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A. 1. a.(1)(a) i) a) 1 .1 .1 .1 .1 .1 .1 .1 T- 4 p9E December 1990`(#1Doc: IEEE P802.11/9101 ,8D4PES  e  yxdddy ,8D4PES yxhdddy    \4 PANE X` hp x (#%'XVXVX(Contribution(%Page `,(#UBruce Tuch 4 p9E  #IEEE 802.11  Xt4 PINE   Wireless Access Method and Physical Layer Specifications yxbdddy   TITLE :TRADEOFF BETWEEN BANDWIDTH EFFICIENCY AND MEDIUM REUSE EFFICIENCY DATE $5 March, 1991 AUTHOR :$Kiwi Smit  Figure 1  Figure 1  y!@/ V8LOGOPCX.NCRy Systems Engineering b.v. V  !Zadelstede 110 3431 JZ Nieuwegein !The Netherlands Phone +31 3402 76479 Fax +31 3402 39125 yxdddy   1 INTRODUCTION To a certain extend the development of a MAC protocol and the design of a PHY layer can be carried out independently. However some dependencies exists. This contribution shows the impact of the SNR per bit, required for reliable communication, on radio medium reuse, a major architectural concept. The required SNR is directly related to the bandwidth efficiency and the complexity of the detector, both important issues in the PHY layer. If one defines a PHY layer, without taking into account the architectural wish of medium reuse, one would try to optimize the bandwidth efficiency, and therefore the raw bitrate, by making the SNR per bit as high as possible. This in turn can be accomplished by using a transmit power as high as allowed or economically feasible. If, from the other hand, the product of raw bitrate and the number of BSA's, in which communication can take place simultaneously, has to be maximized, the SNR per bit has an optimum value, depending on the attenuation characteristics of the channel. Note that the medium reuse efficiency is not defined in terms of the bitrate per squared or cubic meter. The reasons for this is that it is believed that the BSA's should cover a certain minimum area, such that a typical office floor can be serviced with one BSA. Therefore, increasing the bitrate per squared or cubic meter by decreasing the transmit power, and so the coverage area of the BSA, is possible only to a certain extend (see paper on this subject by Bruce Tuch, .......). The medium reuse efficiency, given this size constraint, depends only on the number of BSA's that can be active simultaneously.  +Ԍ In the derivation of the optimum SNR per bit, some assumptions are made that make the optimization tractable, but may not be appropriate for indoor environments. This analysis gives therefore an insight in the mechanism and a direction for further research rather than absolute quantative results. Medium reuse efficiency .  In this analysis an isotropic signal decrease is assumed. A certain space (2D or 3D) now is covered by equal sized BSA's. The actual form of BSA is of no importance in this analysis. Boundary effects are not taken into account, so it is assumed that the space under investigation contains many BSA's. With R the distance from an access point to its farthest serviced terminal (defines the size of the coverage area of a BSA) and D the distance between access points at which reliable communication within both BSA's is possible, for the number of channels C necessary to cover the whole 2D area holds: C G 2 c   [D/R]  2 G  with  the 'proportional to' sign [1a] For the 3D case holds: C G 3 '   [D/R]  3 G  [1b] The above relationships can be found in for example [Jakes] It seems reasonable to define the medium reuse efficiency  as the inverse of the number of channels C necessary for covering the whole area. This number defines the percentage of BSA's that can be active simultaneously.  tG 2    [R/D] t 2 -G  [2a]   P"G 3 "   [R/D] P" 3 "G  [2b] Efficiency  as a function of SignaltoInterference Ratio (SIR) A fixed transmit power is assumed for all stations, so no power control mechanism is assumed. For the averaged received signal power P now holds: X `  `  X !P  d + өn +G  with (# +Ԍ d the distance between transmitter and receiver and n the attenuation exponent. Given the centertocenter distance D of BSA's, at which reliable communication is possible (BER < 10  өx }G ) and the radius R of a BSA, the worst case SIR occurs in a situation as sketched in figure 1. P Q   A  B      D   `   Figure 1 In this worst case situation station Q has to receive access point B, while station P transmits to access point A. For the SIR holds:  `  SIR  R  өn G  / (D2R)  өn G  [3] By combining [2] and [3] the medium reuse can be expressed as a function of the required SIR:  G 2    [2+SIR  1/n iG ]  ө2 iG  [4a]  G 3    [2+SIR  1/n QG ]  ө3 QG  [4b]  G      EG  As can be seen from figure 2 the medium reuse efficiency increases with decreasing SIR required for reliable communication. However, there is another side of the coin. With decreasing SIR the bandwidth efficiency , expressed in the number of bits per second and per Hz, that can be reliable communicated, will be decreased too. So a tradeoff exists between raw bit rate and medium reuse efficiency. This tradeoff can be shown more explicitly if the following assumptions are made. The system is supposed to be interference limited. A further assumption is that that the interference can be treated as Gaussian noise. For additive white Gaussian noise channels the bandwidth efficiency , defined as the ratio between bitrate and bandwidth, is upperbounded by the well known Shannon capacity formula :  `   = log +G 2 , (1+SNR) [5] +Ԍ Combining [5] and [4], together with the assumptions made above, results in a medium reuse efficiency, bandwidth efficiency product % as a function of SNR and attenuation exponent n.  ` % G 2    [log G 2  (1+SNR)]/[[2+SNR  1/n }G ]  ө2 }G ]444 99x>[6a]  ` % G 3    [log G 2  (1+SNR)]/[[2+SNR  1/n eG ]  ө3 eG ]444 99x>[6b] In figure 3 and 4 respectively % | G 2  and % | G 3  are given for 3 values of n as a function of the SNR. Equation [6] gives an upperbound on %. Without running ahead of the choice for an appropriate modulation scheme, the same calculations may be carried out for Mlevel PSK. A SNR of 10 dB yields for 4PSK a BER of approximately 10 4 ө3 G . Increasing the bandwidth efficiency by 1 bit/sec*Hz requires about 6 dB. For the bandwidth efficiency  in case of MPSK modulation holds:  `    = log G 2 K (M) [7] These figures mentioned above, together with [7], are used to obtain equation [8], in which the relation between bandwidth efficiency  and required SNR for MPSK is given.  `   = [2 + 10*log G 10  (SNR)] / 6 [8] Combining the equations [4],[7] and [8], together with the already discussed assumptions about noiselike interference and interference limited systems, % can be calculated as a function of the number M. % G 2   and % G 3   are sketched in figure 6 and 7 respectively, for n=2,3 and 4.