## BER Curves for Alamouti scheme, high symbol rate

Posted by Ujjval Shah on Tuesday, March 24, 2009
Under: Simulation

As mentioned in previous posts, those curves were plotted at a symbol rate varying from 2-10Hz.

The published ones are plotted at 2bits/sec ie 1symbol/sec for QPSK.

In all the curves shown till now, none of them match exactly to the published ones.

However it is observed that as the symbol rate is gradually increased, the simulated curve tends to become more and more similar to the published ones.

Consider following values:

symbol rate =500

no of samples per symbol =8

no of symbols =5k

doppler spread =1

Symbol rate * No of samples per symbol = sampling frequency = 4000

Warning 21880 says that

"Insufficient profile length (samples) to ensure a valid Rayleigh/Rician distribution of generated samples. profile length (samples) must be at least 10 * sampling frequency/doppler spread (Hz) for a statistically significant fading profile generation." = 40,000 profile length

wo alamouti scheme

here the profile length is ~= 2 (for QPSK ) x #Message symbols x samples per symbol (approx)

(generally the profile length is larger than this due to addition of sync symbols & guard bits)

thus for 5k symbols and 8 samples per symb, the prof length should be around 80k (assuming that the fading will change at every sample), thus for simulation without alamouti scheme there is no problem and hence a good faithful curve is obtained

with alamouti scheme

this scheme requires the channel to be constant for 2 symbol periods and hence the profile length should be decreased by 2x8 (samples per symbol)= 16 times ie the new profile length will be 80k/16 = 5,000 which doesnt satisfy the condition as mentioned in 'Warning 21880'

There are three ways to workaround this problem:

- Increase the no of message symbols: But as the no of symbols increases the computational time increases in an outrageous manner, making it extremely difficult to compute the graph for the entire set of SNR values
- Decrease the symbol rate: but as observed higher symbol rate gives better, faithful curves
- Increase the doppler: high doppler results into more distortion that can be easily seen in signal constellation diagram, thus making it extremely difficult to detect the symbols faithfully

In : Simulation

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