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ð¦€ð–€0€2𑀠𮀠ð“€ðš€>ð˜€ð“€ 𧀕€0€2ðÏ€ ”€ð›€=™€ð“€ 𨀔€0€2ðÏ€ð”€ðœ€;ð™€ð“€ ð©€ð“€0€2ðЀð•€ð�€9ðš€ð“€ ðª€ð’€0€2ðÒ€ð–€ðñ€𔀠¬€’€0€2ðí€ðñ€ðñ€0!€3í€ðñ€ðñ€0€3í€ðñ€ðñ€0€ÿ€Å€ÿ€Å„Ð °°hX ÐÐ hXhh ÐÒT I. A. 1. a.(1)(a) i) a) 1 .1 .1 .1 .1 .1 .1 .1 TÒÕ-ìÑ ¼€Üˆ4 pŽ9ËEÍ ÑDecember 1990Á`(#1ÁDoc: IEEE P802.11/91©01ƒÑ ,8ÜD4P±�¸ES ÑÔ ¸e Ô Úyx°…dddyÚÕո܂¤Ñ ,8ÜD4P±�¸ES ÑÚyx°hdddyÚÔ  Ô Ñ ô\܈4 PŽANEå ÑÐÌX°` ¸ hÀpÈ xÐ (#€%Ø'ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿXVÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÌÐÐÌXVÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿX(ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÌÐContributionÁ(%ÁPage Á`,(#UÁBruce Tuch¸ÕÑ ¼€Üˆ4 pŽ9ËEÍ ÑÁà ì#ÁIEEE 802.11ƒ Ñ Xt܈4 PŽINEäö ÑÁà ì ÁWireless Access Method and Physical Layer Specificationsƒ Úyx°bdddyÚÔ  Ô Ã ÃTITLEÄ Ä:ÁàìÁTRADEOFF BETWEEN BANDWIDTH EFFICIENCYƒ AND MEDIUM REUSE EFFICIENCY à ÃDATEÄ ÄÁà ì$Á5 March,ƒ 1991 à ÃAUTHORÄ Ä:Áàì$ÁKiwi Smitƒ Ò€ÈÈÈÈà ÃFigure 1Ä ÄÈÈÈÈà ÃFigure 1Ä Ä€ÒÁà ìÁÚy!@Àð/ ðV€8à‚ÕÍÿƒLOGOPCX.NCRyÚ Systems Engineering b.v.ƒÔ ðV Ô Áà ì!ÁZadelstede 1©10ƒ Áà ìÁ3431 JZ Nieuwegeinƒ Áà ì!ÁThe Netherlandsƒ Áà ìÁPhone +31 3402 76479ƒ Áà ìÁFax +31 3402 39125ƒ Úyx°dddyÚÔ  Ô Ø€1ØÁ ÁINTRODUCTION 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. Ô +ÔŒ 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. ÃÃMedium reuse efficiency ÀÀ. ÄÄ In this analysis an isotropic signal decrease is assumed. A certain space (2©D or 3©D) 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 2©D area holds: Áà ìÁCÓ G Ó2Ó c¹ÿ Ó À À [D/R]Ó ¹ÿ Ó2Ó ÕG Ó with À À the 'proportional to' sign [1a]ƒ For the 3©D case holds: Áà ìÁCÓ àG Ó3Ó '¹ÿ Ó À À [D/R]Ó à¹ÿ Ó3Ó ™G Ó [1b] ƒ The above relationships can be found in for example [Jakes] It seems reasonable to define the medium reuse efficiency ÀÀ 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. Áà ìÁÀÀÓ tG Ó2Ó »¹ÿ Ó À À [R/D]Ó t¹ÿ Ó2Ó -G Ó [2a] ƒ ÃÃÄÄ Áà ìÁÀÀÓ P"G Ó3Ó —"¹ÿ Ó À À [R/D]Ó P"¹ÿ Ó3Ó "G Ó [2b] ƒ ÃÃEfficiency ÀÀ as a function of Signal©to©Interference Ratio (SIR)ÄÄ 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: ÂX ÂÁ` ÁÁ¸ ÁÁ€` ÁÁ€ÁÁ€° ÁÁ€ XÁÁ€ÁÁ€ÁÁ€ÁÁ€Á Áàì!ÁP À À dÓ Ø+¹ÿ Ó©nÓ ‘+G Ó with ƒÆ(#ÆÔ Ø+ÔŒ d the distance between transmitter and receiver and n the attenuation exponent. Given the center©to©center distance D of BSA's, at which reliable communication is possible (BER < 10Ó Ä¹ÿ Ó©xÓ }G Ó) and the radius R of a BSA, the worst case SIR occurs in a situation as sketched in figure 1. P Q Á Á A ÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀ B ÀÀÀÀ ÀÀÀÀ ÀÀÀÀ ÀÀÀÀ ÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀ D ÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀ Á ÁÁ` ÁÁ¸ Á 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: Á ÁÁ` ÁÁ¸ ÁSIR À À RÓ ì¹ÿ Ó©nÓ ¥G Ó / (D©2R)Ó ì¹ÿ Ó©nÓ ¥G Ó [3] By combining [2] and [3] the medium reuse can be expressed as a function of the required SIR: Áà ìÁÀÀÓ °G Ó2Ó ÷¹ÿ Ó À À [2+SIRÓ °¹ÿ Ó1/nÓ iG Ó]Ó °¹ÿ Ó©2Ó iG Ó ƒ [4a] Áà ìÁÀÀÓ ˜G Ó3Ó ß¹ÿ Ó À À [2+SIRÓ ˜¹ÿ Ó1/nÓ QG Ó]Ó ˜¹ÿ Ó©3Ó QG Ó ƒ [4b] Ó ŒG ÓÓ Ó¹ÿ ÓÓ Œ¹ÿ ÓÓ EG Ó 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 ÀÀ, 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 ÀÀ, defined as the ratio between bitrate and bandwidth, is upperbounded by the well known Shannon capacity formula : Á ÁÁ` ÁÁ¸ ÁÁÁÀÀ = logÓ Ø+G Ó2Ó ,¹ÿ Ó(1+SNR) [5]Ô Ø+ÔŒ Combining [5] and [4], together with the assumptions made above, results in a medium reuse efficiency, bandwidth efficiency product À%À as a function of SNR and attenuation exponent n. Á ÁÁ` ÁÀ%ÀÓ ÄG Ó2Ó ¹ÿ Ó À À [logÓ ÄG Ó2Ó ¹ÿ Ó(1+SNR)]/[[2+SNRÓ Ä¹ÿ Ó1/nÓ }G Ó]Ó Ä¹ÿ Ó©2Ó }G Ó]Á4È4ÁÁ4 9ÁÁ9x>Á[6a] Á ÁÁ` ÁÀ%ÀÓ ¬G Ó3Ó ó¹ÿ Ó À À [logÓ ¬G Ó2Ó ó¹ÿ Ó(1+SNR)]/[[2+SNRÓ ¬¹ÿ Ó1/nÓ eG Ó]Ó ¬¹ÿ Ó©3Ó eG Ó]Á4È4ÁÁ4 9ÁÁ9x>Á[6b] In figure 3 and 4 respectively À%ÀÓ | G Ó2Ó à ¹ÿ Ó and À%ÀÓ | G Ó3Ó à ¹ÿ Ó are given for 3 values of n as a function of the SNR. Equation [6] gives an upperbound on À%À. Without running ahead of the choice for an appropriate modulation scheme, the same calculations may be carried out for M©level PSK. A SNR of 10 dB yields for 4©PSK a BER of approximately 10Ó 4¹ÿ Ó©3Ó íG Ó. Increasing the bandwidth efficiency by 1 bit/sec*Hz requires about 6 dB. For the bandwidth efficiency ÀÀ in case of M©PSK modulation holds: Á ÁÁ` ÁÁ¸ ÁÁÁ ÀÀ = logÓ G Ó2Ó K¹ÿ Ó(M) [7] These figures mentioned above, together with [7], are used to obtain equation [8], in which the relation between bandwidth efficiency ÀÀ and required SNR for M©PSK is given. Á ÁÁ` ÁÁ¸ ÁÀÀ = [2 + 10*logÓ ¼G Ó10Ó ¹ÿ Ó(SNR)] / 6 [8] Combining the equations [4],[7] and [8], together with the already discussed assumptions about noise©like interference and interference limited systems, À%À can be calculated as a function of the number M. À%ÀÓ ŒG Ó2Ó Ó¹ÿ Ó and À%ÀÓ ŒG Ó3Ó Ó¹ÿ Ó are sketched in figure 6 and 7 respectively, for n=2,3 and 4.