Andrea Zanella, Andrea Biral, Michele Zorzi

1
Asymptotic Throughput Analysis of Massive M2M
Access

• Andrea Zanella, Andrea Biral, Michele Zorzi
  
• zanella, biraland, zorzi_at_dei.unipd.it
• University of Padova (ITALY)

2
Outline

• The challenge of massive M2M access
• Random access with MPR and SIC
• Approximate throughput model
• Asymptotic analysis
• Conclusions

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Challenges for M2M access

• Massive number of users
• Sporadic traffic
• Short messages
• Current access schemes are not adequate for this
  type of scenario
• Costly first access mechanisms
• Lack of effective ways for massive access

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Techniques for improved access

• Capture phenomenon
• Successful reception in the event of a collision
• Many models exist, based on power/time of
  arrival/distance relationships, number of
  overlapping signals/etc.
• Many papers in the literature
• Multi-Packet Reception capability
• The ability of a receiver to decode multiple
  overlapping packets
• Requires some advanced PHY technique (CDMA, MIMO,
  IC, etc.)

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Massive asynchronous access

• Approach
• move complexity to BS
• use advanced MAC/PHY
• MPR multi packet reception
• SIC successive interference cancellation
• Some relevant questions
• How many transmitters can be served?
• What is the maximum cell throughput?
• How can it be achieved?

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Physical capture model
TX1
TXn
RX
TX2
TXj
TX3
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Performance analysis
System parameters

• Number of simultaneous transmissions (n)
• Statistical distribution of the received signal
  powers (Pi)
• Capture threshold (b)
• Max number of SIC iterations (K)
• Interference cancellation ratio (z)

Capture probability? System throughput?
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Performance analysis

• Capture probability
• Cn(rK)Prr signals out of n are captured within
  at most K SIC cycles
• Computing Cn(rK) is difficult because the SINRs
  are all coupled
• E.g.
• Computation of Cn(rk) becomes more and more
  complex as the number n of signals increases
• SIC makes things even more complex

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Computation of capture probs

• Narrowband (bgt1), No SIC (K0)
• ZorziRao,JSAC1994,TVT1997 derive the
  probability Cn(10) that one signal is captured
• MPR and SIC are not considered
• Wideband (blt1), No SIC (K0)
• NguyenEphremidesWieselthier,ISIT06, ISIT07
  derive the probability 1-Cn(00) that at least
  one signal is captured
• Expression involves n folded integrals, does not
  scale with n
• Wideband (blt1)SIC (Kgt0)
• ViterbiJSAC90 shows that SIC can achieve
  Shannon capacity in AWGN channels
• Requires suitable received signal power
  allocation
• Narasimhan, ISIT07 studies outage rate regions
  in presence of Rayleigh fading
• Eqs can be computed only for few users
• Weber et al, TIT07 study SIC in ad hoc wireless
  networks
• Derive bounds on the transmission capacity based
  on stochastic geometry arguments
• ZanellaZorzi, TCOM2012 provide a scalable
  method for the numerical evaluation of the
  capture probability distribution Cn(rK), and
  simple approximate expressions

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Approximate mean number of captures first
reception

• Iteration h0 number of undecoded signals n0n
• decoded signals, with
  mean
• Approx capture threshold
• Approx capture condition
• Mean number of decoded signals
• Mean number of still undecoded signals

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Approximate mean number of captures h-th
iteration

• Iteration hgt0 avg number of undecoded signals
• Approximate capture threshold
• Approximate capture condition
• Mean number of decoded signals
• Mean number of still undecoded signals and
  average throughput

• Interf. from undecoded signals

• Residual interf.

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SICMPR throughput
High congestion
Low congestion
Approx
Simulation
b0.02 Rayleigh fading
optimal of concurrent transmissions
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Fixed point throughput approx.

• Letting of SIC cycles go to infinity, the
  residual interference can
• either go to zero ? all signals are eventually
  decoded and the throughput equals the number n of
  overlapping transmissions
• or reach a steady value I8(n) which is the
  fixed-point solution of the equation
• Average throughput in the limit

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Approx asymptotic throughput

• Throughput grows linearly with n until the
  equation returns non-zero solution(s) xgt0
• Max throughput equals where n is the
  value of n for which x is minimized
• To find n, we rewrite the eq. as

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Minimizing the fixed-point solution of recursive
eq.
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Approx asymptotic throughput

• We can also prove that n is the optimal number
  of transmissions, i.e.,
• In fact
• Which is true since

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Asymptotic performance

• Analytical throughput estimate is reasonably good
  for small values of b
• Analysis is accurate in the range of interest
  (massive low-rate access)
• Optimal throughput scales linearly with 1/b
• It is possible to serve twice as many users at
  half the rate
• An arbitrarily large number of nodes can be
  served (but check OH)

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Conclusions

• We proposed an approximate analysis of the
  asymptotic throughput of random wireless systems
  with MPR SIC
• The mathematical model is shown to be slightly
  optimistic in estimating the throughput, but it
  captures correctly the fundamental behaviors
• With ideal SIC, MPR capabilities can be fully
  exploited even using a simple slotted random
  access mechanism
• Achieving the optimal performance requires an
  accurate control of the total number of
  transmitters
• Throughput grows almost linearly with 1/b

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Future work

• Improve the accuracy of the mathematical model
  for large values of SIC iterations
• Some ideas in the paper
• Relax some simplifying assumptions, such as ideal
  SIC
• Account for residual interference
• Include protocol aspects into the model
• How to control access in a decentralized fashion
• Investigate energy aspects
• Very sensitive in M2M scenarios