On the Arrival of the Paths in Multipath Fading Indoor Radio Channels by dandanhuanghuang


									where the state vector x(k) represents the output signals at the            are free from zero-input limit cycles and only the highpass
delays. It is proved4 that the constant-input limit cycles in this          section is free from both zero and constant-input limit cycles.
filter can be eliminated by employing the technique of                      We show now that lowpass and bandpass structures of Refer-
controlled-rounding if                                                      ence 2 can also be stabilised against constant-input limit
                                                                            cycles by making some simple modifications. The modified
         p = c p , p z ... ~ . - J ~ = ( I - A ) - ~ B                (2)   lowpass and bandpass structures are shown in Figs. 2 and 3,
                                                                            respectively, and their A, B and P matrices are given in eqns. 4
is machine representable. The structures given in References                and 5, respectively:
1-3 are free of zero-input limit cycles, and hence for elimi-
nating constant-input limit cycles they can be modified so that
they satisfy eqn. 2. During this process, the recursive part of
the filter is not altered so that the passband sensitivity pro-
perty of the modified filter remains the same as that of the                                                                                    (4)
original filter. Fig. 1 shows the modified structure of the one

                                                                            The transfer functions H&)         of Fig. 2 and H,,(z) of Fig. 3 are
                                                                            as follows:

                                                                                                         + mlXz + 1)’
                                                                                   HLA4    =
                                                                                               2’   + (m,    + (1 + rn, + m2)
                                                                                                            - m2)z

                                                                                                     (1 + m,X1 - zz)
                                                                                   H,‘z)   = zz + (m, - mz)z + (1 + m , + m2)

                                                                            Based on passive gyrator configurations, Kwan3 has proposed
                  -1                  “1                 a2
                                                                            several digital biquads which are free of zero-input limit
                                                                            cycles. In fact the structure of Reference 1 is also one of these.
                                                            m               These structures can also be modified in a similar way to
Fig. 1 Modified version of structure of Reference I                         make them free from constant-input limit cycles.

proposed in Reference 1. For this modified structure, the A, B              Y. V. RAMANA RA0                                      21st March 1989
and P matrices are given below:                                             C. ESWARAN
                                                                            Department of Electrical Engineering
                                                                            Indian Institute of Technology
                                                                            Madras 600 036. India

Since P is machine representable, this structure can be stabil-             References
ised against constant-input limit cycles also using the tech-
                                                                               MEERKOTTER, K.,     and WEGENER, w.: ‘A new second-order digital
nique of controlled-rounding. The transfer function H ( z )                    filter without parasitic oscillations’,Arch. Elek. Ubertragung, 1975,
realised by this structure is given below:                                     29, (7/8),pp. 312-314
                                                                               ANTONIOU, and REZK, G.: ‘Digital filter synthesis using
                          zz   - (az -     k , - k,)z ( k , + k,a,)
                                                     -                         concept of generalised-immittance convertor’, IEE J. Electron. Cir-
         H ( z ) = -2
                              z2   - (a,   + az)z + (1 + a1 - a z )            cuits & Syst., 1977, 1, pp. 207-216
                                                                               KWAN, H : ‘Design of passive second-order digital filters’. Proc.
                                                                               IEEE Int. Conf. on Acoustics, Speech and Signal Processing, 1982,
Based on the GIC analogue configuration, Antoniou and                          pp. 286289
Rezk’ have proposed five second-order digital structures                       DINIZ, P. s. R., and ANTONIOU,   A.:‘On the elimination of constant-
which realise lowpass, highpass, bandpass, notch and allpass                   input limit cycles in digital filters’, IEEE Trans. Circuits Syst.,
transfer functions. It is known5v6 that all these five structures              1984, CAS-31, (7), pp. 67M71
                                                                               FSWARAN, c., and GANAPATHY, v.: ‘On the stability of digital filters
                                                                               designed using the concept of generalised-immittance convertor’,
                                                                               IEEE Trans. Circuits & Syst., 1981, CAS-28, pp. 745-747

                                                                               PRASAD, K. s., and ESWARAN, c.: ‘Constant-input stability and
                                                                               multiple-output realization of GIC digital filters’, IEEE Trans.

                       A -I
Fig. 2 Modified GIC lowpass structure
                                                     1                         Circuits Syst., to be published

                                                                            ON ARRIVAL OF PATHS IN FADING
                                                                            MULTIPATH INDOOR RADIO CHANNELS

                                                                                    Indexing terms : Radiowave propagation, Radiocommunication,
                                                                                    Radio links, Data transmission

                                                                                    Arrival of the paths in fading multipath channels obtained
                                                                                    from several manufacturing floors and college campus labor-
                                                                                    atories at 910 MHz are studied. The discrepancies between
                                                                                    the empirical distribution of the arriving paths and Poisson
                                                                                    arrivals are discovered. The modified Poisson process is
                                                                                    shown to fit the arriving paths closely.

                                                                            Introduction: Recently, wideband meas~rementsl-~      and sta-
                                                          1708131           tistical modelling4 of indoor radio channels has attracted tre-
Fig. 3 Modified GIC bandpass structure                                      mendous attention for applications in oflices, manufacturing
ELECTRONICS LETTERS 8th June 1989 Vol. 25 No. 12                                                                                              763
floors, warehouses, campuses and hospitals.' All the reported              Results and discussion: For the path arrival distribution, the
wideband measurements and modellings are concerned with                    arrival time of the paths in each profile is divided into 5ns
the statistics of the multipath spread. The only attempt in                bins. The empirical curves were obtained by counting the
modelling the arrival of the paths in a building, is reported by           number of paths in the first N bins of each measured profile.
Saleh and V a l e n ~ u e l a . ~                                          The probability of occupancy in each bin was then plotted
   Saleh and Valenzuela4 use the mathematical model orig-                  against the arriving delay (path index) and these points were
inally suggested by Turin for urban radio data communica-                  connected by curves for clarity. The procedure is repeated for
tions.' In this model, the complex envelope of the channel                 arriving paths in the first 5, 10, 15 and 20 bins. After careful
impulse response is represented by                                         visual inspection of many profiles, the threshold level
                  L                                                        employed to detect a genuine path in any bin was fixed at
        h(t) =   1 Clk 6(t
                 k= 1
                              - Tk)e'"                                     30dB below the highest peak in the profile.

The transmitted impulse d(t) is received as the sum of L paths.
The path k has amplitude akrdelay 7k and carrier phase shift
Ok. Based on the measurements in a research laboratory, the
arrival of the paths is modelled as a Poisson process. The
paths are presumed to have independent uniform phases, and
independent Rayleigh amplitudes.
   This letter reports the discrepancies following the Poisson
arrival presumption and, based on empirical data collected
from different manufacturing floors and college campus areas,
presents a more accurate modified Poisson process to fit the
arrival of the paths.

Measurements: The measurement set-up for the multipath
propagation experiments, involved modulation of a 910 MHz
signal by a train of 3 ns (3 dB width) pulses with 500 ns repeti-                0         2        4     6     8 / 1 0    1
                                                                                                                           2      14
tion period.' The stationary receiver included a digital storage                                         path index          15oo1,l
scope and a personal computer. The transmitter and the recei-
ver used vertically polarised quarter-wave dipole antennas                 Fig. 3 Comparison of empirical and theoretical Poisson distribution for
placed about 1.5m above floor level. The transmitter was                   college laboratory areas
moved to various locations in the site, and the received multi-
                                                                              Figs. 2 and 3 show a comparison between the empirical
path profiles were stored in the computer. The distance
                                                                           path number distributions and the theoretical Poisson dis-
between the transmitter and the receiver varied between 1 and
                                                                           tributions, for various values of N , for the manufacturing floor
50m. A total of about 480 profiles were collected from mea-
                                                                           areas and the college campus areas, respectively. The theoreti-
surements made in five areas on three different manufacturing
                                                                           cal curves governed by the Poisson hypothesis use a mean
floors' and two areas on college laboratory floors. Each
profile was an average over time of 64 profiles collected over             path arrival rate A for any value of N . The Poisson path
15-20s. A typical multipath profile, obtained from one of the              number distribution is then given by
locations is shown in Fig. 1.
                                                                                     P , ( K ) = - e-'
   52                                                                                            K!

                                                                           This is plotted as a continuous curve though it has values for
                                                                           only integer path numbers. We observe considerable discrep-
                                                                           ancies between the empirical and the Poisson distributions for
                                                                           all values of N . This discrepancy reflects a tendency of the
                                                                           paths to arrive in clusters, rather than in a random manner.
                                                                           To explain similar discrepancies a modified Poisson model
                                                                           was proposed by Suzuki for urban radio channel modelling.6
                                                                              According to the modified Poisson model, whenever there is
                                                                           a path in a bin, the mean arrival rate for the next bin is
                                                                           changed by a factor of K . The process becomes a standard
                                                                           Poisson sequence for K = 1. Depending on whether K is
    200      250            300        350   400   450                     greater or less than 1, the probability that there will be
                             time , n s                                    another path within the next bin increases or decreases,
                                                                           respectively. The underlying path occupancy rate Ai,is calcu-
Fig. 1 Multipath profle obtained from location on manufacturingfloor

        0    2          4        6       8   10    1
                                                   2     14                      0         2        4     6     8 1 0 1 2 1 4
                                path index                                                               path index
                                                   PT                                                                       1580141
Fig. 2 Comparison of empirical and theoretical Poisson distribution for    Fig. 4 Comparison of empirical and modified Poisson distribution for
manufacturing floor areas                                                  manufacturing floor areas

764                                                                       ELECTRONICS LETTERS                 8th June 1989 Vol. 25 No. 12
 lated from the empirical path occupancy rate r i by the follow-                       BULTITUDE, R. J. c., MAHMOUD, s. A.,and SULLIVAN, w. A.: ‘A com-
 ing relation :                                                                        parison of indoor radio propagation characteristics at 910 MHz
                                                                                       and 1.75GHz’. IEEE JSAC, Jan. 1988,pp. 2Cb-30
                                                                                                                             R. A.:
                                                                                       SALEH, A. A. M.,and VALENZUELA, ‘A statistical model for
                                 rn                                                    indoor multipath propagation’. IEEE JSAC, Feb. 1987, pp.
             I.”   =                           nZ1
                       (K   -   l)rn-l   +1                                            128-137
                                                                                       PAHLAVAN, K.: ‘Wireless intra-office networks’, A C M Trans. O f .
 where 1, = r I . The path number distribution is then calcu-                          Inf Syst., 1988,(2)
 lated successively, using the recursive formulas given for this                       SUZUKI, H.: ‘A statistical model for urban radio propagation’,
 model in Reference 6. Figs. 4 and 5 show a comparison                                 IEEE Trans. Commun., 1977, COM-25
                                                                                                 .                    O NT N .
                                                                                       TURIN, G L., CLAPP, F. D., J H S O , T L., FINE, S. B., and LAVRY, D.:
 between the empirical path number distributions and the                               ‘A statistical model of urban multipath propagation’, IEEE Trans.
 modified Poisson distributions for the manufacturing floors                            Veh. Technol., 1972, ( I ) , pp. 1-9
 and college campuses, respectively. The curve fittings show
 considerable improvement over those of the Poisson model.

                                                                                  1 0 M H z CMOS OTA-C
                                                                                  VOLTAGE-CONTROLLED QUADRATURE
                                                                                  OSCl LLATOR

                                                                                            Indexing terms: Circuit theory and design, Oscillators, Inte-
                                                                                            grated circuits, Nonlinear networks
                                                                                            A quadrature-type voltage-controlled oscillator with oper-
                                                                                            ational transconductance amplifiers and capacitors (OTA-C)
                                                                                            is presented. A monolithic integrated CMOS test circuit
                                                                                            is introduced to verify theoretical results. The attainable
                                                                                            frequency range of oscillation of the chip test circuit is
                                      path index
                                                                                            3-10.34 MHz. The total harmonic distortion (THD) is 0.2&
                                                                                            1.87% for corresponding peak-to-peak amplitude voltages
 Fig. 5 Comparison of empirical and modified Poisson distribution for                       between lOOmV and 1V. This amplitude can be controlled
 college laboratory areas                                                                   either by using a diode connection of two MOS transistors
                                                                                            or a proposed nonlinear resistor.
 This improvement is because the modified Poisson model uti-
 lises the empirical probability of occupancy for each bin,
 whereas the Poisson model just uses the sum of the probabil-                     Introduction: The quadrature mode of operation is a well-
 ities of occupancy for all bins. The optimum values of K                         known mode of waveform generation in the field of sinewave
 calculated for the manufacturing floors and the campus                            oscillator^.'-^ Two sinewaves in quadrature, that is with 90”
 environments are shown in Table 1.                                               phase difference, are generated. This is accomplished with a
                                                                                  two-integrator loop. Besides this, some form of regeneration is
Table 1 OPTIMUM VALUES OF K                                                       usually included to ensure that the oscillation is created. The
                                  Number               Number of bins N           poles are initially located in the right half-plane (RHP) of the
                                    of                                            complex frequency plane and then pulled back by a nonlinear
           Area                  locations         5       10      15     20      amplitude limiter.
                                                                                    To make a quadrature oscillator into a voltage-controlled
     Manufacturing                    288     1.184      0.904    1.03    2.46    oscillator (VCO), the integrators can be implemented using
     floors                                                                       OTAs. The output current of a CMOS-OTA is controlled by
                                                                                  the differential input voltage and its transconductance gain 9,.
     College                          196     0.892      0.64     0.61    0.75
                                                                                  Furthermore, g, can be varied over several octaves by adjust-
                                                                                  ing an external DC amplifier bias current IOk ,4 i.e.

Conclusions: Fading multipath profiles obtained from several
different manufacturing floors and some college laboratories
at 910 MHz, have been used to model the arrival of the paths.                     where h, is a process-dependent parameter.
The empirical distribution was compared with the Poisson                             In this letter an integrated CMOS OTA-C quadrature VCO
and the modified Poisson distributions and the modified                           using a 3 pm double metal technology (processed by MOSIS,
Poisson model is shown to provide a better fit. This observa-                     Marina del Rey, CA) is presented. The frequency of oscillation
tion indicates that the paths tend to arrive in clusters rather                   can be externally adjusted by nearly two octaves with a THD
than in a random manner.                                                          less than 1.9%. The real part of the poles can be adjusted, in
                                                                                  practice, independently of the frequency of oscillation.
 A c k n o w l e d g m e n t ; This work was supported in part by the
 National Science Foundation under contract NCR-8703435.                           I                        1

 R. GANESH                                                       8th March 1989
Department of Electrical Engineering
Worcester Polytechnic Institute
Worcester, M A 01609, U S A
                                                                                  A          -I-&
                                                                                              - -          L L
                                                                                                           - -            1
                                                                                                                          -       m
                                                                                  Fig. 1 Proposed O T A - C quadrature oscillator structure
   PAHLAVAN, K.,GANFSH, R., and HOTALING, T.: ‘Multipath propaga-
                                                                                  T h e o r y : The proposed quadrature VCO architecture’ is
   tion measurements on manufacturing floors at 910 MHz’, Electron.               shown in Fig. 1. It has one inverting (gml,C,) and one nonin-
   Lett., 1989, 25, pp. 225-227                                                   verting integrator ( g m 2 , C2). R , is a nonlinear resistor whose
 2 DEVASIRVATHAM, D. M. I.: ‘Time delay spread measurements of                    i / v characteristics are depicted in Fig. 2a. R , provides the
   850 MHz radio waves in building environments’. GLOBECOM                        nonlinear amplitude limiter function. Implementations are dis-
   1985 Conf. Rec., vol. 2, Dec. 1985, pp. 970-973                                cussed later. The OTAs associated with gm3 and gm4 allow
ELECTRONICS LETTERS 8th June 1989 Vol. 25 No. 12                                                                                                       765

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