Estimating the RMS Delay Spread
from the Frequency-Domain Level Crossing Rate
Contributed by Klaus Witrisal
The root-mean-square (RMS) delay spread is probably the most important
single measure for the delay time extent of a multipath radio channel.
Since the impulse response (IR) and the transfer function (TF) of a channel
are related by the Fourier transform, it is intuitively understandable
that the TF's magnitude shows more fades per bandwidth, the longer the
IR.
As shown by Witrisal et al. [2], [3], there exists a well-defined
relationship between the so-called level crossing rate in the frequency-domain
(LCRf) and the RMS delay spread (Trms), written as
LCRf = Trms * f(K, r', u).
(1)
As seen from this equation, Trms and the LCRf
are proportional, where the proportionality factor is a function of
-
the Ricean K-factor K
-
the threshold value at which the LCRf is determined, r' (r'
is normlized to the RMS amplitude value of the TF)
-
and the channel model, expressed by u. (This influence is very small, therefore
it can be neglected [2].)
For the LCRf at the RMS amplitude value of the channel transfer
function, the factor f(K,r' = 1,u = 0) can be approximated by
.
Application to Channel Measurements
Equation (1) allows for the estimation of a complete set of wide-band channel
parameters (average received power, Ricean K-factor, and RMS delay spread)
from rather simple swept-frequency power measurements of the channel. (Note
that the Fourier transform cannot be used to calculate an IR from a measured
power response, due to the lack of phase information). The following measurement
procedure is suggested:
-
Measure the narrowband power (or magnitude) response of the channel as
a function of frequency. (A continuous wave frequency generator and a spectrum
analyzer can be used to conduct such measurements).
-
Calculate the average received power and the Ricean K-factor from the measured
power response.
-
Count the number of level crossings at a specific threshold, preferably
at the RMS amplitude.
-
Use equation (1) for estimating Trms.
An observation bandwidth of 10/Trms (equivalent to the observation
of approx. 20 level crossings) allows for estimating Trms at
an accuracy in the order of 10 %. Higher bandwidths can enhance the accuracy.
Alternatively, multiple measurements from within a small local area can
be combined to increase the observation bandwidth without modifying the
measurement equipment.
Other issues that should be considered when applying this method for
channel investigations are:
-
Influence of the sampling interval of the channel's frequency response:
The sampling interval must be selected according to the sampling theorem,
otherwise some fades may be missed when counting the level crossings.
-
Influence of measurement equipment noise: Noise may introduce additional
level crossings, which would lead to overestimation of Trms.
The sampling interval mentioned above should be as large as possible to
minimize this effect



Wireless Communication ©
Klaus
Witrisal
Centre for Wireless Personal Communications (CEWPC)
TU-Delft, IRCTR
Mekelweg 4
NL-2628 CD Delft
The Netherlands
Phone: +31(0)15-27-87371
Fax: +31(0)15-27-84046
email: K.Witrisal@ITS.TUDelft.NL