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\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 1Figure 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.