Frequency Reuse Underwater:

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Frequency Reuse Underwater Capacity of an
Acoustic Cellular Network
Milica Stojanovic millitsa_at_mit.edu
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(No Transcript)
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Problem statement
xn? xkax(f)
Acoustic propagation
2D base stations on the surface (radio-based
infrastructure) or on the bottom
(cable-based infrastructure)
Design Given the bandwidth B Hz and a
desired density of users ? users/km2, design a
cellular system i.e., find cell radius and
reuse number (R,N) such that the performance
requirements are met (i) co-channel SIR
SIRo (ii) per-user bandwidth WWo
Capacity analysis What is the maximal user
density ?max that can be supported by a cellular
architecture within a given bandwidth B?
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System design SIR in acoustic channels
BoB/N for TDMA (B/N)/U for FDMA
A(x,f)A0 xk ax(f)

• R does not cancel out. SIR depends on both R,N.
• for every N, radius must satisfy RRo(N).

SIR also depends on frequency allocation (fmin,
B).
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SIR, SNR and SINR
Attenuation grows with fmin for signal and
interference. Overall effect SIR increases
with fmin.
Bandwidth allocation across N cells (each B/N)
(f1- f2), (f2- f3), , (fN-1- fN,) ? design for
the worst case, fminf1, band-edge.
SIR used as a figure of merit for system design ?
interference dominates over noise.
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SIR requirement and the minimal cell radius
User bandwidth requirement and the maximal cell
radius
At least one user per cell
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Cell radius and the reuse number Admissible
region (R,N)
Possible solutions (R,N) for the cellular system
topology lie between R0(N), R1(N), and the
straight line (a?)-1/2.

• R0(N) decays faster than R1(N)
• Admissible values of N
• between Nmin, Nmax
• For every admissible N, there is
• a range of admissible cell radii

• Small N
• easier frequency allocation
• minimal loss with guard band insertion

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Sensitivity of solution (R,N) to performance
requirements (SIRo,Wo) and system parameters
(?,B)
Stricter performance requirements cause the
admissible region to narrow. Increasing SIR0
causes R0 to increase. Increasing W0 causes R1
to decrease.
No solution! It is not possible to employ
cellular system architecture to meet the
required (SIRo,Wo) for the given (?,B).
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Capacity analysis
Def. capacity maximal user density that can be
supported within given bandwidth.
Maximal user density that can be supported for a
given N (conditional capacity)
Maximal user density (capacity)
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Capacity example

• Capacity increases with bandwidth.
• Below the solid curve lies the region (?,B)
• for which a cellular system can be designed.
• Capacity-achieving architectures are
• characterized by N that grows with ?max.

x
Practical system small N, ?max (N).

• Capacity depends on
• system requirements (SIR0,W0)
• (less for stricter)
• band-edge frequency fmin
• (through R0)

?max ?max (Ni) for B?NiW0,Ni1W0)
Ni3,4,7,9,etc. ?Ni is the capacity-achieving
architecture in this region
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Capacity and the band-edge frequency fmin
Increasing fmin improves the SIR, allows R0(N)
to be reduced.
x
Moving to higher frequencies enables support of
a greater user density within the same bandwidth.
Is there a price to be paid?
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Power and bandwidth allocation
Greater fmin greater SIR, capacity - greater
attenuation ? must increase transmission power
System design assumption SNRgtgtSIR, i.e.
SINRSIR ? use SIR as a figure of merit.
Ex. System design SIR015 dB, W01 kHz
?1 user/km2, B20 kHz N7 determine
fmin from the capacity curves ?max(7)
satisfactory at fmin20 kHz determine R
from the admissible region fmin? R0(7) ? R1 km

Is the SNRgtgtSIR assumption justified?
Def. PTn transmission power for the n-th cell
operating in the frequency region
fn,fnB/N. fnfmin(n-1)B/N, n1,2,N.
PTn,min minimal power for which SINRnSIRn?
e.g., deviation of no more than 1 dB.
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Determining the transmission power SIR, SINR

• Equal power for all cells
• SINRn curves are shifts of SINRN.
• Design assumption must be
• justified for the highest band, nN.
• It will automatically hold for all
• lower bands, nltN.
• Power is wasted.

Unequal power allocation A cell operating in a
lower band requires less power to meet the 1 dB
deviation rule than one operating in a higher
band.
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Minimal transmission power, cell radius, and the
band-edge frequency
SIR015 dB, W01 kHz ?1 user/km2, B20 kHz N7
Fixed cell radius R PTn,min increases with fmin
Minimal cell radius R0 PTn,min decreases with
fmin
Savings in power that result from transmission
over a shorter distance outweigh the expenses
required for transmission at a higher frequency.
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Summary

• Spatial frequency reuse ? appealing for
  underwater acoustic networks?
• Acoustic propagation simple rules of cellular
  radio system design do not apply.
• Reuse number N and cell radius R must satisfy a
  set of constraints in order to constitute
• an admissible solution for a cellular network
  topology. The range of solutions depends on
• performance requirements (SIRo,Wo) band-edge
  frequency (fmin)
• system parameters (?,B),
• System capacitymaximal user density that can be
  supported within given bandwidth
• ?max increases with B,
• defines a boundary for the region (?,B) in which
  a cellular system can be designed.
• Capacity-achieving architectures N that grows
  with ?max (but that is okay).
• Capacity increases as the operational bandwidth
  is moved to higher frequencies.
• Transmission power does not have to be increased
  if the cell radius is kept minimal.

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Number of users per Hz of occupied bandwidth
To maximize C (s.t.c. SIRSIRo, WWo), choose
RR1(N).
(Alternatively, to maximize per-user bandwidth W,
choose minimal R. )
Depending upon R(N), W,SIR, C and U will have
values between some min. and max.
W
C
SIR
U
?0.25 users/km2, B50 kHz, SIRo15 dB, Wo1 kHz.