Whitepaper: Spread Spectrum Time-Domain Reectometry www.T3Innovation.com
1474 IEEE SENSORS JOURNAL, VOL. 5, NO. 6, DECEMBER 2005
normally be implemented on controlled impedance twisted pair
wire). For an SNR of
24 dB, STDR has an error of about
24 cm, and SSTDR had less than 3 cm of error. SSTDR still
had less than 6 cm of error down to and SNR of
53 dB below
the MilStd 1553 data signal. Both methods could be used ef-
fectively, since the required SNR for MilStd 1553 is
17 dB,
however the advantage of SSTDR for a high frequency noisy
environment was clearly demonstrated.
V. S
IGNAL-TO-NOISE
RATIO
The SNR is defined as the signal power divided by the av-
erage noise power. For a digital signal such as Mil-Std 1553,
this would be expressed as
(20)
In the case of STDR/SSTDR, the STDR and SSTDR signals
are the desired signals, and other signals are noise. Therefore,
considering the signal-to-noise power of the STDR and SSTDR
signals in the presence of another signal (Mil-Std 1553 in this
example), gives
(21)
after correlation, where
means “cross-correlated
power.”
The reflection terms
represent the reflec-
tions at various distances down the cable. To detect each of these
signals, the correlator offset is set to time
. All other re-
flection terms are considered noise terms. The received signal
after cross correlation is
(22)
From (22) and (19), the SNR is
(23)
The integral in (23) needs to be carried out for every signal
of interest that could be a noise source. For spectrally narrow
noise, such as the 115 V 400 Hz on aircraft, (23) simplifies to
Hz Hz
(24)
From this, it can be seen that if
has very little of its
energy centered at
Hz, the SNR will be large.
For noise signals that are broad in frequency spectrum, the
integral in (23) is quite involved, and is best handled numerically
on a case-by-case basis.
The effects of changing certain parameters can be studied an-
alytically in such a way as to provide excellent insight into fac-
tors other than signal and noise power that affect the SNR. These
analyzes are carried out below.
A. Changing the Length of the STDR/SSTDR Signal
In order to approximate a signal with
times the number of
chips as
, let us define a new signal such that
is proportional to , and let the duration of be
. Letting the amplitude of be the same as
(25)
In the frequency domain
(26)
which is what would be expected if the duration of
were
increased by a factor of
by adding more chips to its sequence.
Letting
(27)
gives
(28)
which is the noise energy in the cross correlation of
with
over the time . The expected value of the noise
power over the interval
is the noise power over the
interval
, given by
(29)
which is valid because
.
The central peak of the autocorrelation is given by
(30)
The signal power is
(31)
From (31) and (29), the SNR is
(32)
Equation (32) shows that doubling the length of the PN code
while leaving all other parameters the same will double (in-
crease by 3 dB) the SNR. This is true for any noise type in-
cluding 400-Hz ac, Mil-Std 1553, and white noise.
(5 pages)
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