Dear all,
I would like to compare the SNR at the input of the modulation
detector in a 1x1 system (1 transmit and 1 receive antenna) and in a
2x1 system employing Alamouti. We considering that the same amount of
power is transmitted in both systems. We also consider a narrowband
system such as OFDM (one subcarrier in this case).
In the 1x1 system I have that the received symbol is:
r = h * s_i + n_i
where h denotes the complex narrowband channel and could be expressed
as h = a * exp(j * phi)
I would express the SNR at the input of the demodulator in for this
system as:
SNR_11 = |h|^2 * |s_i|^2/N_0 = a^2 * Ps / N_0
where Ps is the power of the transmitted signal (assuming all symbols
have the same power) and N_0 is the power of noise.
Now in the 2x1 system with Alamouti two symbols are transmitted in two
times and then the decoding is performed and the two symbols are
submitted to the demodulator. So let's focus in the decoding of one
symbol to compare it with the 1x1 system. In this case at the entrance
of the demodulator we have:
s'_0 = (|h_0|^2 + |h_1|^2)*s_0 + (h_0*)n_0 + (h_1)n_1
Where s'_0 is the estimate of symbol s_0 after having received the two
consecutive symbols and applying Alamouti decoding in the receiver.
Now I want to compare this SNR with the one of the 1x1 system. The SNR
in this case would be:
SNR_21 = (a_0^2 + a_1^2)^2 * (Ps/2)/(2*N_0)
Where I have divided the transmitted power by 2 because if the same
power is transmitted in the 1x1 and the 2x1 system then in the 2x1
system each symbol is transmitted with half the power.
So my question is, are the two previous SNRs, SNR_11 and SNR_21,
computed correctly ? Am I comparing the two systems in a fair way ?
Best Regards
Daniel
