Measured Impact of Antenna Setup and Transmission Bandwidth on the MIMO Spectral Efficiency in Large-Scale and Small-Scale In-Room Scenarios

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1 Measured Impact of Antenna Setup and Transmission Bandwidth on the MIMO Spectral Efficiency in Large-Scale and Small-Scale In-Room Scenarios Andreas Knopp, Christian Hofmann, Mohamed Chouayakh, and Berthold Lankl Department of Electrical and Electronics Engineering, Institute for Communications Engineering Munich University of the Bundeswehr, 85579, Neubiberg, Germany (scheme): <first Abstract We present results from broadband measurements derived with a fast 5 5 MIMO channelsounder in a typical, large-scale as well as a small-scale, non-mobile, in-room office scenario where we focus on Line-of- Sight (LOS) transmission channels. We assume the positions of transmitter and receiver being random variables and therefore derive a spatial statistic from our measurements across the room areas. The accessible MIMO spectral efficiency is compared to its theoretic counterpart which would have been obtained provided that the LOS signal existed without any reflections. The LOS signal component is shown to be beneficial to the MIMO spectral efficiency mainly due to its SNR-enhancing impact, an advantage which can hardly be balanced by any measures in the Non-LOS case. The statistical results generally indicate the spectral efficiency staying fairly high and only slightly dependent upon the current geometric antenna setup for both scenarios. Additionally, we investigate the transmission bandwidth s impact on the spectral efficiency s variations over the measured positions resulting in hints on the smallest, appropriate bandwidths in terms of keeping those variations low. Key words: MIMO, channel measurement, capacity, indoor radio channel, Line-Of-Sight 1. Introduction Multiple Input-Multiple Output (MIMO) transmission systems promise high channel capacity gains and reliability improvements for fixed bandwidth and transmit power [1],[]. Especially broadband indoor transmission channels and as a subgroup in-room channels 1 are for several reasons totally different from common statistical modelling approaches due to their strong LOS signal component in coincidence with low mobility. As common statistical models can hardly be used to predict the accessible channel capacity in such in-room cases the necessity of measurement campaigns and new modelling approaches is supported. Furthermore, as already has been indicated in [3], [4] the 1 here transmitter as well as receiver are located within the same room in-room channel capacity depends upon the geometric antenna setup at transmitter (Tx) as well as receiver (Rx), i.e. the antennas spacings and orientations within the room and towards each other. In the consequence the MIMO capacity varies for different Tx-Rx positions what complicates the prediction of the obtainable capacity for arbitrary positions. From this point of view simple rules for the system design, which are appropriate to mitigate the capacity s spatial selectivity and keep the capacity high all over a room, would be helpful. In our paper we at first investigate this spatial selectivity for two differently scaled in-room office scenarios and quantify it for different numbers of antennas and setups by means of capacity cumulative distribution functions as well as outage capacities. From our measurements we show, how the spectral efficiency s variations across the rooms depend upon the used transmission bandwidth as well as the antenna number, what in the consequence leads to some basic hints on the system design.. Channel description and capacity calculation.1 Preliminary presumptions on the channel In the context of MIMO applications and their capacity the indoor WLAN channel is commonly statistically modelled, where many modelling approaches presume only Non-LOS (NLOS) transmission paths forming numerous and variously reflected waves ( rich scattering ). To fulfill these assumptions the LOS component must be distinctly attenuated by shadowing effects, or the LOS signal and the reflected signal components must range within the same order of magnitude, coinciding with high reflection factors ξ 1. Here for narrow bandwidths and high mobility the well known Rayleigh fading model [5] can be applied and the entries of the channel transfer matrix (CTM) are assumed to be uncorrelated, zero mean, i.i.d. complex Gaussian random variables, a case which describes a convenient transmission channel for MIMO applications as its ergodic capacity is high [1] as long as the receive signal correlation is kept low. According to [6] the latter condition can be achieved by antenna spacings of about halfwavelength (λ/) what therefore has become a common design issue for MIMO antenna arrays. Such statistical narrowband approaches are widely used when discussing early indoor transmission systems and they are included in the Copyright 006 WPMC 1

2 popular, cluster based indoor channel model introduced by Saleh [7]. Contrarily, in the case of the in-room propagation scenario discussed in the sequel a dominant LOS signal component that carries most of the signal energy is always present which leads to correlated signals at the receiver inputs. Here the Rayleigh fading model is no longer adequate for several reasons. Of course also in indoor scenarios the LOS signal component is sometimes obstructed and therefore diffracted by objects but it is known from the theory of diffraction that no significant losses arise as long as the obstructing obstacle s size stays below the first Fresnel zone s dimension. Besides, one set of antennas (Tx or Rx) is typically mounted at the ceiling which distinctly reduces the risk of obstruction. By geometrically optimizing the antenna positions and spacings at the Tx and the Rx resulting in proper phase angle relations among the entries of the CTM, it is possible to make accessible the maximum MIMO capacity even in the case of correlated channels. The approach of [3] is a powerful, geometric optimization as it shows a strategy to construct antenna arrangements providing capacities close to the maximum even for arbitrary numbers of antennas, although some typical drawbacks imposing practical restrictions can not be mitigated. Noteworthy are especially the persisting lack of mobility or the need of unpractically large antenna spacings especially in the case of growing Tx-Rx distances. More important, it is inevitable that the LOS signal component never exists without reflections which destroy the carefully constructed phase angle relations within the channel matrix entries. Here the necessity of the optimum LOS channel construction becomes questionable and will be further discussed in the sequel by means of our results. Nevertheless, it was shown by measurements that in many indoor scenarios with low mobility the choice of larger antenna spacings supports higher and more reliable channel capacities [4]. A further aspect that must be taken into account in the case of current WLAN applications, which again contradicts the Rayleigh flat fading model, is the distinctly larger transmission bandwidth in comparison to earlier applications leading to a frequency selective fading channel instead of the narrowband flat fading one. Here the capacity for single channel realizations gets also frequency selective. Hence, we consider the following, widely deterministic description of the MIMO transmission channel. It is motivated and supported by the measurements in [4]. For a single input-single output frequency selective, deterministic transmission channel the equivalent baseband channel transfer function for the time invariant case is given by H(f) = K 1 k=0 a k e jπfτk = K 1 k=0 a k e jπ L k λ, (1) In scenarios with high mobility, which is not the case for the measurements presented here, this frequency selectivity of course does not hold for the ergodic channel capacity as it is defined as the capacity s expectation. where the sum is evaluated over the K different transmission paths consisting of K 1 reflected signal parts, and where the LOS signal component is incorporated by the index k = 0. The complex amplitude factor a k includes the phase information φ k, the path loss as well as the power-loss due to the complex reflection factor ξ k, i.e. a k = ξkλ 4πL k e jφk. The time τ k denotes the signal part s delay for the particular transmission path which is clearly linked to its path length L k by the speed of light c 0, i.e. τ k = L k /c 0. The right part of the equation additionally introduces H(f) depending on the wavelength λ. For a nonmobile scenario a k and τ k are mainly constituted by the location s geometry, i.e. primarily by the Tx s and Rx s positioning within the room as well as their arrangement in relation to the main reflection layers like walls, bottom, ceiling or large scale objects. If the amount of mobility is kept low and no further statistical modelling over time has to be performed. Applying equation (1) to the MIMO case, for a time invariant frequency selective M N-MIMO system consisting of N transmit and M receive antennas the vector of receive signals y(t) C M 1 is calculated by an inverse Fourier transform of the spectrum of the transmit signal vector X(f) C N 1 multiplied by the frequency selective CTM H(f) C M N, i.e. Y (f) =H(f) X(f)+Υ(f), () where Υ(f) C M 1 denotes the spectral vector of the additive noise η(t). The noise is assumed to be zero-mean complex Gaussian with covariance matrix R η =E[ηη H ]= σηi M, where I M C M M denotes the identity matrix and ση is the noise power at each receive antenna. Here each entry H mn (f) in H(f) has the structure of equation (1) whereas the values K and hence, a k and τ k differ.. Capacity calculation from measured data According to [1] and [] if uncorrelated transmit signals and equal power at each Tx antenna are presumed the time invariant channel spectral efficiency C, which denotes the channel capacity normalized by the transmission bandwidth (unit [Bit/sec/Hz]), for a frequency selective MIMOchannel in the absence of channel knowledge at the Tx is calculated from ( C = 1 log B [det I M + σ x B ση H(f)H H (f) df, (3) where B denotes the transmission bandwidth, I M C M M is the identity matrix, σx denotes the mean transmit power that is allocated to each transmit antenna. Furthermore (.) H abbreviates the complex conjugate transpose. When the overall bandwidth is partitioned into sufficiently narrow, say S, segments each segment can be treated frequency flat and the integral of equation (3) reduces to a sum over the segments capacity contributions, i.e. C = 1 S ( log S [det I M + σ x ση H[f s]h H [f s]. (4) s=1 Copyright 006 WPMC

3 A crucial aspect when evaluating measured channel transfer functions in terms of the channel capacity is the choice of the signal to noise ratio (SNR) in equation (3). Generally, we suggest a choice that best represents the nature, which transmission systems have to cope with, keeping the user s degrees of freedom in terms of the system design. For each receiver branch m those are mainly the transmit power per transmit antenna σx and the noise power at each frequency segment ση,m[f s ] per receiver branch m as the latter includes the Rx noise figure F m [f s ]. This noise figure depends upon the chosen hardware and it is regularly different for the M Rx branches as it adjusts according to the current input power level. Therefore ση,m[f s ] is calculated from the thermal noise power ση,th within the considered bandwidth dependent upon the noise figure as well as the bandwidth Δf s of each frequency segment f s, i.e. σ η,m[f s ]= σ η,th Δf s f s+δf s/ f s Δf s/ F m (f) df σ η,th F m [f s ], where the equation s right hand side includes the approximation of the frequency dependent noise figure by a mean noise figure F m [f s ] in each segment. By means of this equation (4) is again redescribed as C = 1 S ( log S [det I M + R[f s] H[f s]h H [f s]. (5) s=1 where R[f s ] C M N is a diagonal matrix consisting of σ the SNR of all the Rx branches x R[f s]=diag σx ση,1 [fs],..., σ ση,m [fs], i.e. x T ση,m [fs]. (6) In the sequel as an optimum bound we presume an optimum receiver in terms of the noise figure for each Rx branch as well as for each frequency segment f s, what especially means a noise figure F m [f s ]=1, s {1,..., S}. Hence, the matrix R[f s ] has identical entries on the diagonal and its frequency dependence can be skipped. So equation (5) again simplifies to equation (4). This seems to be convenient in order to calculate the maximum capacity which in theory could be achieved. Contrarily, in practice it must be kept in mind that the entries of R[f s ] might be distinctly different depending upon the different receive power levels at each Rx branch as well as upon the Rx architecture. This effect might distinctly reduce the obtainable capacity in practical systems. Of course, our so defined ratio σ x/σ η does not yet meet the typical SNR which describes the frequency dependent vector of receive signal to noise ratios ρ[f s ] C M 1 at the Rx input, but ρ[f s ] clearly could be calculated from σ x/σ η although this is not explicitly needed in the sequel. For this purpose it must be multiplied by the channel s frequency dependent power transfer factor in each Rx branch m, i.e. ρ[f s]=σ x/σ η H[f s] 1 N 1 (7) Here the matrix operation. just means that the absolute values of every matrix entry are squared and 1 N 1 denotes the N 1 vector of entries 1 each. As it becomes obvious from equation (7) for the determination of the receive power of Rx branch m the power transfer factors of the m-th row in H[f s ] are summed up for each frequency bin, assuming uncorrelated transmit signals of equal power emitted from the different Tx antennas. Furthermore, no particular equalization strategy is taken into account for the SNR calculation. In our evaluation of the channel capacity the path loss of each channel matrix entry is completely incorporated in the CTM which causes ρ[f s ] at the Rx input being dependent upon the distance between Tx and Rx as well as the number and power of impinging waves. What is more important, the LOS signal part as well as all the reflections are included with their true power contributions. For the capacity calculation presented in this paper the value of σ x/σ η was chosen 80 db resulting in each entry of ρ being approximately 10 log 10 (ρ m ) (8+10 log 10 (N)) db for the large-scale office and 10 log 10 (ρ m ) ( log 10 (N)) db for the small-scale office dependent upon the particular Tx-Rx distance. Choosing σ x/σ η a particular value simply assumes a certain hardware configuration which does not necessarily have to be further specified. Finally, for the following discussion it is useful to give some bounds on the channel spectral efficiency in order to classify the measured results for the different situations. Unfortunately in the presence of reflections it is impossible to calculate a single value for the spectral efficiency s maximum which is valid all over the room area. This is a consequence from the fact that the true SNR varies all over the room and is widely unknown. Therefore we decided to calculate only the LOS spectral efficiency s bounds for different antenna numbers provided that any reflections are neglected. This bounds are unchanged as long as the Tx-Rx distance stays unchanged what was the case for all of our measurements (see subsection 3.). For simplicity we assumed the LOS path loss H LOS [f s ] being constant over frequency within the measurement bandwidth and furthermore replaced the different path lengths L k in equation (1) by a constant path length L 0, a convenient measure as the L k only slightly differed for our antenna arrays. Hence, H LOS [f s ] H LOS 1 = λ c 4πL 0 1 M N f s B, (8) where λ c denotes the center frequency of the transmission channel and 1 M N is the M N matrix with entries 1 each. For L 0 we chose the distance between the Tx and Rx arrays centers. Using all our presumptions the bounds for an M N MIMO system without channel knowledge at the Tx are calculated according to Cmax LOS = min{m,n} ld 1+ σ x H LOS max{m,n} ση Cmin LOS = ld (1 + σx/σ η H LOS M N), (9) Copyright 006 WPMC 3

4 where ld denotes log. The values Cmax LOS and Cmin LOS for the different setups are given in the particular figures in section 3. As can be seen from the two equations, if the Tx antenna number is increased, the overall transmit power is also increased as every Tx antenna emits σx, which again means identical power Evaluation of the measurements 3.1 Measurement equipment For the channel measurements we used a 5 5 MIMO channelsounder with a bandwidth of 80 MHz at a carrier frequency of.45 GHz endowed with λ/ dipole antenna arrays positioned in form of equidistantly-spaced uniform linear arrays (ULAs). The maximum bandwidth ranges some factor above the typical bandwidths proposed for current and future indoor applications and hence, achieves a higher time resolution. The channel information was collected by sequentially deriving the entries of the CTM, i.e. by collecting the complex baseband channel impulse responses (CIRs) and channel transfer functions (CTFs). We used 196 pilot symbols and due to our sampling rate of 100 MHz we achieved a frequency resolution of 510 khz ( khz = 100 MHz), but for the capacity evaluation we reduced the considered bandwidth off line to the particular bandwidth under investigation by digital filtering. The measurement of one complete channel matrix consisting of 5 entries took about 160 μs. This measurement time is short enough by far to consider the channel invariant during that time, especially in the chosen scenarios with low mobility and it is much faster than even a single SISO network-analyser measurement which typically takes around 100 ms. A further advantage of the system is the fact that after measuring the 5 CIRs we are able to arbitrarily combine them in offline mode and virtually built up different MIMO systems by antenna selection from the measured data, in fact ( 5 5 ) M)( N combinations are possible for an M N MIMO system. 3. Scenario description and measurement procedure We performed measurements in two locations mainly differing in their dimensions. Both scenarios with their dimensions as well as their special properties in terms of furniture and materials are depicted in figure 1 for illustration. Both rooms were located within one building and therefore had the same material properties in terms of walls, bottom and ceiling. The larger room was equipped with a number of equidistantly spaced rows of single-person working desks with a large, metal blackboard in the front and huge panorama widows at the rear. In this location we moved both Tx and Rx arrays at a fixed center distance of 4 m along the tiers in steps of 1. m. At every position we took a complete 5 5 measurement snapshot for the two possible 3 Although this presumption may complicate the comparison of MIMO systems differing in their Tx antenna number it seems to be more appropriate in practice as for reasons of the link budget the Tx power per antenna not simply can be reduced only for reasons of growing antenna number. Figure 1: measurement scenarios and antenna arrangements array orientations, broadside and perpendicular. By means of this we obtained measurement results all over the room at diverse positions. We assumed a sort of spatial statistic treating the Tx-Rx position as a random variable which is appropriate to statistically evaluate the accessible spectral efficiency within a certain location. A similar procedure was performed in the small-scale office, but the Tx-Rx distance was reduced to.5 m according to the room dimensions. Here we did not move along a certain grid in distinct steps but moved arbitrarily around, keeping the arrays orientations towards each other fixed, either broadside or perpendicular. To be able of quantifying the transmission bandwidth s impact on the MIMO spectral efficiency we took our measurements over a bandwidth if 80 MHz and further reduced it during the evaluation to the particular value of interest by digital filtering. No persons were moving around during the measurements and therefore the mobility was kept low. Finally, as we were able to arbitrarily combine any Tx-Rx antenna pairs we had the chance to evaluate results for different antenna spacings at both, Tx and Rx, dependent upon the selected antennas. 3.3 Discussion of the results To start with the discussion figure depicts cumulative distribution functions (CDFs) which were empirically obtained from the measured data when treating the position of Rx and Tx within the room as a random variable (see the previous paragraph). The abscissa denotes the spectral efficiency which is normalized by min{m,n}, the maximum linear capacity increase possible for an M N MIMO system. Such normalization appears to be convenient to compare the MIMO gain of configurations which differ in their antenna number as it gives an idea how close the particular configuration approaches its maximum linear MIMO gain. Furthermore the maximum and minimum LOS spectral efficiencies Cmax LOS as well as Cmin LOS, i.e. the bounds for Copyright 006 WPMC 4

5 Figure : capacity CDFs for different office scenarios the spectral efficiency provided that the pure LOS signal part would exist without any reflections, were calculated according to equation (9). The different curves belong to different MIMO systems in terms of the assumed number of antennas as well as in terms of the presumed transmission bandwidth B. At first, for both office types it is observed that the spectral efficiency generally is fairly high, even in the range of the optimum pure LOS case or slightly below. This result on the one hand suggests that the reflected signals help to increase the Rx signal power and therefore the SNR, which in the consequence lies distinctly above the SNR taken into account for the calculation of the pure LOS spectral efficiency s bounds. In our measurements this SNR increase was amounted to 4-6 db, where the value in the small-scale office topped the one of the large-scale office due to the shorter distances which the reflected waves had to travel. On the other hand, the reflections distinctly influence the CTM s rank and especially in the case of lowrank pure LOS CTMs help to increase the MIMO capacity. This effect for example can be seen from the curves for the MIMO system with perpendicular antenna assembly. When neglecting all the reflections such setup leads to a CTM with rank 1 corresponding to the minimum MIMO capacity. If the rank had not been increased by the reflections the spectral efficiency could never have been shifted from its minimum to the observed values only due to the observed power gain of at maximum 6 db. Nevertheless, the LOS signal s impact can still be observed from the curves as the ones for the broadside antenna configurations, which are much more beneficial in order to obtain high-rank CTMs [3], lie at higher capacities than the curves for the perpendicular configurations. In the large-scale office this effect is slightly more stamped as here the reflected waves are of lower power than in the small-scale office. Admittedly, in both cases the effect causes spectral efficiency deviations around 10 % what in practice should be of less relevance. So it is concluded that in the presence of reflections the LOS signal component does not harm the MIMO spectral efficiency even if the CTM of the LOS signal was low-rank if neglecting the reflections. The LOS is beneficial as it significantly increases the SNR and the reflections help to increase the rank of low-rank pure LOS CTMs. If the spectral efficiency s variations over the measured room area is observed the steepness of the curves in figure offers an appropriate criterion. The steeper a curve in the figure is the less the spectral efficiency varies over the investigated spatial area. The variations are of interest, because from a practical point of view high variations should be considered problematic as the accessible channel spectral efficiency for a single channel use and a moving Tx or Rx is hard to predict. In order to cope with this problem, the measurements mainly suggest two strategies: Firstly, for the case of narrow bandwidths the particular curves in figure indicate a higher number of antennas being appropriate for reducing the spectral efficiency s variations over frequency, even in low - rank LOS channels. Especially in asymmetric MIMO systems with increased antenna number at the Rx such effect is observable 4. This effect can be ascribed to the fact that a higher number of Rx antennas increases the overall receive signal energy what in the consequence raises the MIMO spectral efficiency. Furthermore the use of a higher number of antennas reduces the risk of simultaneous fading or signal loss at every antenna. This could be a promising approach in the case of narrowband transmission systems where the following, second approach can not be applied. This second approach suggests to generally use larger bandwidths in order to reduce the spectral efficiency s spatial variations. The beneficial effect of larger bandwidths can at first be seen from the increased steepness of the curves for B=0 MHz in comparison to their counterparts for the narrowband case. In addition the upper part of figure 3 more clearly depicts the impact of the bandwidth on the outage capacity. On the abscissa the bandwidth which was used to calculate the spectral efficiency is denoted and from the ordinate the ratio of the normalized spectral efficiency (which means the calculated capacity divided by the particular bandwidth on the abscissa as well as by min{m,n}) and the normalized Cmax LOS (which means the maximum pure LOS spectral efficiency according to equation (9) also normalized by min{m,n}). The curves themselves depict the value of C norm /Cnorm,max LOS which was achieved in 99% of the 4 despite, this system does of course not provide the highest absolute capacities per bandwidth unit as the normalized curves for the 4 system have to be multiplied only by but for the 4 4 case the multiplier is 4 Copyright 006 WPMC 5

6 4. Conclusion Finally, from the results the following basic system design hints can be outlined: Figure 3: statistical analysis of the bandwidth s impact cases for each bandwidth. The higher this value the steeper the CDF according to figure 3 will be and the less the capacity varies. The curves indicate growing 99% outage capacities for enlarged B where only in the case larger bandwidths seem to play a relevant role. Almost independently from the geometric setup an increase from 75% of to 90% can be observed what states a significant enhancement 5. For the higher-order systems the same effect of enlarged B is observed, whereas with increasing Rx antenna number the bandwidth s impact reduces. Furthermore in these cases the effect is of less relevance as the gap between the capacity s extrema is even larger, for the 4 4 C LOS max over B. It can be seen that higher Rx antenna numbers play the more important role compared to the Tx antenna number. MIMO systems for example the value of C LOS /Cmin LOS lies around 5 % of C LOS /Cmax LOS what shows that an outage capacity enhancement of 5% is of low impact. Contrarily to the system for the asymmetric 4 case also an only low benefit of larger bandwidths is noticed supporting the idea of increased Rx antenna numbers being especially appropriate to reduce the capacity s variations, which already was mentioned above. This result is finally confirmed by the lower part of figure 3 which shows the standard deviation of the normalized C LOS /C LOS max 5 It must be remembered that in the case the maximum and minimum capacity just differ from a factor of less than, what especially means that the 55% value in the curve already states the minimum case. 1. The antenna assembly has a measurable but small effect on the outage capacities. If there is room for its design, configurations which are beneficial for the LOS signal part should be preferred. The effect gets less eminent for declining room dimensions.. Larger bandwidths especially for MIMO systems with low antenna number at Tx and Rx help to reduce the spectral efficiency s variations in spatial domain and therefore enhance its high-percentage outage value. A bandwidth in the range of the channel s coherence bandwidth is sufficient at a first glance (10 MHz to 0 MHz for the observed scenarios). The bandwidth s impact for higher antenna numbers distinctly reduces. 3. Generally higher antenna numbers are appropriate to reduce the capacity s spatial variation. Especially asymmetric MIMO systems with a higher number of Rx antennas show this beneficial effect. Besides, if match with symmetric systems of identical Rx antenna number, the asymmetric ones are more efficient in terms of achieving their maximum linear capacity increase. For the MIMO capacity as well its deviations across the measured areas in the presence of a strong LOS signal component the results are very sufficient as the capacity widely stays high with low variations. References [1] E. Telatar, Capacity of Multi-Antenna Gaussian Channels, AT&T-Bell Technical Memorandum, [] G.J. Foschini and M. Gans, On the Limits of Wireless Comunications in a Fading Environment when Using Multiple Antennas, Wireless Personal Communication, vol. 6, pp , [3] F. Bohagen, P. Orten, G.E. Oien, Construction and Analysis of High-Rank Line-of-Sight MIMO Channels, Wireless Communications and Networking Conference, pp , March 005. [4] J.-S. Jiang, M.A. Ingram, Spherical-Wave Model for Short-Range MIMO, IEEE Transactions on Communications, vol. 53, No.9, September 005. [5] M. Paetzold, Mobile Fading Channels, John Wiley & Sons, 00. [6] W.C. Jakes, Microwave Mobile Communications, John Wiley & Sons, [7] A.A.M. Saleh, R.A. Valenzuela, A Statistical Model for Indoor Multipath Propagation, IEEE J. Select. Areas Commun., vol.5, pp , Copyright 006 WPMC 6