Clarke, R.H., "A statistical theory of mobile radio reception," Bell System Technical Journal, pp. 957-1000, JulyAugust 1968.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....channel is characterized by the half power bandwidth of the Fourier transform of , and the normalized half power bandwidth is referred to as the Doppler spread [22] of the th channel. In our examples, we consider an exponential time correlation function [22] and a Bessel time correlation function [23] (sometimes referred to as the Clarke Jakes model) Another parameter of interest is the power ratio, defined by , which is the ratio of the specular power to the average diffuse power in the components of the received signal associated with the th cluster of paths of channel . III. SYSTEM ....

R. H. Clarke, "A statistical theory of mobile-radio reception," Bell Syst. Tech J , vol. 47, no. 4, pp. 957--1000, July--Aug. 1968.

....A common approach to describe the channel is to assume that the transmitted radio waves, causing the interference pattern, act as plane wave fronts from di#erent directions, due to the multipath propagation. A statistical description of such mobile radio channels has been developed by Clarke [10] and Jakes [11] The properties of the channel is deduced from a scattering propagation model which assumes that the field incident to the receiver antenna is composed of an infinite number of randomly phased azimuthal plane waves of arbitrary azimuthal angles. The dynamics of the channel ....

....as the mobile station. Whether it acts as a receiver or transmitter does not matter, as the channel is the same in both directions due to reciprocity. Thus both the up and down links are treated. 2. 1 Multipath Propagation via Reflectors and Scatterers In the classical papers by Clarke [10] and Jakes [11] a statistical passband description of the mobile radio channel is developed. The model treats a scenario where N plane waves are arriving at the receiver from random directions. The di#erent propagation paths cause the waves to have di#erent attenuation and phase shifts. In Figure ....

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R.H. Clarke, A statistical theory of mobile-radio reception, The Bell System Technical Journal, 47(6):957--1000, July-August 1968.

....u(t) is the input, h(t; is the time varying channel impulse response function, and n(t) is white Gaussian noise. Owing to the high complexity of such channels, a stochastic characterization is useful. Considering a single tone transmitted to a moving receiver with isotropic scattering, Clarke [5] showed that the complex envelope of the signal at the receiver is a complex valued wide sense stationary (WSS) Gaussian random process with the zerothorder Bessel function as the autocorrelation function. The magnitude at each time instance has the Rayleigh distribution. Bello [1] analyzed random ....

G. C. Clarke, \A statistical theory of mobile radio reception," Bell System Tech. Journal, vol. 47, pp. 957-1000, 1968.

....the real world fading channel of Section II and assesses the performance of the proposed iterative schemes in the light of those bounds. Finally, Section V concludes the paper. II. CHANNEL MODEL A widely accepted statistical model for nondispersive wireless fading channels has been introduced in [17] and is commonly referred to as Clarke s fading model. According to this model, after matched filtering and proper sampling, the discrete representation of the received signal at time is (1) where transmitted constellation point (in this paper from an PSK constellation) i.i.d. white) complex ....

R. H. Clarke, "A statistical theory of mobile radio reception," Bell Syst. Tech J . , pp. 957--1000, July 1968.

....evaluate the performances of the MRE method in a digital wireless communications situation at 900 MHz with sensors distributed on an uniform circular array. The propagation channel is generated based on the model of Clarke Fig. 3. Channels impulses responses. TABLE I TU CHANNELS PATH PROFILE [32]. At sensor , the multipath channel is obtained through (15) where path has amplitude and delay . is the number of rays impinging on the sensor within each path. is an i.i.d. uniform process in . Assuming planar wavefronts, is the propagation delay of a ray with random angular incidence from the ....

R. H. Clarke, "A statistical theory of mobile radio reception," Bell Syst. Tech. J., vol. 47, pp. 987--1000, 1968.

....is large enough. That is, if the fading processes observed at the di#erent antennas are sufficiently uncorrelated. For receivers operating in rich scattering environments where it can be assumed that the waves arrive from all directions with equal probability (Clarke s isotropic scattering model [Cla68] it 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Normalized envelope autocovariance Figure 2.1: Normalized envelope auto covariance function as a function the normalized distance between two sensors in multiples of the wavelength. can be shown ....

R. Clarke. A Statistical Theory of Mobile Radio Reception. Bell System Technical Journal, 47:957--1000, 1968.

....(CCF) of 1 (t) and 2 (t) is zero. In general, a real Gaussian noise process is completely described by its mean and autocorrelation function (ACF) 16] For an omnidirectional receiving antenna in a two dimensional isotropic scattering environment, it was shown in the pioneering work of Clark [17] that the ACF of i (t) can be represented by r i i ( oe 0 J 0 (2f max ) i = 1; 2 (2) where f max denotes the maximum Doppler frequency, and J 0 ( Delta) is the zeroth order Bessel function of the first kind. The Fourier transform of (2) gives the Doppler power spectral density (PSD) ....

R.H. Clarke, "A statistical theory of mobile-radio reception," Bell Syst. Tech. J., vol. 47, pp. 957--1000, Jul. /Aug. 1968.

....the mobile fading channel that all the incoming directions of the received waves are equally distributed in the interval [0; 2 ) which results in a symmetrical Doppler power spectral density (PSD) function. A widely accepted Doppler PSD function for mobile fading channel models is the Jakes PSD [17, 18] as shown in Fig. 2a (see dashed line) But the equal distribution hypothesis usually does not tally with real fading environments, as some of the multipath signals are blocked by obstacles or absorbed by the electromagnetic properties of the physical environment, then the resulting Doppler PSD of ....

....noise process (t) S (f ) becomes asymmetrical. In addition to that, the shape of the Doppler PSD S (f) is strongly in uenced by the antenna pattern. For example, if the mobile receiver uses a beam antenna directed along vehicle motion, then S (f) gets also an asymmetrical shape [18,28]. How to get for the received multipath signal component a Doppler PSD with asymmetrical shape by taking also into account a slowly time varying LOS component is the topic of this subsection. Therefore, we use for the Doppler PSD of the process 1 (t) the following shape [18,28] S 1 1 (f) ....

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R.H. Clarke, \A Statistical Theory of Mobile-Radio Reception," Bell Syst. Tech. Journal., vol. 47, pp. 957-1000, July/Aug. 1968.

....to get a correct description on the space selectivecharacter of the fading as seen from the di erentantenna elements. This model was rst developed to analyze spatial diversity systems, where two or more receiver antennas should be placed su ciently separated to get uncorrelated fading, see [Cla68, Jak74, AFWP86] Later, the same model has been applied in combination with array processing, for example in [Ban71, ZO95, TO96] A thorough development of this and related models for di erent propagation environments both in uplink and downlink, is given in [Zet97] Similar models result if each ....

R.H. Clarke. A statistical theory of mobile-radio reception. The Bell System Technical Journal, 47(6):9571000, July August 1968.

....due to the existing LOS path. The quadrature components 1 (t) and 2 (t) of (2) being statistically independent real Gaussian random processes with zero mean and common variance V arf i (t)g = oe 0 (i = 1; 2) For the two dimensional isotropic scattering model, which was first suggested by Clark [17], the autocorrelation function (ACF) of i (t) is given by r i i ( oe 0 J 0 (2f max ) i = 1; 2 (4) where J 0 ( Delta) is the zeroth order Bessel function of the first kind, and f max denotes the maximum Doppler frequency. From the statistical independence of 1 (t) and 2 (t) it follows ....

R.H. Clarke, "A statistical theory of mobile-radio reception," Bell Syst. Tech. Journal, vol. 47, pp. 957--1000, Jul. /Aug. 1968.

....losses inside the packet, the SIR profile used for determining the packet loss must be finely sampled. In this case, we need to include short scale fading as well as long scale fading for the TxRxFade module shown in Figure 3. We have implemented models of short scale Rayleigh and Ricean fading [28] with i) wave superposition method [29] ii) spectrum shaping method [30] and also iii) a quantized channel state Markovian model [31] WiPPET packet generates Rayleigh fading using the spectrum shaping method based on Clarke s model. The Rayleigh fading for O. E. Kelly et al. Scalable ....

R. H. Clarke. A statistical theory of mobile-radio reception. Bell System Technical Journal, 47:957--1000, 1968.

.... symbol, data symbols per packet, with training symbols at each end, three packets per frame, Rayleigh fading, three channel taps with equal mean power spread evenly over the delay spread T, taps generated by filtering white noise with a five tap autoregressive filter to approximate Clarke s model [27], no synchronization offsets, perfectly known channel parameters, the forward backward algorithm, and a tap predictor. No noise limiting filter or sampler is required, as these are implicit in the discretization of time. Therefore, the OCIR autocovariance approximates (49) The simulation ....

R. H. Clarke, "A statistical theory of mobile-radio reception," Bell Syst. Tech J , vol. 47, pp. 957--1000, July/Aug. 1968.

....the real world fading channel of section II and assesses the performance of the proposed iterative schemes in the light of those bounds. Finally, section V concludes the paper. II. CHANNEL MODEL A widely accepted statistical model for non dispersive wireless fading channels has been introduced in [17], and is commonly referred to as Clarke s fading model. According to this model, after matched filtering and proper sampling, the discrete representation of the received signal at time is: 1) where is the transmitted constellation point (in this paper from an ....

R. H. Clarke. A statistical theory of mobile radio reception. Bell Syst. Tech. J., pages 957--1000, July 1968.

.... antenna shown in Figure 2 with two parasitics shorted (S) to ground and one open (O) plus three hardwired to ground (S) 3 The correlation coefficients for the complex voltage patterns corresponding to the power radiation patterns in Figure 3 and 4 are calculated assuming the Clark scenario [11] with pdf S( 2) 2 sin ) to model a ring of dense sources on a horizon about the receiving antenna. We assume that three (two) parasitics are always shorted, to get four (three) different directions with 90 (120 ) separation. This gives the correlation coefficient for adjacent ....

R.H.Clarke. A statistical theory of mobile radio reception. Technical report, Bell System Technical Journal, 1969.

.... shown in Figure 2 with two parasitics shorted ( to ground and one open ( plus three hardwired to ground ( 3 The correlation coefficients for the complex voltage patterns corresponding to the power radiation patterns in Figure 3 and 4 are calculated assuming the Clark scenario [11] with pdf ) ML (5 ONQP . PR8B9 ; to model a ring of dense sources on a horizon about the receiving antenna. We assume that three (two) parasitics are always shorted, to get four (three) different directions with 90 S (120 S ) separation. This gives the correlation ....

R.H.Clarke. A statistical theory of mobile radio reception. Technical report, Bell System Technical Journal, 1969.

....reads y[k] g[k] x[k] n[k] 2) where the fading process g[ and the noise process n[ are mutually independent correlated and uncorrelated zero mean complex Gaussian random processes with variances 2 g and 2 n , respectively. According to the widely used Clarke fading model [38] (also known as Jakes model [39] with maximum Doppler frequency f d , the autocorrelation function of the fading process is given by R g [ 4 = E g fg [k]g[k ]g = 2 g J 0 (2 f d T ) 3) where E f g denotes expectation with respect to , J 0 ( is the zeroth order Bessel ....

R.H. Clarke. A Statistical Theory of Mobile{Radio Reception. Bell System Technical Journal, 47:957-1000, July/August 1968.

.... diversity and a WSSUS channel with N discrete fading paths with equal power, so the channel s autocovariance has the form, P l m T i N R l m T zz d e r N ttaa d e r i N , x x d x x d x t 1 2 1 2 1 1 0 1 1 (9) The time autocovariance of [8] generalises to a time antenna autocovariance [10] R l m T J d e A l m f T d e A l m f T ttaa d e r D r D r , cos = 0 2 2 2 2 p j (10) for multiple antennae in a linear array, spaced every A wavelengths at angle j to the receiver s velocity. ....

R.H.Clarke, "A Statistical Theory of Mobile-Radio Reception," Bell Syst. Tech. J., vol 47, pp957-1000, July-Aug. 1968

.... k u v w H u v w , g G g (22) where the kernel, G u,v,w , is a Hermitian symmetric matrix, defined by (19) or (20) The covariance matrix of g, R gg , is given by ( R gg R 0 R 0 R R R R R gg zz ze nn ne ez en ee = 1 2 E H (23) An isotropic scattering model is assumed [12], so the fading autocorrelation matrix is the usual Bessel function, R zz ik i k D E z z J f T i k r = 1 2 0 2p (24) where f D is the one sided fading bandwidth and f DT is the fractional Doppler spread. For ideal CSI and pilot tone CSI, the noise autocorrelation matrix is ....

R.H.Clarke, "A Statistical Theory of MobileRadio Reception," Bell Syst. Tech. J., vol 47, JulyAug. 1968, pp957-1000

.... 2 1 2 1 2 1 2 1 2 E c c h l ir T h m kr T E z lT z mT d d l ir ir b m kr d r r b r d r = x x x x x x (16) A Wide Sense Stationary, Uncorrelated Scattering[10] channel model is assumed, with the conventional ( J x 0 2p l autocorrelation function in space, x[11]. Diversity is achieved through a receiver antenna array, comprising D antennae in a row, equispaced at A wavelength intervals. For frequency flat fading, the expectation in (16) reduces to ( 1 2 1 2 1 1 2 0 2 2 2 E z lT z mT J d b Acos m l f T d b Asin ....

R.H.Clarke, "A Statistical Theory of Mobile-Radio Reception," Bell Syst. Tech. J., vol 47, July-Aug. 1968, pp9571000

.... 2 1 2 1 2 E c c h l ir T h m kr T E z lT z mT d d l ir ir b m kr kr d r r b r d r = x x x x x x (30) Assuming a wide sense stationary, uncorrelated scattering (WSSUS) 17] channel, with P independently faded paths with equal mean power, isotropic scattering [22], and a space diversity receiver with D antennae in a row, spaced every W wavelengths, then the expectation in (30) reduces to ( 1 2 1 2 1 2 1 0 1 0 2 2 1 1 2 E z lT z mT P p P J d b Wcos m l f T d b Wsin b r d r p P D r , x x d x x d x t p q q = ....

R.H.Clarke, "A Statistical Theory of Mobile-Radio Reception," Bell Syst. Tech. J., vol 47, July-Aug. 1968, pp957-1000

.... models suggested for land mobile radio channels [16] As an example for the Doppler power spectrum, consider two dimensional isotropic scattering 2 : p f D (f D ) 10) 8 : 1 fDmax p 1 Gamma(f D =f Dmax ) 2 if jf D j f Dmax 0 else; where f Dmax is the maximum Doppler frequency [2, 3]. Application of (9) gives f Dn = g f D (u n ) f Dmax Delta cos(u n ) 11) As an example for the delay power spectrum, consider a one sided exponentially distributed random variate: p ( e Gamma =T T (1 Gammae Gamma max=T ) if 0 max 0 else; 12) where max is the maximum ....

R.H. Clarke, "A statistical theory of mobile-radio reception," Bell Syst. Techn. J., vol. 47, pp. 957-1000, JulyAug. 1968.

....for the Doppler spectrum, firstly consider 2 D isotropic scattering, compare Fig. 1 and Fig. 2: p fD (f D ) 1 fDmax p 1 Gamma(f D=fDmax ) 2 if jf D j f Dmax 0 else; 11) where fDmax is the maximum Doppler frequency. This is the classical Doppler spectrum derived by R.H. Clarke [12], 13] but sometimes dubbed Jakes spectrum . Application of (10) gives f Dn = g fD (un ) fDmax Delta cos(un ) 12) where 0 un 1 is uniformly distributed. If the scattering is 2 D uniform within a narrow beamwidth of, let us say L H (where L is the lowest angle and H is the ....

R.H. Clarke, "A statistical theory of mobile-radio reception, " Bell Syst. Techn. J., vol. 47, pp. 957-1000, JulyAug. 1968.

....the effect of imperfections in the signal power measurement, channel estimation and RAKE combining, and synchronization on the current capacity estimates should be investigated as extensions to this work. APPENDIX A Derivation of the Autocorrelation of A n The flat fading amplitude, from [17], follows a Rayleigh distribution. Following the traditional analysis, the fading process is generated from two independent Gaussian processes, Xn and Yn . The power in the fading process, Zn , is exponentially distributed (or chi squared distributed with 2 degrees of freedom) with a pdf given by ....

....of the means of A i and A j yields the autocovariance function, Cov[A i A j ] 100 ln 2 10 Gamma ae 2 i;j F (ae 2 i;j ; 2; 1) Delta ; A:9) where ae i;j is the correlation coefficient of the underlying Gaussian processes X i ; X j or Y i ; Y j . For the standard Doppler spectrum [17], the correlation coefficient for the process X or Y is ae i;j 4 = E[X i ; X j ] oe x oe y = J o (2f d (i Gamma j)T b ) where f d is the Doppler bandwidth, and T b is one bit duration. The resulting expression for Cov[A i ; A j ] becomes Cov[A i A j ] fl 2 J o ( d (i Gammaj)T b ) 2 ....

R. H. Clarke, "A statistical theory of mobile radio reception, " The Bell Systems Technical Journal, pp. 957-999, July-August 1968.

....) is the normalized autocovariance function of the complex Gaussian random process whose A. Chockalingam and Laurence B. Milstein Open Loop Power Control. 5 envelope is the Rayleigh process. If the received waves are travelling only horizontally, i.e. there is no vertical component, then from [15], ae( J 0 (2f d j j) 4) where f d = v= is the Doppler bandwidth, v is the speed of the mobile relative to the base station, and is the wavelength (we assume that the system bandwidth is much smaller than the absolute value of the carrier frequency) J 0 ( is the Bessel function of the ....

R. H. Clarke, "A statistical theory of mobile radio reception," Bell Syst. Tech. Jl., vol. 47, pp. 957-1000, July 1968.

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Clarke, R.H., "A statistical theory of mobile radio reception," Bell System Technical Journal, pp. 957-1000, JulyAugust 1968.

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R. H. Clarke, "A statistical theory of mobile-radio reception," Bell Syst. Tech J , vol. 47, pp. 957--1000, 1968.

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R.H. Clarke, "A statistical theory of mobile radio reception", Bell Syst. Tech. J., Vol. 47, 1968, pp. 957-1000.

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R.H. Clarke, "A statistical theory of mobile radio reception", Bell Syst. Tech. J., Vol. 47, 1968, pp. 957-1000.

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R. H. Clarke, "A statistical theory of mobile radio reception," Bell Syst. Tech. J., vol. 47, pp. 957--1000, July 1968.

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R. H. Clarke, "A statistical theory of mobile radio reception," Bell Syst. Tech J . , vol. 47, pp. 957--1000, 1968.

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R. H. Clarke, "A Statistical Theory of Mobile-radio Reception ", Bell Systems Technical Journal, Vol. 47, pp. 957-1000, 1968.

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R. H. Clarke, "A statistical theory of mobile radio reception," Bell Syst. Tech J . , pp. 957--1000, July 1968.

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R. H. Clarke, "A statistical theory of mobile radio reception," Bell Syst. Tech J , vol. 47, pp. 957--1000, July--Aug. 1968.

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R. H. Clarke, "A statistical theory of mobile-radio reception," Bell Syst. Tech. J., pp. 957--1000, July--Aug. 1968.

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R. H. Clarke, "A Statistical Theory of Mobile-Radio Reception," The Bell System Technical Journal, Vol. 47, No. 6, July-Aug. 1968, pp. 957-1000.

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R. H. Clarke, "A statistical theory of mobile-radio reception," in Bell Syst. Tech . J . , vol. 47, No. 6, pp. 957--1000, July-Aug 1968.

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R. H. Clarke. A statistical theory of mobile-radio reception. Bell Systems Technical Journal, 47:9571000, 1968.

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R.H. Clarke, A statistical theory of mobile radio reception, Bell Labs Technical Journal, vol. 47, pp. 957#000, Sep. #968.

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R. H. Clarke, "A statistical theory of mobile-radio reception," Bell System Technical Journal, vol. 47, pp. 957-1000, Nov. 1968.

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R. H. Clarke, "A statistical theory of mobile radio reception," Bell System Technical Journal, vol. 47, pp. 1779--1803, 1968.

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R.H. Clarke, "A statistical theory of mobile radio reception", Bell Syst. Tech. J., 47, pp. 987-1000, 1968.

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R. H. Clarke, "A Statistical Theory of Mobile-Radio Reception," Bell System Tech. Journal, pp. 957-1000, July -- Aug. 1968. 04/27/00 170

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R.H. Clarke, "A Statistical Theory of Mobile-Radio Reception", The Bell Systems Technical Journal, Vol. 47, pp. 957-1000, 1968.

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Clarke, R. H., "A statistical theory of mobile radio reception," Bell Syst. Tech. J., 47, no. 6, pp. 957-1000, July-Aug. 1968.

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R.H. Clarke, "A statistical theory of mobile radio reception," Bell. Syst. Tech. J., vol. 47, pp. 957-1000, July/Aug. 1968.

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Clarke R., "A Statistical Theory of Mobile Radio Reception," Bell Systems Technical Journal, vol. 47, 1968.

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R. H. Clarke, A Statistical Theory of Mobile Radio Reception, Bell Syst. Tech. J., Vol 47, pp. 957--1000, July 1968.

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R. H. Clarke. A statistical theory of mobile-radio reception. Bell System Technical Journal, 47(6):9571000, July-August 1968.

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R. H. Clarke. A statistical theory of mobile-radio reception. Bell Systems Technical Journal, 47:957--1000, 1968.

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R.H.Clarke, "A Statistical Theory of Mobile-Radio Reception," Bell Syst. Tech. J., vol 47, pp957-1000, July-Aug. 1968

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