A. Paulraj, et. Al. “Array Processing for Mobile Communications.” 2000 CRC Press LLC. <http://www.engnetbase.com>. ArrayProcessingforMobile Communications A.Paulraj StanfordUniversity C.B.Papadias StanfordUniversity 68.1IntroductionandMotivation 68.2VectorChannelModel PropagationLossandFading • MultipathEffects • Typical Channels • SignalModel • Co-ChannelInterference • Signal- Plus-InterferenceModel • BlockSignalModel • Spatialand TemporalStructure 68.3AlgorithmsforSTP Single-UserST-MLandST-MMSE • Multi-UserAlgorithms • SimulationExample 68.4ApplicationsofSpatialProcessing SwitchedBeamSystems • Space-TimeFiltering • Channel ReuseWithinCell 68.5Summary 68.6References 68.1 IntroductionandMotivation Thischapterreviewstheapplicationsofantennaarraysignalprocessingtomobilenetworks.Cellular networksarerapidlygrowingaroundtheworldandanumberofemergingtechnologiesareseentobe criticaltotheirimprovedeconomicsandperformance.Amongtheseistheuseofmultipleantennas andspatialsignalprocessingatthebasestation.ThistechnologyisreferredtoasSmartAntennasor, moreaccurately,asSpace-TimeProcessing(STP).STPreferstoprocessingtheantennaoutputsin bothspaceandtimetomaximizesignalquality. Acellulararchitectureisusedinanumberofmobile/portablecommunicationsapplications.Cell sizesmayrangefromlargemacrocells,whichservehighspeedmobiles,tosmallermicrocellsorvery smallpicocells,whicharedesignedforoutdoorandindoorapplications.Eachoftheseoffersdifferent channelcharacteristicsand,therefore,posesdifferentchallengesforSTP.Likewise,differentservice deliverygoalssuchasgradeofserviceandtypeofservice:voice,data,orvideo,alsoneedspecific STPsolutions.STPprovidesthreeprocessingleverages.Thefirstisarraygain.Multipleantennas capturemoresignalenergy,whichcanbecombinedtoimprovethesignal-to-noiseratio(SNR).Next isspatialdiversitytocombatspace-selectivefading.Finally,STPcanreduceco-channel,adjacent channel,andinter-symbolinterference. Theorganizationofthischapterisasfollows.InSection68.2,wedescribethevectorchannelmodel forabasestationantennaarray.InSection68.3wediscussthealgorithmsforSTP.Section68.4outlines theapplicationsofSTPincellularnetworks.Finally,weconcludewithasummaryinSection68.5. c  1999byCRCPressLLC 68.2 Vector Channel Model Channel effects in a cellular radio link arise from multipath propagation and user motion. These create special challenges for STP. A thorough understanding of channel characteristics is the key to developing successful STP algorithms. The main features of a mobile wireless channel are described below. 68.2.1 Propagation Loss and Fading The signal radiated by the mobile loses strength as it travels to the base station. These losses arise from the mean propagation loss and from slow and fast fading. The mean propagation loss comes from square law spreading, absorption by foliage, and the effect of vertical multipath. A number of models exist for characterizing the mean propagation loss [22, 30], which is usually around 40 dB per decade. Slow fading results from shadowing by buildings and natural features and is usually characterized by a log-normal distribution with standard deviation agreed to 8 dB. Fast fading results from multipath scattering in the vicinity of the moving mobile. It is usually Rayleigh distributed. However, if there is a direct path component present, the fading will be Rician distributed. 68.2.2 Multipath Effects Multipath propagation plays a central role in determining the nature of the channel. By channel we mean the impulse, or frequency response, of the radio channel from the mobile to the output of the antenna array. We refer to it as a vector channel, because we have multiple antennas and, therefore, we have a collection of channels. The mobile radiates omnidirectionally in azimuth using a vertical E-field antenna. The transmitted signal then undergoes scattering, reflection, or diffraction before reaching the base station, where it arrives from different paths, each with its own fading, propagation delay, andangle-of-arrival. Thismultipathpropagation, inconjunctionwithusermotion, determines the behavior of the wireless channel. Multipath scattering arises from three sources (see Fig. 68.1). There are scatterers local to the mobile, remote dominant scatterers, and scatterers local to the base. We will now describe these three scattering mechanisms and their effect on the channel. FIGURE 68.1: Multipath propagation has three distinct classes, each of which gives rise to different channel effects. c  1999 by CRC Press LLC Scatterers Local to Mobile Scattering local to the mobile is caused by buildings in the vicinity of the mobile (a few tens of meters). Mobile motion and local scattering give rise to Doppler spread, which causes time-selective fading. For a vertical, polarized E-field antenna, it has been shown [22] that the fading signal has a characteristic classical spectrum. For a mobile traveling at 55 MPH, the Doppler spread is about +/- 200 Hz in the 1900 MHz band. This effect results in rapid signal fluctuations also called time- selective fading. While local scattering contributes to Doppler spread, the delay spread will usually be insignificant because of the small scattering radius. Likewise, the angle spread will also be small. Remote Scatterers The emerging wavefront from the local scatterers may then travel directly to the base and also be scattered toward the base by remote dominant scatterers, giving rise to specular multipath. These remote scatterers can be terrain features or high rise buildings. Remote scattering can cause significant delay and angle spreads. Delay spread causes frequency-selective fading, and the angle spread results in space-selective fading. Scatterers Local to Base Once these multiple wavefronts reach the base station, they may be scattered further by local structures such as buildings or other structures that are in the vicinity of the base. Such scattering will be more pronounced for low elevation below-roof-top antennas. The scattering local to the base can cause severe angle spread. FIGURE 68.2: Multipath model. 68.2.3 Typical Channels Measurements in macrocells indicate that up to 6 to 12 paths may be present. Typical channel delay, angle, and one-sided Doppler (1800 MHz) spreads are given in Table 68.1. c  1999 by CRC Press LLC FIGURE68.3: Channel frequencyresponseat fourdifferentantennas forGSMin atypicalhilly terrain channel at 1800 MHz. Mobile speed is 100 KPH. The response is plotted at four time instances spaced 66 µsecs apart. TABLE 68.1 Typical Delay, Angle and Doppler Spreads in Cellular Applications Environment Delay spread ( µ sec) Angle spread ( deg ) Doppler spread (Hz) Flat rural (Macro) 0.5 1 190 Urban (Macro) 5 20 120 Hilly (Macro) 20 30 190 Microcell (Mall) 0.3 120 10 Picocell (Indoors) 0.1 360 5 A multipath channel structure is illustrated in Fig. 68.2. Typical path power and delay statistics can be obtained from the GSM 1 standard. Angle-of-arrival statistics have been less well studied but several results have been reported (see [1, 2, 3]). The resulting channel is shown in Fig. 68.3.We show a frequency response at each antenna for a GSM system. Since the channel bandwidth is 200 KHz, it is highly frequency-selective in a hilly terrain environment. Also, the large angle spread causes variations of the channel from antenna to antenna. The channel variation in time depends on the Doppler spread. Notice that since GSM uses a short time slot, the channel variation during the time slot is negligible. 68.2.4 Signal Model We study the case when a single user transmits and is received at a base station with multiple antennas. The noiseless baseband signal x i (t) received by the base station at the ith element of an m element antenna array is given by 1 Global System for Mobile communications. c  1999 by CRC Press LLC x i (t) = L  l=1 a i (θ l )α R l (t)u(t − τ l ) (68.1) where L is the number of multipaths, a i (θ l ) is the response of the ith element for an lth path from direction θ l , α R l (t) is the complex path fading, τ l is the path delay, and u(·) is the transmitted signal that depends on the modulation waveform and the information data stream. In the IS-54 TDMA standard, u(·) is a π/4 shifted DQPSK, gray-coded signal that is modulated using a pulse with square-root raised cosine spectrum with excess bandwidth of 0.35. In GSM, a Gaussian Minimum Shift Keying (GMSK) modulation is used. See [12, 30, 55] for more details. For a linear modulation (e.g., BPSK), we can write u(t) =  k g(t − kT )s(k) (68.2) where g(·) is the pulse shaping waveform and s(k)represents the information bits. In the above model, we have assumed that the inverse signal bandwidth is large compared to the travel time across the array. For example, in GSM the inverse signal bandwidth is 5 µs, whereas the travel time across the array is, at most, a few ns. This is the narrowband assumption in array processing. The signal bandwidth is a sum of the modulation bandwidth and the Doppler spread, with the latter being comparatively negligible. Therefore, the complex envelope of the signal received by different antennas from a given path are identical except for phase and amplitude differences that depend on the path angle-of-arrival, array geometry, and the element pattern. This angle-of-arrival dependent phase and amplitude response at the ith element is a i (θ l ) [37]. We collect all the element responses to a path arriving from angle θ l into an m-dimensional vector, called the array response vector defined as a(θ l ) =[a 1 (θ l )a 2 (θ l ) . a m (θ l )] T where (·) T denotes matrix transpose. In array processing literature the array vector a(θ) is also known as the steering vector. We can rewrite the array output at the base station as x(t) = L  l=1 a(θ l )α R l (t)u(t − τ l ) (68.3) where x(t) =[x 1 (t) x 2 (t) . x m (t)] T and x(t) and a(θ l ) are m-dimensional complex vectors. The fade amplitude |α R (t)| is Rayleigh or Rician distributed depending on the propagation model. The channel model described above uses physical path parameters such as path gain, delay, and angle of arrival. When the received signal is sampled at the receiver at symbol (or higher) rate, such a model may be inconvenient to use. For linear modulation schemes, it is more convenient to use a “symbol response” channel model. Such a discrete-time signal model can be obtained easily as follows. Let the continuous-time output from the receive antenna array x(t) be sampled at the symbol rate at instants t = t o + kT . The output may be written as x(k) = Hs(k) + n(k) (68.4) where H is the symbol response channel (a m × N matrix) that captures the effects of the array response, symbol waveform, and path fading. m is the number of antennas, N is the channel length c  1999 by CRC Press LLC in symbol periods, and n(k) is the sampled vector of additive noise. Note that n(k) may be colored in space and time, as will be shown later. H is assumed to be time invariant, i.e., α R is constant. s(k) isavectorofN consecutive elements of the data sequence and is defined as s(k) =    s(k) . . . s(k − N + 1)    (68.5) It can be shown [49] that the ij th element of the H is given by [H] ij = L  l=1 a i (θ l )α R l g((M d +  − j)T − τ l ), i = 1 .,m ; j = 1, .,N (68.6) where M d is the maximum path delay and 2T is the duration of the pulse shaping waveform g(t). 68.2.5 Co-Channel Interference In wireless networks a cellular layout with frequency reuse is exploited to support a large number of geographicallydispersed users. InTDMAandFDMAnetworks, whenaco-channelmobile operatesin a neighboring cell, co-channel interference (CCI) will be present. The average signal-to-interference power ratio (SIR), also called the protection ratio [24], depends on the reuse factor (K). It is 18.7 dB for reuse K = 7 (IS-54), and 13.8 dB for reuse K = 4 (GSM). In sectored cells, CCI is significant mainly from cells that lie within the sector beam. The received signal at a base station will therefore be a sum of the desired signal and co-channel interference. 68.2.6 Signal-Plus-Interference Model The overall signal-plus-interference-and-noise model at the base station antenna array can now be rewritten as x(k) = H s s s (k) + Q−1  q=1 H q s q (k) + n(k) (68.7) where H s and H q are channels for signal and CCI, respectively, while s s and s q are the corresponding data sequences. Note that Eq. (68.7) appears to suggest that the signal and interference are band synchronous. However, this can be relaxed and the time offsets can be absorbed into the channel H q . In multi-user cases, all the signals are desired and Eq. (68.7) can be rewritten to reflect this situation. 68.2.7 Block Signal Model It is often convenient to handle signals in blocks. Therefore, we may collect M consecutive snapshots of x(·) corresponding to time instants k, .,k+ M − 1, (and dropping subscripts for a moment), we get X(k) = HS(k) + N(k) (68.8) where X(k), S(k), and N(k) are defined as X(k) =[x(k) ···x(k + M − 1)] (m × M) S(k) =[s(k) ···s(k + M − 1)] (N × M) N(k) =[n(k) ···n(k + M − 1)] (m × M) c  1999 by CRC Press LLC Note that S(k) by definition is constant along the diagonals and is therefore Toeplitz. 68.2.8 Spatial and Temporal Structure Given the signal model at Eq. (68.8), an important question is whether the unknown channel, H, and data, s, can be determined from the observations X. This leads us to examine the underlying constraints on H and S(·) which we call structure. Spatial Structure From Eq. (68.6), the jth column of H is given by H 1:m,j = L  l=1 a(θ l )α R l g((M d +  − j)T − τ l ) (68.9) Spatial structure can help determine a(θ l ) if the angles of arrival θ l are known or can be estimated. a(θ l ) lies on a array manifold A, which is the set of all possible array response vectors indexed by θ. A ={a(θ)|θ ∈ } (68.10) where  is the set of all possible values of θ. A includes the effect of array geometry, element patterns, inter-element coupling, scattering from support structures, and objects near the base station. Temporal Structure The temporal structure relates to the properties of the signal u(t) and includes modulation format, pulse-shaping function, and symbol constellation. Some typical temporal structures are • Constant modulus (CM) In many wireless applications, the transmitted waveform has a constant envelope (e.g., in FM mod- ulation). A typical example of a constant envelope waveform is the GMSK modulation used in the GSM cellular system which has the following general form u(t) = e j(ωt+φ(t)) where φ(t) is a Gaussian-filtered phase output of a minimum shift keyed (MSK) signal [40]. • Finite alphabet (FA) Another important temporal structure in mobile communication signals is the finite alphabet. This structure underlies all digitally modulated schemes. The modulated signal is a linear or nonlinear map of an underlying finite alphabet. For example, the IS-54 signal is a π/4 shifted DQPSK signal given by u(t) =  p A p g(t − pT ) + j  p B p g(t − pT ) A p = cos(φ p ), B p = sin(φ p ), φ p = φ p−1 + φ p (68.11) where g(·) is the pulse shaping function (which is a square root raised cosine function in the case of IS-54), and φ p is chosen from a set of finite phase shifts { 5π 4 , 3π 4 , π 4 , 7π 4 } depending on the data s(·). These finite set of phase shifts represent the FA structure. • Distance from Gaussianity c  1999 by CRC Press LLC The distribution of digitally modulated signals is not Gaussian, 2 and this property can be exploited to estimate the channel from the higher-order moments such as cumulants, see e.g., [15, 33]. Clearly CM signals are non-Gaussian. These higher order statistics (HOS) based methods are usually slower converging than those based on second order statistics. • Cyclostationarity Recent theoretical results [14, 28, 39, 44] suggest that exploiting the cyclostationary characteristic of the communication signal can lead to second-order statistics based algorithms to identify the channel, H, and therefore a more attractive approach than HOS techniques. It can be shown [10] that the continuous-time stochastic process x(t) defined in Eq. (68.1) (as- suming the fade amplitude α R is constant) is cyclostationary. Moreover, the discrete sequence {x i } obtained by sampling x(t) at the symbol rate 1 T is wide-sense stationary, whereas the sequence ob- tained by temporal oversampling (i.e., at a rate higher than 1/T ) or spatial oversampling (multiple antenna elements) is cyclostationary. The cyclostationary signal consists of a number of sampling phases each of which is stationary. A phase corresponds to a shift in the sampling point in temporal oversampling and different antenna element in spatial oversampling. The cyclostationary property of sampled communication signals carries important information about the channel phase, which can be exploited in several ways to identify the channel. The cyclo- stationarity property can also be interpreted as a finite duration property. Put simply, this says that the oversampling increases the number of samples in the signal x(t) and phases in the channel, H, but does not change the value of the data for the duration of the symbol period. This allows H to become tall (more rows than columns) and full column rank. Also, the stationarity of the channel makes H Toeplitz (or rather block Toeplitz). Tallness and Toeplitz properties are key to the blind estimation of H. • The temporal manifold Just as the array manifold captures spatial wavefront information, the temporal manifold captures the temporal pulse-shaping function information [48, 49]. We define the temporal manifold k(τ ) as the sampled response of a receiver to an incoming pulse with delay τ. Unlike the array manifold, the temporal manifold can be estimated with good accuracy because it depends only on our knowledge of the pulse-shaping function. Table 68.2 summarizes the duality between the array and the temporal manifold. TABLE 68.2 The Duality Between the Array and the Time Manifold Manifold Indexed by: Characterizes: Array Angle θ Antenna array response Time Delay τ Transmitted pulse shape The different structures and properties inherent in the signal model are depicted in Fig. 68.4 2 The distribution may, however, approach Gaussian when constellation shaping is used for spectral efficiency [56]. c  1999 by CRC Press LLC FIGURE 68.4: Space-time structures. 68.3 Algorithms for STP The history of array signal processing goes back nearly four decades to adaptive antenna combining techniques using phase-lock loops for antenna tracking. An important beginning was made by Howells [21], when he proposed the sidelobe canceller for adaptive nulling, and later Applebaum developed a feedback control algorithm for maximizing SINR. Another significant advance was the LMS algorithm proposed by Widrow [54]. Yet another important milestone was the work of Capon who proposed an adaptive antenna system [8] using a look direction constraint that resulted in the minimum variance distortionless beamformer. Further advances were made by Frost [13] and Griffiths and Jim [17] among several others. See [50] for a review on spatial filtering. Because of significant delay spread in the channel, array processing in mobile communications can be greatly leveraged by processing the signals in space and in time (STP) to minimize both co-channel interference and inter symbol interference while maximizing SNR. See [35] for a review of channel equalization. We begin with the single-user case where we are only interested in demodulating the signal of interest. We therefore treat interference from other users as unknown additive noise. This is an interference-suppression approach [53]. Later in the section, we will discuss multi-user detection which jointly detects all impinging signals. 68.3.1 Single-User ST-ML and ST-MMSE The first criterion for optimality in space-time processing is Maximum Likelihood (ML) or is usually referred to as Maximum Likelihood Sequence Estimation (MLSE). ST-MLSE seeks to estimate the data sequence that is most likely to have been sent given the received vector signal. Another frequently used criterion is Minimum Mean Square Error (MMSE). In ST-MMSE we obtain an estimate of the transmitted signal as a space-time weighted sum of the received signal and seek to minimize the mean square error between the estimate and the true signal at every time instant. 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