This module shows the results and conclusions for our DMT project.
Results
In order to test our DMT system, we investigated how the probability of bit error changed with the signal-to-noise ratio of the transmitted signal in our channel. In particular, we compared how these PE - SNR curves changed as the cyclic pad length was varied. As a comparison, we also looked at how DMT stacked up with a simple model of single-carrier modulation in these same regards.
Dmt vs single - carrier (sc)
We ran our tests of the system with the following constraints:
Bitstream length: 512
Block-size: 128 (DMT), 1 (SC)
AWGN amplitude: .00001 - 1
Channel impulse response length: 1 (wire), 16
Cyclic prefix length (DMT): 0, 8, 16
Impulse noise: 0
Constellation size: 16-point
The results of our tests were as expected. For wire channel, SC and DMT were comparable. They both demonstrated a Q-function behavior, dropping to zero error once the SNR was high enough and leveling off to about 0.5 (i.e. a coin flip) for very low SNR. For impulse response length
L less than cyclic prefix
C , DMT dropped to a error fell from 0.5 as SNR increased, but leveled off once ISI began to have a more prominent effect. Single-carrier also demonstrated this same behavior, though there was no cyclic prefix involved. This was a little strange, but this project's goal was to study DMT, not SC. Once the cyclic pad length was larger than the impulse response length, DMT again displayed Q-function behavior as ISI was no longer a problem.
L = 1
This is shows how bit error probabilities compare for DMT (red) and SC (blue) with a wire channel impulse response (length
L = 1).
L>C
This is shows how bit error probabilities compare for DMT (red) and SC (blue) with a length
L = 16 channel impulse response and a DMT cyclic prefix of length
C = 8.
L<C
This is shows how bit error probabilities compare for DMT (red) and SC (blue) with a length
L = 16 channel impulse response and a DMT cyclic prefix of length
C = 16.
Conclusions
From our results and experience implementing our DMT system, we reached the following conclusions:
It is possible to implement a working DMT system in MATLAB. It looks as though a more complicated extension of the system, possibly involving variable frequency allocation, a time-varying channel freq. response, more complicated constellations or a transmitter-receiver synchronization process, should also be quite feasible.
DMT's advantages over other modulation schemes are difficult to see with such a simple system; they would be more apparent in a system including a more realistic model of data assignment to the various frequencies (instead of evenly distributing all data over the first 256).
The need for a cyclic prefix is readily verifiable; as soon as the prefix length is correct, bit error drops to zero at high SNR.
Communications engineering and DSP are fun (except when you have to stay up all night writing connexions modules)! Looking forward to 431 next semester!
