1.4 SMALL SCALE MULTIPATH FADING EFFECTS
The third component of variation of received signal strength is called the small scale
fading or microscopicfading. In the small scale fading component, the signal strength
fluctuates over 30dB within a very short time scale of the order of milli-second as
illustrated in Figure 1.4. There are two independent dimensions in microscopic fading,
namely the multipath dimension and the time-varying dimension. They are elaborated
below.
Figure 1.5 illustrates the concept of multipath dimension and time varying dimension
of microscopic fading. For example, a narrow pulse transmitted at t = t o results
in one resolvable received pulse. The received pulse in general has a different shape
compared with the transmitted pulse because of multipaths propagation. At t = t l ,
the same transmit pulse results in two resolvable pulses with the first pulse stronger
than the second pulse. At t = t 2 , the same transmit pulse results in two resolvable
pulses with the first pulse weaker than the second pulse. Note that the multipath
dimension and the time-varying dimension are two independent dimensions. We
quantify the two dimensions below.
Multipath dimension: To quantify the multipath dimension in microscopic fading,
we can either look at the delay spread or coherence bandwidth. Delay spread
Figure 1.4 Illustration of the envelope and phase variations in microscopic fading.
Figure 1.5 Illustration of the multipath and time-varying dimensions in microscopic fading.
is defined as the range of multipath components with significant power when
an impulse is transmitted as illustrated in Figure 1.6 In Figure 1.6(a), a narrow
pulse (in time) at the transmitter results in a spread of energy across the delay
dimension. The graph of received power versus delay is called the powerdelay
profile and is used to measure the delay spread experimentally. Typically,
the delay spread in enclosed indoor environment is smaller than the outdoor
environment because the range of delays in the multipaths are more contained
in the indoor environment.
On the other hand, to quantify the multipath dimension [167], an equivalent
parameter, namely the coherence bandwidth, can be used. Figure 1.6(b) illustrates
the concept of coherence bandwidth. Suppose at the transmitter, we
transmit two single tone signals (impulse in frequency domain) with unit power
and frequencies fi and f2 respectively. At the receiver, the two single tones will
be received with received powers a1 and a2 respectively. cq and a2 represent
the random channel attenuation (or fading) experienced by the two single-tone
signals. It is found that if If1 - f2l > B,, the attenuation a1 and a2 are uncorrelated.
Otherwise, the attenuation a1 and a2 are correlated. Hence, the
minimum separation of frequency such that uncorrelated fading is resulted is
called the coherence bandwidth, B,. It is found that for 0.5 correlation coefficient
between al and a2, the coherence bandwidth is related to the delay
spread oT by:
Typical values of the coherence bandwidth for indoor and outdoor environment
are lMHz and lOOkHz respectively. Note that delay spread and coherence bandwidth
are two sides of the same coin to characterize the multipath dimension
of microscopic fading.
to be continue........