Section 8.1. What s Different about UWB System Simulations?

8.1. What's Different about UWB System Simulations?

For one familiar with Monte Carlo simulation as applied to communication systems, an important first step is to address why it is important to revisit this subject when targeting UWB systems. In other words, what's different about UWB systems that requires us to take a second look at simulation methodology? In the following, we will see that direct/quadrature signal decomposition, which is a fundamental technique used to shorten the required simulation runtime for narrowband systems, no longer provides the dramatic savings in runtime when applied to UWB signals. In addition, data collection for channel model development is a nontrivial task because the wide bandwidth required for UWB channel sounding significantly complicates the process. Also, component modeling and simulation development introduce challenges unique to the UWB signal environment.

8.1.1. Direct/Quadrature Signal Decomposition

The simulation methodology for a UWB communications system is quite a bit different from that used in a traditional narrowband system. When simulating narrowband systems, the carrier is usually translated to zero frequency using direct/quadrature decomposition of the modulated carrier so that the simulation model can be based on signals having relatively small bandwidth. In other words, if a bandpass signal having center frequency f_c and bandwidth B is represented as

Equation 8.1

where the direct channel signal, x_d (t), and the quadrature channel signal, x_q (t), have bandwidth B/2. This allows the simulation sampling frequency to be significantly reduced compared to what would otherwise be required. This of course reduces the required execution time for the simulation [1].

UWB systems, however, are typically simulated as baseband systems, and direct/quadrature decomposition is not used. Consider Figure 8.1, which illustrates the spectrum of a bandpass signal having a carrier frequency f₀ Hz and a bandwidth of B Hz. The highest frequency contained in the bandpass signal is

Equation 8.2

Figure 8.1. Spectrum of Wideband Signal.

Treating this signal as a baseband signal, as done with UWB signals, gives a minimum sampling frequency of

Equation 8.3

Equation 8.4

On the other hand, if the signal is narrowband and direct/quadrature decomposition is used, two lowpass signals are created, each of which has bandwidth B/2. Thus the minimum sampling frequency for both the direct and the quadrature channel signals is B Hz. Thus, the minimum sampling frequency for the narrowband signal is because the minimum sampling frequency for both the direct and quadrature channel signals is B. We have interest in the ratio R defined as

Equation 8.5

Large values of R imply that a significant savings in simulation runtime results by using direct/quadrature decomposition, while small values of R imply that a relatively small savings in simulation runtime results.

In order to illustrate the role of the ratio R, we compute R for two signals. Assume that the first signal is a narrowband signal having a carrier frequency of 1 GHz (1,000 MHz) and a bandwidth of 1 MHz. For this case

Equation 8.6

and the value of R is

Equation 8.7

indicating that considerable savings results from using narrowband (direct/quadrature) signal processing techniques.

Now assume that the second signal is a UWB signal that extends from 30 MHz to 3 GHz. The center frequency (effective carrier frequency) is (3,000 - 30)/2 = 1,485 MHz and the bandwidth is (3,000 - 30) = 2,970 MHz. For this case the value of R is

Equation 8.8

indicating that there is no advantage to using direct/quadrature signal decomposition. This is clearly an extreme case but it makes the point that the reduction in sampling frequency resulting from direct/quadrature signal representations becomes less significant with increasing signal bandwidth.

Accordingly, direct/quadrature decomposition is not typically used in the simulation of UWB systems, and very high simulation sampling frequencies are often necessary. As a result, long simulation runtimes are common. It is therefore very important that the simulation be developed so that only the essential features are included in the simulation model and that the simulation code is as efficient as possible.

8.1.2. Model Development for UWB Systems

The development of models for UWB communication systems is made more difficult for two reasons: established models are not widely available, and the challenges associated with developing new models are often significant. Although UWB communications systems were first introduced in 1973 [3], the wireless community's interest in UWB is relatively recent. Accordingly, UWB has not had the benefit of time to develop and refine an extensive library of tested and validated models.

For narrowband systems, a large body of well-understood models has been developed. Thus, model development is often easily and quickly accomplished. In narrowband simulations, model development often simply involves identification of the model that best fits expected conditions or experimental data for the scenario under study. For instance, consider the simulation of a channel for a UMTS signal, a signal for which an astounding number of large-scale and small-scale channel models exist and have been formally standardized by the ITU. In addition to traditional channel models such as LOS, Rayleigh, and Ricean, the ITU defines simulation models for the following situations [4]:

1. Indoor office environments with parameters based on the number of floors and number and type of walls.

2. Outdoor to indoor and pedestrian environments with considerations for urban canyons, trees, and building penetration.

3. Vehicular environments with parameters for operating in urban, suburban, and rural environments.

However, when simulating a UWB system, we are not as fortunate. While a handful of channel models have been developed, most notably the Saleh-Valenzuela small-scale model [5], the Cassioli large scale model [6], and the 802.15.3a model [7], the actual number of appropriate models is limited. Similar model deficits are encountered when examining other aspects of a UWB communications system, such as amplification, signal recovery, and data conversion. Thus, when simulating UWB systems we frequently must develop new models from experimental data rather than simply extracting a previously developed and validated model from an existing model library.

For example, the multipath magnitudes for a UWB channel do not generally follow a Rayleigh or Ricean distribution. It has been observed from experimental measurements that multipath magnitudes tend to obey a Nakagami-m distribution, which requires additional parameterization (the value of m) to model a channel. It should be noted that the Nakagami-m distribution reduces to a Rayleigh distribution for m = 1 and can closely approximate a Ricean distribution for higher values of m. A more detailed treatment of the Nakgami, Rayleigh, and Ricean distributions was provided in Chapter 3.

Another difficulty encountered in UWB systems deals with phase response. UWB signals have, by definition, very large bandwidth because transmission takes place using pulses with very short duration. In order for these pulses to pass through the channel, as well as other signal-processing system components, without distortion, the amplitude response of the component in question must be constant and the phase response must be linear over the bandwidth of interest. If these conditions are not satisfied, pulse distortion occurs. Removal of this pulse distortion requires equalization. As the bandwidth increases, the constraint of constant amplitude response and linear phase response becomes increasingly difficult to satisfy. Equalization also becomes more difficult with increased bandwidth.

The condition of linear phase response across the bandwidth of interest is often most troublesome. Linear phase response implies a constant group delay because group delay is the negative derivative of phase response. (Recall that phase delay is the delay imposed at a single frequency.) Maintaining a constant group delay across a large bandwidth is very difficult.

Another critical narrowband modeling concept that fails under UWB conditions is the assumption of steady-state operation. Consider an I-UWB system with a small duty-cycle. Under this condition, it is relatively safe to assume the transmitter components return to a relaxed state between pulses. Thus, the transmitter is constantly operating in a transient mode, and the assumption of a steady-state would not be valid.

The assumption of steady-state operation vastly simplifies model development. Under steady-state conditions, the analog behavior of a circuit can be readily described with transfer function models and simple impedance-based equations. However, under transient conditions, models have to rely on the solution of differential equations, a significantly more complicated process.

8.1.3. UWB Simulation Development Challenges

Problems also arise during the simulation development step. Fundamental to UWB communications systems is the ultra-wide bandwidth of the signals. As previously discussed, a UWB signal has a bandwidth greater than 500 MHz with fractional bandwidth of at least 20%. If we assume a signal bandwidth of 2 GHz and apply an over-sampling factor of four to ten as would be used by traditional simulation techniques, a simulation sampling rate of 8-20 GHz is required. A detailed low-level simulation that models all aspects of the system would then be expected to run for days, if not weeks. Thus, any simulation solution must consider ways to reduce simulation run-time by simplifying the simulation model or using semi-analytic techniques, which will be discussed in the following section.