# Wireless Channel Modeling

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## 1.2 The Case for Space

This book places particular emphasis on spatial channel modeling, because this is both the most complicated aspect of the wireless channel and, not surprisingly, the least understood. This section provides several arguments for why space is crucial in the future study of wireless communications.

### 1.2.1 Complexities of Wireless Channels

The wireless channel is often neglected in texts and courses on communications. Rarely does an engineer ever study anything more complicated than the additive white Gaussian noise (AWGN) channel. In AWGN channel modeling, the received signal is set equal to the transmitted signal with some proportion of Gaussian white noise added. The AWGN model, pictured in Figure 1.6, works well for very simple communications through band-limited channels corrupted mostly by thermal noise.

Figure 1.6 In contrast to the idealized additive white Gaussian noise (AWGN) channel, the true wireless radio channel has numerous dependencies.

For realistic wireless channels, however, there will be signal distortion that is described by a channel transfer function. Many engineers have working knowledge of "black-box" transfer functions that represent linear, time-invariant channel eAects - those described by a single time dependency using the operation of convolution. The wireless channel, on the other hand, has multiple dependencies. In fact, some channels may have up to 16 diAerent dependencies! Consider the following dependencies (we will discuss some of these in detail in the next chapter):

Frequency: The wireless channel depends on the transmitted frequency.

Time: The wireless channel is time-varying.

Receiver Translation: The wireless channel depends on the position movement (called translation) of the receiver antenna. In three-dimensional space, translation is actually three diAerent scalar dependencies in the wireless channel.

Transmitter Translation: What is true for the receiver is also true for the transmitter. The freedom to change transmitter position in three-dimensional space adds another three dependencies to a wireless channel representation. Receiver Orientation: Translation is only one type of spatial dependency. A receiver antenna may be reoriented in any direction in space, which changes the polarization and gain pattern interaction of the receiver antenna with incoming radio waves. An antenna may be rotated in azimuth or elevation or be tilted laterally. Changes in orientation add up to three dependencies to a wireless channel representation.

Transmitter Orientation: The radio channel also depends on the transmitter antenna orientation. This adds three more dependencies to the wireless channel.

Multi-Element Receiver: The use of multiple antenna elements at the receiver adds one discrete dependency to a wireless channel.

Multi-Element Transmitter: The use of multiple antenna elements at the transmitter adds another discrete dependency.

So there are the 16 total radio channel dependencies. A characterization of the realistic wireless channel can be overwhelming.

Note that most of the dependencies can be categorized as spatial aspects of the wireless channel, summarized in Figure 1.7. Translation, orientation, and multi-element dependencies all influence the spatial filtering of the channel. They also happen to be the least-understood aspects of the wireless channel. Indeed, space really is the final frontier for channel modeling.

Figure 1.7 There are many types of spatial dependencies in a wireless channel: antenna translation, antenna rotation, and multiple ports for both transmitter (TX) and receiver (RX).

There is both a pessimistic and optimistic way of viewing all of these dependencies. Each dependency is another layer of complexity for understanding the transmission of wireless information. Each dependency is also a potential source of fading and unpredictability. On the other hand, each dependency may be viewed as an opportunity to increase channel capacity. Just as bandwidth or transmission time can be increased to send additional data, the spatial dimensions of a wireless channel may also be exploited similarly to increase capacity, so the 16 dependencies implies 16 potential opportunities to increase channel capacity. There are many fascinating design issues involving wireless channels with multiple dependencies.

### 1.2.2 Channel Primacy in Communications

When Shannon derived channel capacity equations, he showed that the fundamental limit on data rate in a communications system depended almost solely on the amount of power (in proportion to noise) delivered to a receiver. This limit is universal, independent of any of the signal-processing operations that may occur at either the transmitter or the receiver. The principle of the Shannon limit has key implications for wireless system design.

The modern approach to digital communication design requires wireless engineers to use a baseband block-diagram approach for building transmitters and receivers that span a radio link [Skl01]. In this scheme, the transmitter performs operations such as source coding, channel coding, multiplexing, modulation, and multiple access operations on a stream (or streams) of information. Each of these operations is represented by a functional block in Figure 1.8. The operation of the receiver is functionally the inverse of the transmitter, performing block operations in the reverse order to recover the original information.

Figure 1.8 Some basic operations of a digital wireless communications system may be broken into functional blocks. (See B. Sklar's textbook [Skl01] for an outstanding, exhaustive block-diagram analysis of digital systems.)

In between the baseband block operations of transmitter and receiver, the signal passes through the wireless channel and the radio-frequency (RF)/antenna hardware that physically interacts with this channel. It is this part of the transmission, on the right side of Figure 1.8, that determines Shannon channel capacity. Thus, the communications engineer is at the mercy of whatever happens in this part of the link. The engineer selects appropriate blocks from an arsenal of signal-processing schemes and, upon success, has designed a system that approaches the available channel capacity. Engineering the baseband blocks of a digital communications link is a very close-ended problem: We know that an optimum design is achieved if the link performance approaches the Shannon limit.

Not so for the RF engineer, who works with the hardware and antennas that interface with the wireless channel. The physical and spatial interface with the radio channel is an open-ended problem, with no guarantee that even a successful solution is an optimal solution. From this viewpoint, studying the wireless channel interface has some of the richest design possibilities.

### 1.2.3 Wasted Space

Commercial wireless has mostly operated under the single-port paradigm: A single antenna element - usually a metal loop or whip - is attached to a user terminal. The first AM and FM radios, walkie-talkies, and pagers all used a single antenna. Despite all of the vaunted advances in signal processing and radio portability, a survey of digital handsets and wireless LAN terminals at the start of the 21st century would show the exact same single-port architecture. The single antenna element for radio terminals is a lot like the lead-acid battery for cars: A century of innovation has passed them by.

The single-port architecture has two Achilles' heels that make it terminally unattractive for radio design. First of all, a single-port receiver is always susceptible to catastrophic fading. In a spatial fading channel, there are receiver positions in space that cannot accommodate wireless communications. These "blind spots" occur unpredictably, even in environments with high average signal strength. Thus, all receivers operate in the fading equivalent of a mine field, encountering sporadic pockets of fades that threaten to sever the wireless link.

Space itself is not the only source of catastrophic fading. The immediate environment of the single antenna element can be problematic, as coupling with the human body, close-in objects, and even the casing and circuitry of the receiver itself can skew the pattern and radiation impedance of the antenna. There is no bullet-proof radio design for a single, static antenna element. When multiband operation is considered - using multiple, noncontiguous frequency bands - the antenna problem can seem hopeless.

Without an additional spatial port, the receiver is stuck with a single channel. The inability to overcome deep fades with a single-port receiver is the main reason cellular phones drop calls in mid-conversation. If there were additional spatial ports, the phone could at least employ some form of selection diversity (discussed in Chapter 10) and use an alternative signal if one port experiences a catastrophic fade.

The second critical problem with the single-port architecture is the wasted opportunities for power coupling into the receiver. Consider the case of the simple whip antenna fixed to the typical cellular handset. The eAective electromagnetic aperture - roughly the area of space from which an antenna can sink radio power -is small compared to the handset itself. Most of the propagating radio power that impinges upon a handset is unused, reflected oA into free space.

As Figure 1.9 shows, it would be much more desirable to design a handset that could somehow absorb radio power across its entire body. Furthermore, multipath radio waves have a polarization that cannot couple completely into any single antenna. From the electric-field point of view, there are three distinct polarizations (due to the three-dimensionality of space). Moreover, researchers have even shown benefits from separate sensing of the three magnetic-field components of propagating multipath waves in addition to the three electric-field components [And01].

Figure 1.9 In a multipath channel, a single-port radio wastes much of the impinging signal power.

Clearly a lot of potential radio power and opportunity is going to waste in a single-port radio. More power and multiple spatial ports can overcome the thermal noise and in-band interference that signal processing alone cannot remove.

Needless to say, space-wasting receivers have persisted for good reasons. There are two major challenges facing multiport receiver designs. First, multiplying spatial ports on a receiver also multiplies complexity in the radio-frequency hardware - a critical expense in the production of user terminals. Second, it is diLcult and expensive to incorporate more than one low-profile antenna into a terminal. This problem is particularly acute for handsets, where aesthetics is important for user-acceptance. Nobody wants to carry around a pin cushion of antennas.

Still, multiport receivers are a certainty for wireless communication that desires to maximize data transmission. If the goal is to develop a receiver that can sustain a reliably high data rate, then the goal must be a power-stingy receiver that wastes no space.