Tse and Viswanath:Fundamentals of Wireless Communication 20 of new tradeoff-optimal space-time codes.In particular,we discuss an approach to design universal space-time codes that are tradeoff-optimal. Finally,Cha pter 10 studies the e of multiple tran tand receive antennas in mul- tiuser and lar systems;this is als d space-divi Here,in addition to providing spatial multiplexing and diversity,multiple antennas can also be used to mitigate interference between different users.In the uplink.inter ference mitigation is done at the base station via the SIC receiver.In the downlink, interference mitigation is also done at the base station and this requires precoding:we study a precoding scheme,called Costa or dirt-paper precoding,that is the natural us to relate the performanc of a SIC receiver in the uplink with a corresponding precoding scheme in a reciproca downlink.The Arraycomm system is used as an example of an SDMA cellular system
Tse and Viswanath: Fundamentals of Wireless Communication 20 of new tradeoff-optimal space-time codes. In particular, we discuss an approach to design universal space-time codes that are tradeoff-optimal. Finally, Chapter 10 studies the use of multiple transmit and receive antennas in multiuser and cellular systems; this is also called space-division multiple access (SDMA). Here, in addition to providing spatial multiplexing and diversity, multiple antennas can also be used to mitigate interference between different users. In the uplink, interference mitigation is done at the base station via the SIC receiver. In the downlink, interference mitigation is also done at the base station and this requires precoding: we study a precoding scheme, called Costa or dirt-paper precoding, that is the natural analog of the SIC receiver in the uplink. This study allows us to relate the performance of a SIC receiver in the uplink with a corresponding precoding scheme in a reciprocal downlink. The Arraycomm system is used as an example of an SDMA cellular system
Chapter 2 The Wireless Channel a good understanding of the wireless channel.its key physical parameters and the odeling issues,lays the foundation for the rest of the book.This is the goal of this chapter A defining characteristic of the mobile wireless channel is the variations of the channel strength over time and over frequency.The variations can be roughly divided into two types: .large-scale fading,due to path loss of signal as a function of distance and shad owing by large objects such as buildings and hills.This occurs as the mobile moves through a distance of the order of the cell size,and is typically frequency independent. .small-scale fading,due to the constructive and destructive interference of the multiple signal paths between the transmitter and receiver.This occurs at the spatial scale of the order of the carrier wavelength,and is frequency dependent. We will talk about both types of fading in this chapter,but with more emphasis on the latter.Large-scale fading is more relevant to issues such as cell-site planning Small-scale multipath fading is more relevant to the design of reliable and efficient communication systems-the focus of this book. We start with the r hysical modeling of the wireless channel in terms of electro magnetic waves We then derive an time varying model for the channel,and define some important physical parameters.Finally we introduce a few statistical models of the channel variation over time and over frequency. 2.1 Physical Modeling for Wireless Channels Wireless channels operate through electromagnetic radiation from the transmitter to the receiver.In principle,one could solve the electromagnetic field equations,in con- 2
Chapter 2 The Wireless Channel A good understanding of the wireless channel, its key physical parameters and the modeling issues, lays the foundation for the rest of the book. This is the goal of this chapter. A defining characteristic of the mobile wireless channel is the variations of the channel strength over time and over frequency. The variations can be roughly divided into two types: • large-scale fading, due to path loss of signal as a function of distance and shadowing by large objects such as buildings and hills. This occurs as the mobile moves through a distance of the order of the cell size, and is typically frequency independent. • small-scale fading, due to the constructive and destructive interference of the multiple signal paths between the transmitter and receiver. This occurs at the spatial scale of the order of the carrier wavelength, and is frequency dependent. We will talk about both types of fading in this chapter, but with more emphasis on the latter. Large-scale fading is more relevant to issues such as cell-site planning. Small-scale multipath fading is more relevant to the design of reliable and efficient communication systems – the focus of this book. We start with the physical modeling of the wireless channel in terms of electromagnetic waves. We then derive an input-output linear time varying model for the channel, and define some important physical parameters. Finally we introduce a few statistical models of the channel variation over time and over frequency. 2.1 Physical Modeling for Wireless Channels Wireless channels operate through electromagnetic radiation from the transmitter to the receiver. In principle, one could solve the electromagnetic field equations, in con- 21
Tse and Viswanath:Fundamentals of Wireless Communication 22 L11111141 Figure 21:Channel quality varies over multiple time scales.At a slow scale,channel varies due to large-scale fading effects.At a fast scale,channel varies due to multipath effects. junction with the transmitted signal,to find the electromagnetic field impinging on the receiver antenna.This would have to be done taking into account the obstructions caused by ground,buildings,vehicles,etc.in the vicinity of this electromagnetic wave. Cellular communication in the USA is limited by the Federal Communication Com- mission (FCC),and by similar authorities in other countries,to one of three frequency bands,one around 0.9 GHz,one around 1.9 GHz,and one around 5.8 GHz.The wave ngth A(f)of electroma ic radiation at any given freq s given by f is where c= 3×10°m/s is the speed of The wavelength in the cellular bands is thus a fraction of a meter,so to calculate the electromagnetic field at a receiver the locations of the receiver and the obstructions would have to be known within sub- meter accuracies.The electromagnetic field equations are therefore too complex to solve,especially on the fly for mobile users.Thus,we have to ask what we really need to know about these channels nd what appr imations might be easonable. One of the important questi ns is where to cho the b ations,and what range of power levels are then necessary on the down k and uplink channels To some extent this question must be answered experimentally,but it certainly helps to have a sense of what types of phenomena to expect.Another major question is what types of modulation and detection techniques look promising.Here again,we need a sense of what types of phenomena to expect.To address this,we will construct stochastic models of the channel ming that different channel behaviors app with different changeovert e(with specific stochastic propertie We will return to the question of why such stochastic models are appropriate,but for r咖inktonwan o o心ag胜 se non-neglig
Tse and Viswanath: Fundamentals of Wireless Communication 22 Time Channel Quality Figure 2.1: Channel quality varies over multiple time scales. At a slow scale, channel varies due to large-scale fading effects. At a fast scale, channel varies due to multipath effects. junction with the transmitted signal, to find the electromagnetic field impinging on the receiver antenna. This would have to be done taking into account the obstructions1 caused by ground, buildings, vehicles, etc. in the vicinity of this electromagnetic wave. Cellular communication in the USA is limited by the Federal Communication Commission (FCC), and by similar authorities in other countries, to one of three frequency bands, one around 0.9 GHz, one around 1.9 GHz, and one around 5.8 GHz. The wavelength Λ(f) of electromagnetic radiation at any given frequency f is given by Λ = c/f, where c = 3 × 108 m/s is the speed of light. The wavelength in these cellular bands is thus a fraction of a meter, so to calculate the electromagnetic field at a receiver, the locations of the receiver and the obstructions would have to be known within submeter accuracies. The electromagnetic field equations are therefore too complex to solve, especially on the fly for mobile users. Thus, we have to ask what we really need to know about these channels, and what approximations might be reasonable. One of the important questions is where to choose to place the base stations, and what range of power levels are then necessary on the downlink and uplink channels. To some extent this question must be answered experimentally, but it certainly helps to have a sense of what types of phenomena to expect. Another major question is what types of modulation and detection techniques look promising. Here again, we need a sense of what types of phenomena to expect. To address this, we will construct stochastic models of the channel, assuming that different channel behaviors appear with different probabilities, and change over time (with specific stochastic properties). We will return to the question of why such stochastic models are appropriate, but for 1By obstructions, we mean not only objects in the line-of-sight between transmitter and receiver, but also objects in locations that cause non-negligible changes in the electromagnetic field at the receiver; we shall see examples of such obstructions later
Tse and Viswanath:Fundamentals of Wireless Communication 23 now we simply want to explore the gross characteristics of these channels.Let us start by looking at several over-idealized examples. 2.1.1 Free space,fixed transmitting and receive antennas In the far field,2 the electric to the direction of propagation from the antenna.They are also proportional to each other,so it is sufficient to know only one of them (just as in wired communication, where we view a signal as simply a voltage waveform or a current waveform).In response to a transmitted sinusoid cos2ft,we can express the electric far field at time t as E(ft,(r0.0vf)cos2mf(t-) 2.1) Here,(r,6,)represents the point u in space at which the electric field is being mea- sured,where r is the distance from the transmitting antenna to u and where (, represents the vertical and horizontal angles from the antenna to u,respectively.The ing an the caling g factor to accou nt for antenna losses. Note that the phase of the field d varies with r/c,corre sponding to the delay caused by the radiation travelling at the speed of light. We are not concerned here with actually finding the radiation pattern for any given antenna.but only with recognizing that antennas have radiation patterns.and that the free space far field behaves as above. It is imp es. the electric field de powe are meter the f ree spa wav decrease This is expecte d,since if we loo at concentric spheres of increasing radiu r around the antenna,the total power radiated through the sphere remains constant, but the surface area increases as r2.Thus,the power per unit area must decrease as r-2.We will see shortly that this r-2 reduction of power with distance is often not valid when there are obstructions to free space nronagation Next,suppose there is a fixed receive antenna at the location u=(r,0).The re ceived waveform(in the absence of noise)in response to the above transmitted sinusoid is then E,,tw=0,女)cos2afL-且 (2.2 where o(0.v.f)is the product of the antenna patterns of transmitting and receive antenas in the given direction.Our approach to (22)is a bit odd since we started with the free space field at u in the ab of an antenna.Placinga receive antenna
Tse and Viswanath: Fundamentals of Wireless Communication 23 now we simply want to explore the gross characteristics of these channels. Let us start by looking at several over-idealized examples. 2.1.1 Free space, fixed transmitting and receive antennas First consider a fixed antenna radiating into free space. In the far field,2 the electric field and magnetic field at any given location are perpendicular both to each other and to the direction of propagation from the antenna. They are also proportional to each other, so it is sufficient to know only one of them (just as in wired communication, where we view a signal as simply a voltage waveform or a current waveform). In response to a transmitted sinusoid cos 2πft, we can express the electric far field at time t as E(f, t,(r, θ, ψ)) = αs(θ, ψ, f) cos 2πf(t − r c ) r . (2.1) Here, (r, θ, ψ) represents the point u in space at which the electric field is being measured, where r is the distance from the transmitting antenna to u and where (θ, ψ) represents the vertical and horizontal angles from the antenna to u, respectively. The constant c is the speed of light, and αs(θ, ψ, f) is the radiation pattern of the sending antenna at frequency f in the direction (θ, ψ); it also contains a scaling factor to account for antenna losses. Note that the phase of the field varies with fr/c, corresponding to the delay caused by the radiation travelling at the speed of light. We are not concerned here with actually finding the radiation pattern for any given antenna, but only with recognizing that antennas have radiation patterns, and that the free space far field behaves as above. It is important to observe that, as the distance r increases, the electric field decreases as r −1 and thus the power per square meter in the free space wave decreases as r −2 . This is expected, since if we look at concentric spheres of increasing radius r around the antenna, the total power radiated through the sphere remains constant, but the surface area increases as r 2 . Thus, the power per unit area must decrease as r −2 . We will see shortly that this r −2 reduction of power with distance is often not valid when there are obstructions to free space propagation. Next, suppose there is a fixed receive antenna at the location u = (r, θ, ψ). The received waveform (in the absence of noise) in response to the above transmitted sinusoid is then Er(f, t, u) = α(θ, ψ, f) cos 2πf(t − r c ) r (2.2) where α(θ, ψ, f) is the product of the antenna patterns of transmitting and receive antennas in the given direction. Our approach to (2.2) is a bit odd since we started with the free space field at u in the absence of an antenna. Placing a receive antenna 2The far field is the field sufficiently far away from the antenna so that (2.1) is valid. For cellular systems, it is a safe assumption that the receiver is in the far field
Tse and Viswanath:Fundamentals of Wireless Communication 24 there changes the electric field in the vicinity of u.but this is taken into account by the antenna pattern of the receive antenna Now suppose, for the given u,that we define H(f):=a(0,v,f)e-2xrle (2.3) We then have E(f,t,u)=H(f)e2f].We have not mentioned it yet,but (2.1) and (2.2)are both linear in the input.That is,the received field (waveform)at u in sm of transmitted waveforms is simply the weighted sum of Thus,H(f)is the system funct UICne time hadl and ts vre Fouer trar the mpuls ion for response.The need for understanding electromagnetism is to determine what this system function is.We will find in what follows that linearity is a good assumption for all the wireless channels we consider,but that the time invariance does not hold when either the antennas or obstructions are in relative motion. 2.1.2 Free space,moving antenna Next consider the fixed antenna and free space model above with a receive antenna that is moving with speed v in the direction of increasing distance from the transmitting antenna.That is,we assume that the receive antenna is at a moving location described as u(t)=(r(t),0,)with r(t)=r+ut.Using (2.1)to describe the free space electric field at the moving point u(t)(for the moment with no receive antenna),we have E(,t.(r+vt0))=a(0.v1)cos2f(t) r。+t (2.4) Note that we can rewrite f(t-r/c-ut/c)as f(1-v/c)t-fr/c.Thus.the sinusoid at rted to a sinu soid of fr que cy f(1-v/c);there has been -fv/c due to the motion the observation point 3 Intuitively each successive crest in the transmitted sinusoid has to travel a little further before it gets observed at the moving observation point.If the antenna is now placed at u(t), and the change of field due to the antenna presence is again represented by the receive antenna pattern,the received waveform,in analogy to(2.2),is E,4(r+t,,)=a8,,fDcs2mf[-北-÷】 ro +vt (2.5) This channel cannot be represented as an LTI channel.If we ignore the time varying attenuation in the denominator of(2.5),however,we can represent the channel in ar g cars. ambul rapidfto rqnc
Tse and Viswanath: Fundamentals of Wireless Communication 24 there changes the electric field in the vicinity of u, but this is taken into account by the antenna pattern of the receive antenna. Now suppose, for the given u, that we define H(f) := α(θ, ψ, f)e −j2πfr/c r . (2.3) We then have Er(f, t, u) = < H(f)e j2πft . We have not mentioned it yet, but (2.1) and (2.2) are both linear in the input. That is, the received field (waveform) at u in response to a weighted sum of transmitted waveforms is simply the weighted sum of responses to those individual waveforms. Thus, H(f) is the system function for an LTI (linear time-invariant) channel, and its inverse Fourier transform is the impulse response. The need for understanding electromagnetism is to determine what this system function is. We will find in what follows that linearity is a good assumption for all the wireless channels we consider, but that the time invariance does not hold when either the antennas or obstructions are in relative motion. 2.1.2 Free space, moving antenna Next consider the fixed antenna and free space model above with a receive antenna that is moving with speed v in the direction of increasing distance from the transmitting antenna. That is, we assume that the receive antenna is at a moving location described as u(t) = (r(t), θ, ψ) with r(t) = r0 + vt. Using (2.1) to describe the free space electric field at the moving point u(t) (for the moment with no receive antenna), we have E(f, t,(r0 + vt, θ, ψ)) = αs(θ, ψ, f) cos 2πf(t − r0 c − vt c ) r0 + vt . (2.4) Note that we can rewrite f(t−r0 /c−vt/c) as f(1−v/c)t − fr0/c. Thus, the sinusoid at frequency f has been converted to a sinusoid of frequency f(1−v/c); there has been a Doppler shift of −fv/c due to the motion of the observation point.3 Intuitively, each successive crest in the transmitted sinusoid has to travel a little further before it gets observed at the moving observation point. If the antenna is now placed at u(t), and the change of field due to the antenna presence is again represented by the receive antenna pattern, the received waveform, in analogy to (2.2), is Er(f, t,(r0+vt, θ, ψ)) = α(θ, ψ, f) cos 2πf (1− v c )t − r0 c r0 + vt . (2.5) This channel cannot be represented as an LTI channel. If we ignore the time varying attenuation in the denominator of (2.5), however, we can represent the channel in 3The reader should be familiar with the Doppler shift associated with moving cars. When an ambulance is rapidly moving toward us we hear a higher frequency siren. When it passes us we hear a rapid shift toward lower frequencies.