2.3.1 The Physics of Propagation
An important issue in wireless communications is of course the amount of information that can be carried over a wireless channel, in terms of bit rate. According to information theory, an upper bound on the bit rateWof any channel of bandwidthHHz whose signal to thermal noise ratio isS/N, is given by Shannon’s formula:
W ẳHlog2 11 S N
ð2:2ị Equation (2.2) applies to any transmission media, including wireless transmission. However, as already mentioned, Equation (2.2) gives only the maximum bit rate that can be achieved on a channel. In real wireless channels the bit rates achieved can be significantly lower, since
apart from the thermal noise, there exist a number of impairments on the wireless channels that cause reception errors and thus lower the achievable bit rates. Most of these impairments stem from the physics of wave propagation. Understanding of the wave propagation mechan- ism is thus of increased importance, since it provides a means for predicting the coverage area of a transmitter and the interference experienced at the receiver. Although the mechanism that governs propagation of electromagnetic waves through space is of increased complexity, it can generally be attributed to the following phenomena: free space path loss, Doppler Shift which is caused by station mobility and the propagation mechanisms of reflection, scattering and diffraction which cause signal fading.
2.3.1.1 Free Space Path Loss
This accounts for signal attenuation due to distance between the transmitter and the receiver.
In free space, the received power is proportional tor22, whereris the distance between the transmitter and the receiver. However, this rule is rarely used as the propagation phenomena described later significantly impact the quality of signal reception.
2.3.1.2 Doppler Shift
Station mobility gives rise to the phenomenon of Doppler shift. A typical example of this phenomenon is the change in the sound of an ambulance passing by. Doppler shift is caused when a signal transmitter and receiver are moving relative to one another. In such a situation the frequency of the received signal will not be the same as that of the source. When they are moving towards each other the frequency of the received signal is higher than that of the source, and when they are moving away from each other the frequency decreases. This phenomenon becomes important when developing mobile radio systems.
2.3.1.3 Propagation Mechanisms and Slow/Fast Fading
As mentioned above, electromagnetic waves generally experience three propagation mechan- isms: reflection, scattering and diffraction. Reflection occurs when an electromagnetic wave falls on an object with dimensions very large compared to the wave’s wavelength. Scattering occurs when the signal is obstructed by objects with dimensions in the order of the wave- length of the electromagnetic wave. This phenomenon causes the energy of the signal to be transmitted over different directions and is the most difficult to predict. Finally, diffraction, also known as shadowing, occurs when an electromagnetic wave falls on an impenetrable object. In this case, secondary waves are formed behind the obstructing body despite the lack of line-of-sight (LOS) between the transmitter and the receiver. However, these waves have less power than the original one. The amount of diffraction is dependent on the radio frequency used, with low frequency signals diffracting more than high frequency signals.
Thus, high frequency signals, especially, Ultra High Frequencies (UHF), and microwave signals require LOS for adequate signal strength. Shadowed areas are often large, resulting in the rate of change of the signal power being slow. Thus, shadowing is also referred to as slow fading. Reflection scattering and diffraction are shown in Figure 2.5.
In a wireless channel, the signal from the transmitter may be reflected from objects (such as hills, buildings, etc.) resulting in echoes of the signal propagating over different paths with
Wireless Communications Principles and Fundamentals 33
different path lengths. This phenomenon is known as multipath propagation and can possibly lead to fluctuations in received signal power. This is due to the fact that echoes travel a larger distance due to reflections and they arrive at the receiver after the original signal. Therefore, the receiver sees the original signal followed by echoes that possibly distort the reception of the original signal by causing small-scale fluctuations in the received signal. The time dura- tion between the reception of the first signal and the reception of the last echo is known as the channel’s delay spread.
Because these small-scale fluctuations are experienced over very short distances (typically at half wavelength distances), multipath fading is also referred to either as fast fading or small-scale fading. When a LOS exists between the receiver and the transmitter, this kind of fading is known as Ricean fading. When a LOS does not exist, it is known as Rayleigh fading.
Multipath fading causes the received signal power to vary rapidly even by three or four orders of magnitude when the receiver moves by only a fraction of the signal’s wavelength. These fluctuations are due to the fact that the echoes of the signal arrive with different phases at the receiver and thus their sum behaves like a noise signal. When the path lengths followed by echoes differ by a multiple of half of the signal’s wavelength, arriving signals may partially or totally cancel each other. Partial signal cancellation at the receiver due to multipath propaga- tion is shown in Figure 2.6. Despite the rapid small-scale fluctuations due to multipath propagation, the average received signal power, which is computed over receiver movements of 10–40 wavelengths and used by the mobile receiver in roaming and power control deci- sions, is characterized by very small variations in the large scale, as shown in Figure 2.7, and decreases only when the transmitter moves away from the receiver over significantly large distances.
Multipath propagation can lead to the presence of energy from a previous symbol during the detection time of the current symbol which has catastrophic effects at signal reception.
Figure 2.5 Reflection (R), diffraction (D) and scattering (S)
This is known as intersymbol interference (ISI) and occurs when the delay spread of a channel is comparable to symbol detection time [1]. This criterion is equivalent to
B.Bc ð2:3ị
whereBis the transmitted signal bandwidth (equivalently, the transmitted symbol rate), and Bcis the channel’s coherence bandwidth, which is the frequency band over which the fading of different frequency components of the channel is essentially the same. When Equation
Wireless Communications Principles and Fundamentals 35
Figure 2.6 Partial signal cancellation due to multipath propagation
Figure 2.7 Variation of signal level according to transmitter–receiver distance
(2.3) applies, the channel is said to be frequency selective or wideband, otherwise it is said to be flat or narrowband. The fading type is known as frequency selective or flat, respectively.
The zones affected by multipath fading tend to be small, multiple areas of space where periodic attenuation of a received signal is experienced. In other words, the received signal strength will fluctuate, causing a momentary, but repetitive, degradation in quality.
2.3.2 Wireless Propagation Modeling
As can be seen from the above discussion, in a wireless system, the actual signal arriving at a receiver is the sum of components that derive from several difficult to predict propagation phenomena. Thus, the need for a model that predicts the signal arriving at the receiver arises.
Such models are known as propagation models [2] and are essentially a set of mathematical expressions, algorithms and diagrams that predict the propagation of a signal in a given environment. Propagation models are either empirical (also known as statistical), theoretical (also known as deterministic) or a combination of the above.
Empirical models describe the radio characteristics of an environment based on measure- ments made in several other environments. An obvious advantage of empirical models is the fact that they implicitly take into account all the factors that affect signal propagation albeit these might not be separately identified. Furthermore, such models are computationally efficient. However, the accuracy of empirical models is affected by the accuracy of the measurements that are used. Moreover, the accuracy of such models depends on the similarity of the environment where the measurements were made and the environment to be analyzed.
Theoretical models base their predictions not on measurements but on principles of wave theory. Consequently, theoretical models are independent of measurements in specific envir- onments and thus their predictions are more accurate for a wide range of different environ- ments. However, their disadvantage is the fact that they are expressed by algorithms that are very complex and thus computationally inefficient. For that reason, theoretical models are often used only in indoor and small outdoor areas where they obviously provide greater accuracy than empirical models.
In terms of the radio environment they describe, propagation models can be categorized into indoor and outdoor models. Moreover outdoor models are subdivided into macrocell models describing propagation over large outdoor areas and microcell models describing propagation over small outdoor areas (typically city blocks). A large number of propagation models have been proposed but detailed presentation is outside the scope of this chapter. The interested reader is referred to corresponding technical papers [2]. In the remainder of this section we describe the behavior of outdoor macrocell/microcell and indoor environments and we describe how propagation occurs in these situations and the factors that affect it.
2.3.2.1 Macrocells
The concept of the cell is described later, however for the purposes of this discussion, a macrocell is considered to be a relatively large area that is under the coverage of a BS.
Macrocells were the basis for organization of the first generation of cellular systems. As a result, the need to predict the received signal power arose first for macrocells.
When free space loss was discussed, it was mentioned that although in free space, the received power is proportional tor22, whereris the distance between the transmitter and the
receiver; this rule, however, is rarely used as the other propagation phenomena affect received signal power. In real situations a good estimator for the received signal strengthPðrịfor a distancerbetween the transmitter and the receiver is given by
Pðrị ẳkr2n ð2:4ị
wherekis a constant and the exponentnis a parameter that describes the environment. A value ofnẳ2 describes propagation into free space, while values ofnbetween 2 and 4 are used for modeling macrocells. The form of Equation (2.4) in a log-log scale is shown in Figure 2.8.
The same power law model also applies to path loss. Thus, the average path loss at a distanceris (in dB)2
PLðrị ẳPLðr0ị110nlog r
r0 ð2:5ị
wherer0is a reference distance that must be appropriately selected and is typically 1 km for macrocells. However, the path loss model of Equation (2.5) does not take into account the fact that for a certain transmitter–receiver distance, different path loss values are possible due to the fact that shadowing may occur in some locations and not in others. To take this fact into account, Equation (2.5) now becomes [3]
Wireless Communications Principles and Fundamentals 37
Figure 2.8 Log-log form of Equation (2.4)
2When we say that the relative strength of signal X, P(X) to that of signal Y, P(Y) is D dB then Dẳ10logðPðXị=PðYịị. Thus dB is a convention used to measure the relative strength of two signals and has no physical meaning, since the relative strength of two signals is just a number.
PLðrị ẳPLðr0ị110nlog r
r0 1Xs ð2:6ị
whereXsis a zero-mean Gaussian-distributed random variable with standard deviations. Macrocells were the basis for the first generation of cellular systems. The first propagation model for such systems was made by Okomura and was based on comprehensive measure- ments of Japanese environments. The model of Okomura was later enhanced by Hata by transforming it into parametric formulas. These works produced results that confirm the above path loss model and although strictly empirical, they have proven to be robust not only for Japanese environments but in other environments as well.
2.3.2.2 Microcells
Microcells cover much smaller regions than macrocells. Propagation in microcells differs significantly from that observed in macrocells. The smaller area of a microcell results in smaller delay spreads. Microcells are most commonly used in densely populated areas such as parts of a city. The model of Equation (2.6) also describes path loss in microcells, with a typicalr0value of 100 m.
Andersen et al. [3] mention the concept of a ‘street microcell’, which is shown in Figure 2.9. This kind of microcell is created by placing transmitter antennas lower than surrounding buildings. Thus, most of the signal power propagates along streets. Even in this case nearby buildings play an important role regarding received signal quality. Assuming the situation of
Figure 2.9 Path loss situations in a street microcell
a street microcell that has the form of a grid comprising square buildings, there exist two possible situations.
† If a LOS exists between the transmitter and the receiver (e.g. receiver A in Figure 2.9), then the path loss model comprises two parts. Up to a certain breakpoint, the exponentnis around 2, as in free-space loss. However, beyond this breakpoint the signal strength decreases more steeply with a value ofn around 4. Andersen et al. [3] mention that the breakpoint is given by 2phbhm/l, wherehbis the antenna height of the base station andhm is the antenna height of the mobile station.
† If a LOS does not exist between the transmitter and the receiver (e.g. receiver B in Figure 2.9), then the path loss is greater for the receiver. Up to the intersection of the two streets, the exponentnis around 2, however beyond the intersectionntakes values between 4 and 8.
Various propagation models for street microcells have been proposed based on ray-optic theory. The preliminary two-ray model calculates received signals for LOS channels by taking into account a direct ray and a ground-reflected ray. Enhancements of this model use more rays for greater accuracy. Hence, the four-ray model also assumes two rays that stem from reflection by nearby buildings, the six-ray model assumes double reflected rays by buildings, etc. Generally, model using a large number of rays is more accurate than a model assuming a smaller number of rays. Other methods also exist that try to take into account corner diffraction of signals and partially overlapping microcells.
2.3.2.3 Indoor propagation and its differences to outdoor propagation
Indoor propagation has attracted significant attention due to the rising popularity of indoor voice and data communication systems, such as wireless local area networks (WLANs), cordless telephones, etc. Although the phenomena that govern indoor propagation are the same as those that govern outdoors (reflection, diffraction, scattering), there are several differences [3] between indoor and outdoor environments:
† Dependence on building type. Radio propagation is more difficult to predict in indoor environments and on a number of factors relating to the building (architecture, materials used for building construction, the way which people move throughout the building, whether windows and doors are open or closed). Thus, several characteristics of a building directly impact propagation of signals within the building. A great number of measure- ments have been performed and researchers have classified buildings into various types, with buildings in each type inducing different propagation behavior to signals. The types of buildings mentioned in the literature [3] are homes in suburban areas, homes in urban areas, office buildings with fixed walls, open office buildings with movable soft panels of height less than the ceiling dividing the office area, factories, grocery stores, retail stores and sports arenas. Inside buildings, two types of transmitter/receiver path exist, based on whether the transmitter is visible to the receiver: LOS paths and obstructed (OBS) paths.
Buildings types are summarized in Figure 2.10, which also gives values fornandsfor transmission at the specified frequency in these environments [3]. The above discussion implies that the path loss model of Equation (2.6) is also good for indoor channels too; a typicalr0value is 1 m.
Wireless Communications Principles and Fundamentals 39
† Delay spread.Inside a building, objects that cause scattering are usually located much closer to the direct propagation path between the transmitter and the receiver. Thus, delay spread due to multipath propagation is typically smaller in indoor systems. Buildings that have few metal and hard partitions have rms delay spreads between 30 and 60 ns, whereas for larger buildings with more metal this number can be as large as 300 ns.
† Propagation between floors. Typically, there will be a reuse of frequencies between different floors of a building in an effort to increase spectrum efficiency. Thus, inter- floor interference will significantly depend on the inter-floor propagation characteristics.
This makes prediction of propagation between floors an important factor. Although this problem is quite difficult some general rules exist: (a) the type of material that separates floors impacts signal attenuation between the floors; solid steel planks induce more signal attenuation than planks that are produced by pouring concrete over metal layers; (b) buildings with a square footprint induce greater attenuation than buildings with a rectan- gular footprint due to signals traveling between floors; (c) the greatest path loss of a signal crossing floors occurs when the signal passes from the originating floor to an adjacent one.
After this point, propagation to the next floors is characterized by smaller path losses for each floor crossed by the signal. This phenomenon is probably due to diffraction of radio energy across the sides of the building and arrival at distant floors of signal energy scattered from nearby buildings. For separation of one floor, Andersen et al. [3] mention a typical loss of 15 dB with an additional loss of 6–10 dB occurring for the next four floors.
For floors further away, the overall path loss increases by a few dB for each floor.
† Outdoor to indoor signal penetration.Indoor environments are often affected by signals originating from other buildings or outdoor systems. This phenomenon should be taken into account since it could generate problems in cases where such systems use the same frequencies. Although exact models for this phenomenon do not exist, Andersen et al. [3]
make some general remarks. It appears that outdoor to indoor signal attenuation decreases for the higher floors of a building. This is due to the fact that at such floors a LOS path with the antenna of the outdoor system may exist. In some reports, however, this is accom- panied by an attenuation increase for floors higher than a certain level, possibly due to shadowing by nearby buildings. Moreover, signal penetration into buildings is reported to be a function of signal frequency with attenuation decreasing for an increasing signal frequency.
Figure 2.10 Values for exponentnandsfor various building types
2.3.3 Bit Error Rate (BER) Modeling of Wireless Channels
Although there are a number electromagnetic wave propagation impairments, such as free- space loss and thermal noise, fading is the primary cause of reception errors in wireless communications. In the previous paragraphs, the discussion was made in terms of received signal strength. However, in most cases one is interested in viewing the effects of wireless propagation impairments from a higher point of view: the way in which bit errors occur.
Wireless channels are more prone to bit errors than wired channels. Apart from the higher BER of wireless channels compared to wired channels, measurements also indicate a differ- ence in the pattern of bit error occurrence. In contrast to the random nature of bit error occurrence in wired channels, bit errors over wireless channels occur in bursts and Markov chain model approximations have been shown to be adequate for wireless channel bit error modeling [4]. Such models comprise two states, a good (G) and a bad (B) state, and para- meters that define the transition procedure between the two states. State G is error free, thus bit errors only occur in state B. Future states are independent of past states and depend only on the present state. In other words, the model is memoryless. Figure 2.11 depicts the transition diagram of a Markov chain.Pis the probability of the channel state transiting from state G to state B,pdefines the probability of transition from state B to state G,Qandqthe probabilities of the channel remaining in states G and B, respectively. Obviously Qẳ12P and qẳ12p. In state B, bit errors are assumed to occur with probabilityh. Values for the model parameters are obtained through statistical measurements of particular channels. These values are different for different channels and physical environments. Markov chain models can efficiently approximate the behavior of a wireless channel and are widely used in simula- tions of wireless systems.