“Can you hear me now?”
The ubiquitous nerd in khaki pants and glasses makes it look so easy ” a seamless network of nationwide wireless access, a utopia of coverage where dropped calls are but a bad memory. Reality, as any regular cellular phone user knows, is more akin to the frustrated businessman in the taxicab, imploring the driver to back up and shoot forward in a vain attempt to grasp the life-giving bars of signal strength. Why does it always seem like you can be having a perfectly clear conversation at one step, and then completely lose the signal at the next step? The answer lies in those two simple, yet ominous words on your phone's display: Signal Faded.
Signals passing through the air are distorted by atmospheric and environmental impairments including multipath scattering and dispersion. This article introduces several commonly used mathematical techniques for simulating real-world channel conditions in various fading environments, provides a justification for why channel simulation is important to device designers, and discusses the traditional test methods used today. A new implementation of channel simulation is demonstrated, promising to alleviate some of the toughest and most cost-intensive test challenges through an innovative all-digital process that offers high bandwidth and integrated, automatically calibrated noise.
What is fading, anyway?
Communications quality between a base station transmitter and mobile (or stationary) receiver depends on a number of factors, including the general quality of the propagation channel through which the signal passes. In wireless applications, cellular communications particularly, the propagation path is terrestrial air with a myriad number of man-made and natural objects that get in the way. As the transmitted signal gets absorbed by the atmosphere and reflects off of buildings and trees, it experiences variable fluctuations in its amplitude and phase. This phenomenon is typically called fading, sometimes referred to as multipath (a specific type of fading) or the more general category of channel impairments. The mechanism of fading can be broken down for better understanding into two different groups based on position of the receiver relative to the transmitter: large-scale fading for channel propagation over long distances, and small scale fading for effects that are found near to the receive antenna. Because the destructive effects of small-scale fading are less predictable and potentially more catastrophic than large-scale fading, the majority of this article will focus on small-scale issues.
Figure 1: Fading can be grouped into large scale effects over long distances and small scale effects close to the receive antenna.
Large Scale Fading
Large scale fading represents the average attenuation of a wireless signal as it travels a long distance or encounters a large object (several hundred wavelengths or more). An ideal signal traveling through free space would experience a path loss proportional to the distance squared. In the real world, a signal's energy is absorbed and reflected by the atmosphere, the curvature of the earth, and obstacles. Obstacles can be natural, such as trees, mountains, and bodies of water, or man-made, such as buildings, billboards, and streets. This physical obstacle course causes the performance to degrade beyond the theoretical inverse-squared free space path loss law. Degradation due to blockage by large objects is sometimes referred to as shadowing, because the fade area is very large and tends to blanket the area in which the mobile is traveling.
Figure 2: Large scale fading is an average path loss with wide peaks and troughs caused by shadowing
Mathematically, large scale fading is simulated by a log-normally distributed fluctuation superimposed on a mean path loss that is distance dependent. The distance dependence describes the average attenuation experienced as the signal travels through the atmosphere. The fluctuations on this average occur from shadowing effects, which are manifestations of the physical principle of diffraction. Diffraction allows signals to “wrap” themselves around corners and over edges of buildings and other large obstructions, as secondary waveletss are produced at intersections of incident waves with boundaries.
Small Scale Fading
In addition to path loss over large distances, the receive antenna will also experience fluctuations in signal level that vary significantly over small distances (on the order of one to tens of wavelengths). This fluctuation is a result of two distinct but related processes: multipath propagation and doppler shift.
A signal transmitted from a base station can take different paths to a receiver, due to reflection, diffraction, and local scattering. (Hence the name 'multipath' fading.) Different paths have different lengths associated with them, which causes the receiver to “see” multiple copies of the signal at different times of arrival and with varying amplitudes. Also, the signal can shift in phase as it is reflected and scattered off of local objects. All of these signals at different power levels and phase converge on the omnidirectional receive antenna with constructive or destructive interference. As the antenna moves through space, it will experience peaks and valleys of signal strength as these interfering wavelets add and subtract at the receiver.
Figure 3: Small scale fading results in small peaks of power, caused by constructive interference, interspersed with large drops in power, caused by destructive interference
Another artifact of motion is Doppler shift. As the receive antenna moves in relation to a fixed transmitter, the incoming signal will modulate in frequency according to the angle of arrival at the antenna. Copies of the signal that arrive via paths directly in front of the moving receiver will seem to have a higher frequency, while copies of the signal arriving via paths behind the moving receiver will seem to have a lower frequency. Copies that arrive perpendicular to the direction of motion experience no Doppler shift.
Common fading profiles
Designers of today's wireless devices need to test their designs under real-world channel conditions. Channel impairments can be simulated by mathematical models that mimic the channel response of a fading channel. These models use statistics to express what an electromagnetic wave will experience as it encounters physical obstacles.
The rayleigh distribution is a good model for channel propagation when there is no strong line of sight path from transmitter to receiver. This can represent the channel conditions seen on a busy street in a city, where the base station is hidden behind a building several blocks away and the arriving signal is bouncing off many scattering objects in the local area. In the time domain, Rayleigh fading looks like periodic peaks of 10dB or less interspersed between deep troughs of 40dB or more. (see figure 4) These deep fades (nulls in signal power) will typically occur at separations of a half-wavelength.
Figure 4: Frequency spread caused by multipath reflection. Fc is the original carrier frequency, and Fd is the Doppler spread seen by the moving receiver.
In the frequency domain, the effect is a U-shaped curve (sometimes called a Batman curve, for obvious reasons). The angle of arrival of the incident rays determines the power they exert (the vertical axis) while the speed of the vehicle determines the breadth of the frequency shift (the horizontal axis.) Because the Doppler shift of the incident rays are direction-dependent, the max positive frequency shift is seen at 0 degrees relative to direction of motion. The max negative shift is seen at 180 degrees, and no shift is seen at 90 and 270 degrees. This is why we see the most spectral density at the edges of the Doppler spread, which correlate to the rays that are coming in directly in front of and directly behind the motion of the antenna. In theory, these edges are infinitely high, but for wireless design verification purposes, the cutoff is typically 6dB between power at Fc and power at Fc Fd.
Rayleigh fading is considered a worst case scenario. In rural environments, where the multipath profile includes a few reflected paths combined with a strong line of sight path, the spectral power follows a Rician distribution. The angle of arrival of the direct ray, as well as the ratio of the power between the direct ray and the mulipath rays, determine how much effect the energy from the direct path has on the normal Rayleigh model. The ratio of direct ray and multipath energy is called the K factor. Observing this effect in the frequency domain, what you see is a spike in power. The magnitude of this spike is determined by the K factor, and the frequency shift corresponds to the cosine of the angle of arrival. If the direct ray hits head on, the spike will be at the maximum Doppler spread, Fc Fd. If it arrives at an angle of 45 degrees in front, the spike will be seen at Fc + 0.707 * Fd.
Figure 5: The Rician fading profile includes a strong direct ray that corresponds to a Line of Sight (LOS) path, Doppler shifted in frequency according to its angle of arrival.
Suzuki fading superimposes small scale fading from multipath onto large scale fading from reflection and diffraction. The large scale follows a log-normal distribution and the small scale follows a Rayleigh distribution.
Figure 6: The Suzuki fading profile superimposes small-scale fading effects (the squiggly fluctuations in power) onto large-scale fading effects (the gently rolling power envelope).
The greatest impact that fading has on a wireless device, such as a cellphone, is to reduce the strength of the signal in an unpredictable, vacillatory manner, taxing the resources of the receiver.
Large-scale direct path fading (path loss) results mostly in attenuation of the overall signal level and is distance-dependent. The effect on the device is to reduce signal to noise ratio (SNR) by lowering received signal power.
Shadowing and large-scale reflection can be represented as deviations from the mean path loss described above. These variations, when measured on a log scale, tend to have a normal (Gaussian) distribution. It will typically degrade the signal 6-10dB in addition to the direct path attenuation described above.
Small-scale fading by multipath and Doppler is the most potentially destructive and can be observed at the receive antenna in a number of ways. Frequency selective fading (when the time needed to send one modulated symbol is longer than the average delay in the channel) causes intersymbol interference (ISI), where adjacent symbols on the transmit side seem to melt together on the receive side, making accurate detection more difficult. Flat fading (where all multipath components are received within one symbol detection period) degrades SNR because reflections cause phasor components to cancel each other out. Fast fading (the channel conditions change more rapidly than the signaling rate) distorts the transmitted baseband pulse, which can cause synchronization problems in phase locked loops. Slow fading (the user bandwidth is larger than the Doppler spread) will reduce SNR similar to flat fading. The worst case scenario for non line of sight (NLOS) small scale fading will degrade the signal 20-30dB in the deepest fades when multipath components come in directly out of phase.
What this means for a device designer is that sufficient “fading margin” must be built into the link budget. The signal power must be strong enough at transmission, or the receiver sensitive enough, to withstand a deep fading condition in excess of 40-50dB.
The screen shots shown below what can happen to a wireless signal when it encounters a deep fade. The first signal shown is a QPSK pilot signal. The ideal positions for the symbol points are at the outer four corners of the constellation diagram. They should be well defined and stationary. The second shot shows the same pilot signal in a deep Rayleigh fade. Notice how the trajectory of the received symbols are rotating (multipath phase change) and falling in toward the origin (attenuated in power.) Not too surprising that you dropped the call, is it?
Figure 7a: Ideal QPSK pilot signal.
Figure 7b: QPSK pilot signal under deep Rayleigh fade.
Why is accurate fading simulation tricky?
Current methods of channel simulation operate on an RF in, RF out basis, or an analog I/Q in, RF out basis. In this process, the signal to be faded is downconverted and/or digitized. The fading profile is added to the digital signal and the result is upconverted back to RF. Then the noise is added in. Noise must be kept separate from the fading profile because AWGN is independent of any multipath channel response. There are two major inefficiencies in this process: conversion loss and noise calibration.
Conversion loss occurs every time a signal is sampled from analog or reconstructed to analog. This adds errors to the system that are caused by the test equipment, not the channel or device under test. This uncertainty is caused by non-linear distortion in the instrument's DAC, quantization error, clipping, sampling misinterpretation, carrier feedthrough, and others. All this extra error margin must be taken into account when testing a new wireless device.
The more you can reduce these errors the more accurate simulation you will achieve.
When adding AWGN to the signal, it is crucial to add it at the right level. It must be inserted after fading so that the background noise doesn't get attenuated. But adding noise changes the total power level as well as the carrier to noise ratio. (C/N) In order to calibrate the noise level to the incoming signal power, it is necessary to determine the carrier power after fading. This can be a time-consuming process, since many measurements must be taken at several output power levels to get a statistically correct power distribution function. Towards the end of a device's design cycle, this extra time can be very expensive.
How an instrument manufacturer help?
Agilent Technologies has developed a new pre-conformance fading solution for baseband device designers called Baseband Studio for Fading. It is seamlessly integrated with the E4438C ESG vector signal generator, eliminating calibration issues associated with traditional fading simulators. The baseband signal from the ESG is sent to the fader, faded, and then noise is added, all in the digital domain. In fact, the entire process remains digital right up to the point where it is upconverted to RF.
Adjusting the value of the AWGN is as simple as entering the C/N or Eb/No value in the user interface. The software automatically queries the ESG for the current power levels and data rates for the various channels. When setting the level of AWGN you can specify to hold C, N, C/N, or C+N constant, making receiver testing extremely simple. For example, the total received power can be fixed as the C/N ratio is changed or the C/N ratio can be fixed as the carrier power is changed. Eb/No enables AWGN to be added by setting the ratio of energy transmitted on a specific channel to the overall noise power spectral density. This is useful for testing the robustness of a particular channel for a given coding scheme. C/N and Eb/No can quickly be changed enabling the characterization of receiver performance over a continuum of AWGN levels without having to readjust separate carrier and noise powers.
Figure 8: Setting up the fading parameters is as easy and point and click with the PC software user interface.
Fade to black
As a cell phone user, you know that dropping a call in the middle of a conversation is annoying, if not dangerous in emergency situations. As a wireless device designer, it is imperative to verify receiver performance in real-world conditions as early in the design cycle as possible. The fading properties described in this article are not unavoidable ” they are physical phenomena. But their impact on wireless communications can be mitigated through intelligent design and thorough testing. So the next time you are in a call, you can carry on your conversation in a normal manner without having to run around saying “Can you hear me now?”
If you are a wireless device designer who needs to verify your receiver's baseband performance under real-world conditions, please visit
to learn more about Agilent's solution for fading test.
Bernard Sklar; Rayleigh Fading Channels in Mobile Digital Communication Systems Part I: Characterization; IEEE Communications Magazine; July 1997
Wally Rasmussen; Simulating the Complex Multipath Signal Conditions of the Mobile Radio Environment; Hewlett-Packard Wireless Communications Symposium; 1993
Theodore Rappaport; Wireless Communications: Principles and Practices; Prentice Hall PTR; 1996
About the author
Noah Schmitz holds a Bachelor's of Science degree in Electrical Engineering and Physics from the University of Oklahoma. He joined Agilent Technologies in 1999 as a product marketing engineer in the Microwave Test Accessories group, leading the launch of a new microwave switch. He is now an applications marketing engineer in the Wireless Business Unit's Industry Marketing Group, where he generates measurement application content for customer education and internal training. The majority of his technical experience is centered around cdma2000 and 1xEV-DO technologies, with a recent focus on the broader topic of fading simulation.