Wireless propagation channels have been studied for more than 50 years, and a large number of channel models are already available. The signal that has propagated through a wireless channel consists of multiple echoes of the originally transmitted signal; this phenomenon is known as multipath propagation. The different multipath components (MPCs) are characterized by different attenuations and delays. The
correct modeling of the parameters describing the MPCs is the key point of channel modeling.
In UWB systems, the intended radiation can cover a bandwidth closed to 10 GHz, and the unintended radiation can cover an even larger frequency range. This large bandwidth can give rise to new effects. For example, only few multipath components overlap within each resolvable delay bin, hence the central limit theorem is no longer suitable, and the amplitude fading statistics are not Rayleigh distributed.
Also, there can be delay bins into which no MPCs fall, and thus are empty. It then becomes necessary to characterize the likelihood that this happens, and that an empty bin is followed by a full one. For a realistic performance assessment, a UWB channel model like the 802.15.3a standard model has to include all those effects.
Three main indoor channel models were considered here: the tap-delay line Rayleigh fading model [21], the Saleh-Valenzuela (S-V) model [22], and the ∆-K model described in [23], as well as several novel modifications to these approaches that better matched the measurement characteristics. Each channel model was parameterized in order to best fit the important channel characteristics described above. Although many good models were contributed to the group, the model finally adopted was based on a modified S-V model that seemed to best fit the channel measurements. In particular, the channel measurements showed multipath arrivals in clusters rather than in a continuum, as is customary for narrowband channels.
3.1.1 Saleh-Valenzuela Model
The S-V model was proposed in [22] to model the multipath of an indoor environment for wideband channels on the order of 100 MHz. Even at this relatively narrow bandwidth, a clustering phenomenon was observed in the channel. In order to
capture this effect, the authors proposed an approach that modeled the multipath arrival times using a statistically random process based on the Poisson process. In other words, the interarrival time of multipath components is exponentially distributed. In addition, the multipath arrivals were grouped into two different categories: a cluster arrival and a ray arrival within a cluster, there are 6 key parameters that define the model [24]:
Λ= cluster arrival rate;
λ= ray arrival rate, i.e., the arrival rate of path within each cluster;
Γ= cluster decay factor;
γ= ray decay factor;
σ = standard deviation of cluster lognormal fading term (dB). 1
σ = standard deviation of ray lognormal fading term (dB). 2
σx =standard deviation of lognormal shadowing term for total multipath realization (dB).
Multipath model
The amplitude statistics in the original S-V model were found to best match the Rayleigh distribution, the power of which is controlled by the cluster and ray decay factors. However, the measurements in UWB channels indicated that the amplitudes do not follow a Rayleigh distribution. Rather, either a lognormal or Nakagami distribution can fit the data equally well, which has been validated using Kolmogorov-Smirnov testing with a 1 percent significance level. Based on these results, the S-V model was modified for the IEEE model by prescribing a lognormal
amplitude distribution. The model also includes a shadowing term to account for total received multipath energy variation that results fromblockage of the line-of-sight path. The discrete time impulse response multipath model can be given by
τk l is the delay of the kth multipath component relative to the lth cluster arrival time
( )
Tli ,{ }
Xi represents the log-normal shadowing, and i refers to the ith realization.By definition, we have τ = . The distribution of cluster arrival time and the 0,l 0 ray arrival time are given by the independent interarrival exponential probability density function
The channel coefficients are defined as follows:
( ) (
12 22)
, , ,, 20 log10 , Normal ,,
k l pk l l k l l k l k l
α = ξ β ξ β ∝ µ σ +σ (3.4)
where n1 ∝Normal 0,
(
σ12)
and n2 ∝Normal 0,(
σ22)
are independent and correspond to the fading on each cluster and ray, respectively,,
the first cluster, and pk,l is equiprobable +/-1 to account for signal inversion due to
In the above equations, ζ reflects the fading associated with the lth cluster, l and βk l, corresponds to the fading associated with the kth ray of the lth cluster.
Finally, since the log-normal shadowing of the total multipath energy is captured by the term, X , the total energy contained in the terms i
{ }
,i
αk l is normalized to unity for each realization. This shadowing term is characterized by
20 log10( )Xi ∝Normal(0,σx2).
Note that, a complex tap model was not adopted here. The complex baseband model is a natural fit for narrowband systems to capture channel behavior independently of carrier frequency, but this motivation breaks down for UWB systems where a real-valued simulation at radio frequency (RF) may be more natural.
Figure 3.1 illustrates the equivalent model for simulation of passband system in terms of complex baseband system. Therefore the real-valued passband multipath channel response is simplified as follow
( ) 1
( )
where α is the real-values channel coefficient. The equivalent baseband i multipath channel response is described by
( ) 1 2
( )
1 i( )
The proposed model parameters were designed to fit measurement results, and
Table 3.1 provides the results of this fit for four kinds different channel environments (LOS refers to line of sight, NLOS to non-LOS).
1. CM1 is based on LOS (0 – 4 m) channel measurements.
2. CM2 is based on NLOS (0 – 4 m) channel measurements.
3. CM3 is based on NLOS (4 – 10 m) channel measurements.
4. CM4 is generated to fit a 25 ns RMS delay spread to represent an extreme NLOS multipath channel.
Figures 3.2 and 3.3, along with the channel measurement characteristics listed in Table 3.1, highlight characteristics of the multipath channel that are important to discuss. First, the multipath spans several nanoseconds in time, which results in ISI if UWB pulses are closely spaced in time. However, this interference can be mitigated in a number of ways through proper waveform design as well as signal processing and equalization algorithms. Second, the ultra wide bandwidth of a transmitted pulse results in the ability to individually resolve several multipath components.