and this is spanned by the channel vector.> In my understanding what the transmitter is doing in this case is > analyzing the two spatial channels between himself and the receiver > and putting all the energy through the best spatial channel. Instead > Alamouti is doing MRC (maximal ratio combining) among the two spatial > channels. Is it then correct to say that in this case Alamouti should > be better than beamforming ?Depends on your definition of doing better. Diversity-wise, both have diversity order of 2. Performance-wise, beamforming is probably better. Beamforming is actually doing MRC at the transmitter instead of the receiver, while Alamouti is equivalent to doing an averaging of the two channels. The advantages of Alamouti is that it is open loop (no need to information at transmitter), and ML is decoupled at the receiver (hence simple receiver).

Reply by ●June 15, 20082008-06-15

On 12 jun, 11:20, Kenneth Chin <whc...@gmail.com> wrote:> > The MIMO channel matrix is in this case H = [h_0 h_1]. Then the > > transmitter would perform the SVD of the channel matrix obtaining a > > 2x2 transmit processing matrix V that would represent the transmit > > beamforming. What the transmitter would then transmit is: > > > x = V*s, where s = [a 0]', a vertical vector containing the modulation > > symbol "a" and a zero. > > for MISO case, the optimal beamforming vector is simply the conjugate > of H, as the eigenspace of the channel is only 1 and this is spanned > by the channel vector. > > > In my understanding what the transmitter is doing in this case is > > analyzing the two spatial channels between himself and the receiver > > and putting all the energy through the best spatial channel. Instead > > Alamouti is doing MRC (maximal ratio combining) among the two spatial > > channels. Is it then correct to say that in this case Alamouti should > > be better than beamforming ? > > Depends on your definition of doing better. Diversity-wise, both have > diversity order of 2. Performance-wise, beamforming is probably > better. Beamforming is actually doing MRC at the transmitter instead > of the receiver, while Alamouti is equivalent to doing an averaging of > the two channels. The advantages of Alamouti is that it is open loop > (no need to information at transmitter), and ML is decoupled at the > receiver (hence simple receiver).Dear Kenneth, Thanks for your answer. Could you please explain a bit more your first sentence?> for MISO case, the optimal beamforming vector is simply the conjugate > of H, as the eigenspace of the channel is only 1 and this is spanned > by the channel vector.I understand that what you propose will result in MRC in the reciver since the two spatial channels are coherently added in the receiver, but is not that the same than Alamouti in a 2x1 system then ? And another question is that what I was doing is instead of directly applying the conjugate of the spatial channel, I was applying the SVD to the MISO channel vector and obtaining a 2x2 precoding matrix to be applied in the TX, then the beamforming gain is the eigenvalue of the SVD decomposition, that as I obeserve is exactly the same than the MRC gain (coherently add all the components of the spatial channel), is that correct ? Best Regards Daniel

Reply by ●June 17, 20082008-06-17

On Jun 15, 10:42 pm, Dani Camps <danicamp...@gmail.com> wrote:> I understand that what you propose will result in MRC in the reciver > since the two spatial channels are coherently added in the receiver, > but is not that the same than Alamouti in a 2x1 system then ?No. Alamouti is an open loop system, which means that the transmitter has no channel information. Hence, it is not able to ensure that the signals will add coherently at the receiver. Further more, different information signals are sent through the two antennas, so theres definitely no way the signals can add constructively.> And another question is that what I was doing is instead of directly > applying the conjugate of the spatial channel, I was applying the SVD > to the MISO channel vector and obtaining a 2x2 precoding matrix to be > applied in the TX, then the beamforming gain is the eigenvalue of the > SVD decomposition, that as I obeserve is exactly the same than the MRC > gain (coherently add all the components of the spatial channel), is > that correct ?when you apply SVD to your channel vector, you will get a single eigenmode, which means that only 1 eigenvector is useful, the other is just meaningless. and if you look carefully at your useful eigenvector, it is simply a scaled version of your channel vector conjugated. Essentially, what you are doing is the same as applying the conjugated channel vector as the beamforming weights. Just remember to take care of the transmit power. -K

Reply by ●June 17, 20082008-06-17

On Jun 17, 12:17�pm, Kenneth Chin <whc...@gmail.com> wrote:> On Jun 15, 10:42 pm, Dani Camps <danicamp...@gmail.com> wrote: > > > I understand that what you propose will result in MRC in the reciver > > since the two spatial channels are coherently added in the receiver, > > but is not that the same than Alamouti in a 2x1 system then ? > > No. Alamouti is an open loop system, which means that the transmitter > has no channel information. Hence, it is not able to ensure that the > signals will add coherently at the receiver. Further more, different > information signals are sent through the two antennas, so theres > definitely no way the signals can add constructively. > > > And another question is that what I was doing is instead of directly > > applying the conjugate of the spatial channel, I was applying the SVD > > to the MISO channel vector and obtaining a 2x2 precoding matrix to be > > applied in the TX, then the beamforming gain is the eigenvalue of the > > SVD decomposition, that as I obeserve is exactly the same than the MRC > > gain (coherently add all the components of the spatial channel), is > > that correct ? > > when you apply SVD to your channel vector, you will get a single > eigenmode, which means that only 1 eigenvector is useful, the other is > just meaningless. and if you look carefully at your useful > eigenvector, it is simply a scaled version of your channel vector > conjugated. Essentially, what you are doing is the same as applying > the conjugated channel vector as the beamforming weights. Just > remember to take care of the transmit power. > > -KHi, Thanks again for your clear answer. Just one addition. I understand that in Alamouti the two signals transmitted at one symbol time do not add coherently in the receiver, but under the assumptions of Alamouti. i.e. the channel stays constant over two consecutive symbol times, then after the two symbol times and the processing done in the receiver what I have is the SNR boosted by something equivalent to the coherent addition of the two channel components, i.e. (|h_0|^2+|h_1| ^2) for each transmitted constellation symbol. Should not in this sense, post detection SNR, give Alamouti the same performance than transmit beamforming ? Regards Dani

Reply by ●June 25, 20082008-06-25

> Thanks again for your clear answer. Just one addition. I understand > that in Alamouti the two signals transmitted at one symbol time do not > add coherently in the receiver, but under the assumptions of Alamouti. > i.e. the channel stays constant over two consecutive symbol times, > then after the two symbol times and the processing done in the > receiver what I have is the SNR boosted by something equivalent to the > coherent addition of the two channel components, i.e. (|h_0|^2+|h_1| > ^2) for each transmitted constellation symbol. Should not in this > sense, post detection SNR, give Alamouti the same performance than > transmit beamforming ?Not really. Work out the SNR for Alamouti and work out the SNR for beamforming and you'll find that they are different. Remember, that noise doubles as well when you observe over two time slots. -K