Digital Signal Processing Reference
In-Depth Information
1
10 km/h
50 km/h
10
0
0.5
0
-0.5
0
0.005
0.01
0.015
Time (sec)
10
-
1
14
10 km/h
50 km/h
12
10
4
10 km/h
50 km/h
2
0
-500-400-300-200-100
0.005
0.01
0.015
0.02
0.025
0.03
0
100 200 300 400 500
Time (sec)
(a)
Frequency (Hz)
(b)
FIgure 1.2
Illustration of the effect of mobile speed on time variation, time correlation, and
Doppler spread of radio channel. (a) Channel time variation for different mobile speeds. (b) Time
correlation of channel as a function of the time difference (separation in time) between the sam-
ples, and the corresponding Doppler spectrum in frequency.
broadening caused by the temporal rate of change of the mobile radio channel. There-
fore, time-selective fading and Doppler spread are directly related. The coherence time of
the channel can be used to characterize the time variation of the time-selective channel.
It represents the statistical measure of the time window over which the two signal com-
ponents have strong correlation, and it is inversely proportional to the Doppler spread.
Figure 1.2 shows the effect of mobile speed on channel variation and channel correlation
in time, as well as the corresponding Doppler spread values in frequency domain.
In an adaptive receiver, Doppler information can be used to improve performance
or reduce complexity. For example, in channel estimation algorithms, whether using
channel trackers or channel interpolators, instead of fixing the tracker or interpolation
parameters for the worst-case Doppler spread value (as commonly done in practice),
the parameters can be optimized adaptively based on Doppler spread information [12,
13]. Similarly, Doppler information could be used to control the receiver or transmitter
adaptively for different mobile speeds, like variable coding and interleaving schemes
[14]. Also, radio network control algorithms, such as handoff, cell assignment, and chan-
nel allocation in cellular systems, can utilize the Doppler information [8]. For example,
as will be described later, in a hierarchical cell structure, the users are assigned to cells
based on their speeds (mobility).
Doppler spread estimation has been studied for several applications in wireless
mobile radio systems. Correlation and variation of channel estimates as well as cor-
relation and variation of the signal envelope have been used for Doppler spread estima-
tion [12]. One simple method for Doppler spread estimation is to use
differentials
of the
complex channel estimates [15]. The differentials of the channel estimates are very noisy,
which require low-pass filtering. The bandwidth of the low-pass filter is also a function
of the Doppler estimate. Therefore, such approaches require adaptive receivers that con-
tinuously change the filter bandwidth depending on the previously obtained Doppler
value. A Doppler estimation scheme based on the autocorrelation of complex channel
estimates is described in [16]. Also, a maximum likelihood estimation-based approach,
given the channel autocorrelation estimate, is utilized for Doppler spread estimation in
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