The default settings in
dae.m are used to perform the
equalizer designs for three channels.The source alphabet is a binary
signal.
Each channel has a FIR impulse response, and its outputis summed with a sinusoidal interference and some uniform
white noise before reaching the receiver.The user is prompted for
choice of channels (0, 1, or 2),
maximum delay of the equalizer,
number of samples of training data,
gain of the sinusoidal interferer,
frequency of the sinusoidal interferer (in radians), and
magnitude of the white noise.
The program returns plots of the
received signal,
optimal equalizer output,
impulse response of the optimal equalizer and the channel,
recovery error at the output of the decision device,
zeros of the channel and the combined channel–equalizer pair, and
magnitude and phase frequency responses of the
channel, equalizer, and the combined channel–equalizer pair.
For the default channels and values,
these plots are shown in
[link] –
[link] .
The program also prints the condition number of
, the minimum average squared recovery error
(i.e., the minimum value achieved by the performance functionby the optimal equalizer for the optimum delay
),
the optimal value of the delay
,
and the percentage of decision device output errors inmatching the delayed source.
These values were as follows:
Channel 0
condition number: 130.2631
minimum value of performance function: 0.0534
optimum delay: 16
percentage of errors: 0
Trained least-squares equalizer for Channel 0: Time responses.
The received signal is messy and cannot be used directly torecover the message. After passing through the optimal equalizer,
there is sufficient separation to open the eye.The bottom left figure shows the impulse response of the
channel convolved with the impulse response of the optimalequalizer, it is close to an ideal response (which would be one
at one delay and zero everywhere else). The bottom right plotshows that the message signal is recovered without error.Trained least-squares equalizer for Channel 0: Singularities
and frequency responses. The large circles show the locations of thezeros of the channel in the upper left plot and the locations of the
zeros of the combined channel–equalizer pair in the lower left.The *** represents the frequency response of the channel,
— is the frequency response of the equalizer, and the solid lineis the frequency response of the combined channel–equalizer pair.Trained least-squares equalizer for Channel 1: Time responses.
As in
[link] , the equalizer is able to effectively
undo the effects of the channel.Trained least-squares equalizer for Channel 1: Singularities and
frequency responses. The large circles show the locations of thezeros of the channel in the upper left plot and the locations of the
zeros of the combined channel–equalizer pair in the lower left.The *** represents the frequency response of the channel,
— is the frequency response of the equalizer, and the solid lineis the frequency response of the combined channel–equalizer pair.Trained least-squares equalizer for Channel 2: Time responses.
Even for this farily severe channel, the equalizer is able to effectivelyundo the effects of the channel as in Figures
[link] and
[link] .Trained least-squares equalizer for Channel 2: Singularities
and frequency responses. The large circles show the locations of thezeros of the channel in the upper left plot and the locations of the
zeros of the combined channel–equalizer pair in the lower left.The *** represents the frequency response of the channel,
— is the frequency response of the equalizer, and the solid lineis the frequency response of the combined channel–equalizer pair.
