# SFBC Alamouti Scheme LTE

A sentence I copied from book.

That a 2$\times$1 Alamouti SFBC is referred to as a rate 1 code, two symbols are sent over two adjacent subcarriers.

This question is regarding this SFBC encoder (Alamouti scheme). I understand how the encoder works for the two transmit antenna case. Below I briefly given an example for convenience.

Assuming a BPSK modulator applied to data input $I$. Then we have

$I$ = 0 0 1 1 0 1 1 1

BPSK symbols= 1 1 -1 -1 1 -1 -1 -1

Then the output of the STBC encoder could be found according to the

\begin{array}{lcr} \mbox{} & Antenna1 & Antenna 2 \\ \mbox{$f_1$} & s_1 & s_2 \\ \mbox{$f_2$} & -s_2^* & -s_1^* \\ \end{array}

and so applying this to the BPSK symbols I get the following symbols

Antenna1 symbols: 1 -1 -1 1 1 1 -1 1

Antenna2 symbols: 1 1 -1 -1 -1 1 -1 -1

My question is next, what do we do with these symbols for LTE system ie OFDM modulation, do we send the symbols 1 and 2 over antenna 1 and antenna 2 respectively over the same subcarrier ? i.e I don't understand how transmission over subcarriers takes place? More precisely I don't undersatnd the assignement of the symbols to the different subcarriers?

Thank you.

What I see from your post is SFBC Space Frequency Block Coding. This is different than STBC "Space Time Block Coding." In STBC, which was the original way the Alomouti Code was used, the table you have above would have f1 and f2, the subcarriers replaced by time slots T1 and T2. You show SFBC where symbol 1(s1) is sent over ant1 and subcarrier f1, s2 over subcarrier f1 antenna 2, -s2conj over subcarrier 2 ant 1, etc. If this were STBC then s1 would be sent in timeslot 1 over ant1 s2 in timeslot 1 over ant 2, etc. I pretty sure this is correct..Hope this helps

• thank you, i agree this is SFBC. But it is not clear to me, are we sending symbols s1 and s2 at the same time over subcarrier f1? I know they are sent out of different antenna but what about time and subcarrier? Thanks – Tyrone Apr 30 '15 at 14:12
• ok, I see your point, I'm going to look around and see what I can find. Have you looked into the LTE standards yet? – Ha Nguyen May 1 '15 at 0:43
• thank u. yes i have through the 3GPP website. i think i am misunderstanding how they implement alamouti in LTE... – Tyrone May 1 '15 at 1:17
• My first take on this is that there are two IFFT blocks in the TX one for each antenna. The symbols are sent at the same time. scielo.br/… the link – Ha Nguyen May 2 '15 at 0:01
• tyrone check out this link it might be of use to you dsp.stackexchange.com/questions/16196/… – Ha Nguyen May 4 '15 at 23:19

The Alamouti scheme guards against Rayleigh fading channels. If you were to send two symbols within the same channel within the same coherence time interval, they will experience the same fading. In order to get diversity gain, you need to send them in different channels (different antennas or different frequencies or distant time slots)

• i understand that it is used for diversity purposes, to decrease ber, I don't understand how it is used in LTE and ofdm modulation. For example in this example do we send 1 1 over different antennas and different subcarriers? or same subcarriers? i.e I dont understand the assignement of symbols to subcarriers – Tyrone Apr 27 '15 at 23:30