Hierarchical Cooperation Achieves Linear Scaling in Ad Hoc Wireless Networks David Tse Wireless...
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![Page 1: Hierarchical Cooperation Achieves Linear Scaling in Ad Hoc Wireless Networks David Tse Wireless Foundations U.C. Berkeley MIT LIDS May 7, 2007 Joint work.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d605503460f94a41ff0/html5/thumbnails/1.jpg)
Hierarchical Cooperation Achieves Linear Scaling in Ad Hoc Wireless
Networks
David TseWireless Foundations
U.C. Berkeley
MIT LIDS May 7, 2007
Joint work with Ayfer Ozgur and Olivier Leveque at EPFL
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Scaling of Ad Hoc Wireless Networks
• 2n nodes randomly located in a fixed area.
• n randomly assigned source-destination pairs.
• Each S-D pair demands the same data rate.
• How does the total throughput T(n) of the network scale with n?
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How much can cooperation help?
??T(n) = £(1) T(n) = £(p
n)Gupta-Kumar 00
?
Courtesy: David Reed of MIT
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Main Result
Linear capacity scaling is achievable with intelligent cooperation.
More precisely:
For every > 0, we construct a cooperative scheme that can achieve a total throughput T(n) = n1-.
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Channel Model
• Baseband channel gain between node k and l:
where rkl is the distance apart and kl is the random phase (iid across nodes).
• is the path loss exponent (in power)
®¸ 2
hkl = Gr¡ ®2
kl ej µk l
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Dense networks
• Setting: many nodes all within communication range of each other.
• Number of nodes are large but nearest nodes are still far field from each other.
• Example:– Berkeley campus (1 square km)– n = 10,000 users (n >> 1)– Typical distance between nearest neighbors: 10m– Carrier frequency: 2.4 GHz => wavelength ~0.1m
• Will talk about extended networks later.
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Gupta-Kumar Capacity is Interference-Limited
• Long-range transmission causes too much interference.
• Nearest-neighbor transmission means each packet is transmitted times (multi-hop).
• To get linear scaling, must be able to do many simultaneous long-range transmissions.
• How to deal with interference?• A natural idea: distributed MIMO (Aeron &
Saligrama 06).
pn
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MIMO:Multiple Transmit Multiple Receive Antennas
• The random MxM channel matrix allows transmission of M parallel streams of data.
• Originally conceived for antennas co-located at the same device.
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Distributed MIMO
• MIMO effect can be simulated if nodes within each cluster can cooperate.
• But cooperation overhead limits performance.• What kind of architecture minimizes overhead?
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A 3-Phase Scheme
• Divide the network into clusters of size M nodes.
• Focus first on a specific S-D pair. source s wants to send M bits to destination d.
Phase 1 :Setting up Tx cooperation:1 bit to each node in Tx cluster
Phase 2:Long-rangeMIMO between s and d clusters.
Phase 3:Each node in Rx clusterquantizes signal into k bitsand sends to destination d.
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Parallelization across S-D Pairs
Phase 1:Clusters work in parallel.Sources in each cluster taketurn distributing their bits.
Total time = M2
Phase 2:1 MIMO trans.at a time.
Total time = n
Phase 3:Clusters work in parallel.Destinations in each clustertake turn collecting their bits.
Total time = kM2
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Back-of-the-Envelope Throughput Calculation
total number of bits transferred = nM
total time in all three phases = M2 +n + kM2
throughput: bits/second
Optimal cluster size
Best throughput:
nMM 2 + n + kM 2
M ¤ =p
n
pn
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Further Parallelization
• In phase 1 and 3, M2 bits have to be exchanged within each cluster, 1 bit per node pair.
• Previous scheme exchanges these bits one at a time (TDMA), takes time M2.
• Can we increase the spatial reuse ?• Can break the problem into M sessions, each
session involving M S-D pairs communicating 1 bit with each other:
cooperation = communication
• Any better scheme for the small network can build a better scheme for the original network.
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Recursion
Lemma: A scheme with thruput Mb for the smaller network yields for the original network a thruput:
with optimal cluster size:
n1
2¡ b
M ¤ = n1
2¡ b
f (b) =1
2¡ b
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MIMO + Hierarchical Cooperation-> Linear Scaling
.
Setting up Tx cooperation
Long-range MIMO
Cooperateto decode
At the highest level hierarchy, cluster size is of the order n1- => near network-wide MIMO cooperation.
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Upper Bound
• A simple upper bound: each source node has the benefit of all other nodes in the network cooperating to receive without interference from other nodes.
• Each source gets a rate of at most order log n.• Yields an upper bound on network throughput
• The hierarchical scheme is nearly information theoretically optimal.
Cn · O(n logn)
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Transmit Power Requirement of Scheme
• At all levels of hierarchy, transmit powers in the MIMO phase can be set such that the total average received SNR at each node is 0 dB.
• This yields MIMO rate linear with the cluster size in phase 2.
• This also explains why a fixed number of quantization bits per sample suffices.
• At the total level of hierarchy, the transmit power per node is P/n.
• We have power to spare!
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From Dense to Extended Networks
• So far we have looked at dense networks, where the total area is fixed.
• Another natural scaling is to keep the density of nodes fixed and the networks covers an increasing area.
• Distances are increased by a factor of n1/2 in extended networks.
• Equivalently, an extended network is a dense network with power constraint P/n/2 per node.
• Immediate result: For =2, linear scaling can be achieved
for extended networks.
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Extended Networks: >2
• For > 2, even when each node transmits at full power in the MIMO phase,
total received SNR per node = n1-/2 -> 0
• n by n MIMO transmission is now power-limited:
CMIMO ~ total Rx power = n2-/2
• Can the hierarchical scheme achieve arbitrarily close to this scaling?
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Quantization is a Problem
• Subtle issue: information per received sample per Rx antenna in MIMO goes to zero.
• If we use fixed number of bits to quantize each sample, we are doomed.
• Cannot use vanishing number of bits either.• Use bursty transmission so that during
transmission the SNR at each Rx antenna is again 0db.
• We are still power-efficient but Rx cooperation is no longer onerous.
• We are operating at the boundary of power-limited and degrees-of-freedom-limited regimes.
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Is Our Scheme Optimal for Extended Networks?
We show: for all , the cutset bound scales like the total received power under no Tx cooperation.
A dichotomy: > 3: this total power is , dominated by transfer
between the few boundary users. Multihop is optimal. <3: total power is n2-/2, dominated by transfer between the many interior users . Our scheme is optimal.
Tx cluster: size n1-
Rx cluster: size n1-
Distance p
n
Achievable (Top Level of Hierarchical Scheme) Cutset Bound
pn
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Conclusion
• Hierachical cooperation allows network-wide MIMO without significant cooperation overhead.
• Network wide MIMO achieves a linear number of degrees of freedom.
• This yields a linear scaling law for dense networks.
• It also achieves maximum energy transfer in extended networks when path loss exponent is less than 3.
• Better than Gupta-Kumar scaling is possible in the low attenuation regime.