Channel impairments can be disruptive on RF-based communications devices. Impairments such as fading and multipath, which are often unpredictable, can hinder wireless communications. Because channel impairments are often unpredictable and not repeatable, many engineers face the challenge of supplying a prototype receiver with a reliable model of the real-world signal environment. Fortunately, by understanding the causes of these impairments through the use of modern measurement techniques, including the use of recorded test signals, it is possible to check a receiver’s capabilities of operating effectively in the presence of channel impairments.

Free-space signal propagation can be predicted with reasonable accuracy under ideal conditions. However, factors such as buildings, geographic topography, and other obstructions can significantly impact signal strength in a real world environment. Unfortunately, large-scale channel fading often produces broadcasts that are subject to variations as a result of reflection, diffraction, and scattering.

One of the most common models for predicting signal propagation in free space is the two-ray ground reflection model (Fig. 1).¹ In this model, signals traveling directly from the transmitter to the receiver follow a shorter path than those reflected from other surfaces. According to the law of reflection, the initial signal phase, Θ_i, is equal to the final signal phase, Θ₀. Because of this law, it is possible to determine the difference in distance (for a given wavelength) between the paths of the line-of-sight (LOS) signal component (E_los) and the ground-reflected signal component (E_G). With some simple math, it is possible to determine the difference in distance, d, as shown in Eq. 1.

For RF and microwave signals, even a small difference in the signal propagation path (d,) between a LOS and a reflected signal can produce a substantial effect on the phase of the aggregate of the signal observed by the receiver. In fact, it is possible to calculate the difference in phase between the two paths with Eq. 2.

Equation 2 illustrates that especially for high-frequency signals, where the wavelength (λ) is short, even small changes in the distance between the transmitter and receiver can have substantial changes in phase of the aggregate signal. Moreover, because the LOS signal and the reflected signal are 180 deg. out of phase with one another, the two waves will periodically add or cancel one another, depending on the distance between the transmitter and receiver.

Over long distances, the antenna height is negligible, and the large-scale fading observed in these scenarios is not significantly affected by ground reflections. However, over shorter distances, ground reflections can have a substantial impact on the power observed at the receiver.

Diffraction is a phenomenon by which electromagnetic (EM) waves can propagate around buildings, mountains, and other physically large objects. Like reflection, diffraction can also produce substantial fluctuations in the signal strength observed by a wireless receiver. In addition, this effect becomes more prominent in urban environments, where a large number of buildings are positioned close together. To understand this, consider how diffraction can affect signal strength (Fig. 2). A large object may prevent LOS signal propagation, but EM waves will actually wrap around the object, producing an attenuated but usable signal. Some theoretical models may help to understand just how much signal attenuation can occur as a result of diffraction.

One of the more popular models for analyzing the effects of diffraction on EM waves is the Knife-edge diffraction model.¹ It provides a mechanism for estimating signal strength as a function of wavelength, object height, and distance between the transmitter and the receiver. Based on a geometric model of the physical environment, it is possible to calculate a Fresnel-Kirchoff diffraction parameter using Eq. 3.

As Eq. 3 shows, the diffraction parameter (and hence loss) increases with the height of the obstructing object. In addition, since wavelength, λ  is in the denominator, higher-frequency microwave signals are much more susceptible to attenuation from physical objects. Based on the calculated Fresnel-Kirchoff diffraction parameter, it is possible to calculate the expected loss in signal strength as a result of diffraction. William C. Y. Lee, a pioneer in wireless communications technology, actually approximated the loss/gain due to diffraction, G_d (dB), as a function of the Fresnel- Kirchoff diffraction parameter, v. His derivation follows in Eq. 4.

Figure 3 graphically depicts the diffraction gain/loss, G_d (dB), as a function of the Fresnel-Kirchoff diffraction parameter. Based on the equations above, consider a scenario where a transmitter and receiver are 1 km away (d₁ = d₂ = 500 m) and a 100-m object (such as an urban office building) is equidistant between them. Based on these distances, a 1 GHz signal (λ = 0.3) will have a Fresnel- Kirchhoff diffraction parameter with a value of 11.457. Thus, the receiver will observe a signal strength loss of approximately 34.2 dB. As this exercise illustrates, even a single object (if tall enough) can result in significant loss of signal strength. Thus, compensation for fluctuations in signal strength is an important requirement of wireless receiver design.

While large-scale channel fading often causes rapid changes in signal strength, small-scale channel fading produces distortion in either the phase or amplitude of an EM wave. In a typical environment, a receiver will pull in a signal comprised of signal components from many different signal paths. In this case, an EM wave from each signal path will arrive at the receiver at a different time. Unfortunately, such multipath propagation causes intersymbol interference (ISI) in which symbol n - 1 will distort the phase and amplitude of symbol n. While ISI does not significantly affect the overall power level of a received signal, it does affect the modulation quality.

Two models commonly used to emulate multipath fading are the Rayleigh and Rician fading models. The Rician model includes both LOS propagation between the transmitter and the receiver and non-LOS signal propagation. In this model, a K parameter represents the power of the LOS transmission relative to the aggregate sum of the multipath signal products. When the K parameter is large, multipath products are minimal and the ISI is reduced. When K is small, ISI becomes more significant. Figure 4 shows this effect, comparing the K parameter for a 16 QAM signal with a symbol rate of 3.84 MSymbols/s and the influence of a Doppler frequency shift of 5 kHz.

As Fig. 4 shows, higher ISI significantly reduces the modulation quality, as measured in terms of error vector magnitude (EVM), in situations where LOS signal propagation is not possible. As a result, receiver validation often requires multipath channel emulation to ensure that the receiver will behave as expected in its actual operating environment.

Both large-scale and small-scale fading pose design challenges. To maximum a receiver’s dynamic range, most receivers implement an automatic- gain-control (AGC) circuit to compensate for rapid changes in received signal strength. The ADC is typically placed immediately following a preselector filter in a wireless receiver (Fig. 5).⁴ The AGC ensures that the mixer and intermediate-frequency (IF) levels remain relatively constant, allowing the receiver to achieve adequate dynamic range even with rapid fluctuations in signal strength.

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