Transient Constant Area Surface and Downhole Wave Models - Measurement While Drilling Signal Analysis, Optimization and Design - page 104

Source code XDUCER*.FOR is used for Method 4-1, Run 2. Here, the
incident upgoing black signal is about 0.05 sec wide, nominally a 20 bit/sec run.
The delayed red reflected signal is also shown. The green is the superposition of
the upgoing and reflected signals. It is clearly much wider than the black signal,
and shows the interference of the upgoing and downgoing signals. In fact, the
green line falsely conveys the presence of two signals, and definitely, would
confuse the transducer into “thinking” that there really are two signals. This
widening is not good for high-data-rate telemetry and is also known as
“intersymbol interference.” The top blue curve uses data from the green curve
only, and recovers the black curve successfully. The above run was repeated for
finer sampling, in particular,
x Roundtrip delay = 0.02 sec
x Sampling time = 0.0005 sec = 0.5 ms

Again, when the pulse width is narrow compared to the delay time, the
standpipe transducer will “see” two pulses instead of one, or if the two are
overlapping, one large signal with two “camel humps.” Results appear in Figure
4.1e. The top blue curve recovers the black signal very nicely. Both sampling
rates show same phenomena.

Figure 4.1e . Narrow pulse width - high data rate.

4.1.5 Run 3. Phase-shift keying or PSK.

We consider first a 12 Hz low carrier frequency. This is the frequency
used to transmit siren information at 3 bits/sec or less. The input source code
shown below is used to create the black curve in Figure 4.1f.

C CASE 3. PHASE-SHIFTING (F = FREQUENCY IN HERTZ)
PI = 3.14159
A = 0.25
F = 12.
C G = A*SIN(2.*PI*F*T)