1. Asymptotic Throughput Analysis of Massive M2M Access
Andrea Zanella, Andrea Biral, Michele Zorzi
{zanella, biraland,
University of Padova (ITALY)

2. Outline The challenge of massive M2M access
Random access with MPR and SIC
Approximate throughput model
Asymptotic analysis
Conclusions
ITA

3. 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
ITA

4. 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.)

5. 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?
ITA

6. Physical capture model
Decoding model: SINR threshold
Use of strong coding to achieve Shannon capacity
Pj : power of the j-th signal at the receiver
N0: noise power (neglected)
gj : SINR of the j-th signal
b : capture threshold Pj Pn P1 P2 P3
TX1
TXn RX
TX2
TXj
TX3
gj > b j-th signal is correctly decoded (capture)
Aggregate
interference
gj <= b  j-th signal is collided (missed)
ITA

7. Performance analysis Capture probability? System throughput?
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?
ITA

8. Performance analysis Capture probability
Cn(r;K)=Pr[r signals out of n are captured within at most K SIC cycles]
Computing Cn(r;K) is difficult because the SINRs are all coupled
E.g.
Computation of Cn(r;k) becomes more and more complex as the number n of signals increases
SIC makes things even more complex
ITA

9. Computation of capture probs
Narrowband (b>1), No SIC (K=0)
[Zorzi&Rao,JSAC1994,TVT1997] derive the probability Cn(1;0) that one signal is captured
MPR and SIC are not considered
Wideband (b<1), No SIC (K=0)
[Nguyen&Ephremides&Wieselthier,ISIT06, ISIT07] derive the probability 1-Cn(0;0) that at least one signal is captured
Expression involves n folded integrals, does not scale with n
Wideband (b<1)+SIC (K>0)
[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(r;K), and simple approximate expressions
ITA

10. Approximate mean number of captures: first reception
Iteration h=0: number of undecoded signals n0=n
decoded signals, with mean
Approx capture threshold
Approx capture condition
Mean number of decoded signals
Mean number of still undecoded signals

11. Approximate mean number of captures: h-th iteration
Iteration h>0: 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
Residual interf.
Interf. from undecoded signals

12. optimal # of concurrent transmissions
SIC+MPR throughput
Low congestion
High congestion
Approx
Simulation
b=0.02
Rayleigh fading
# of SIC iterations
optimal # of concurrent transmissions
SIC gain increases with # of cancellation cycles, up to an asymptotic value that only depends on the capture threshold b.
Maximum is reached for a certain optimal collision set size n*
Question: What’s the scaling behavior with more and more nodes that transmit at less and less rate?
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13. 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 I∞(n) which is the fixed- point solution of the equation:
Average throughput in the limit:
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14. Approx asymptotic throughput
Throughput grows linearly with n until the equation returns non-zero solution(s) x>0
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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15. Minimizing the fixed-point solution of recursive eq.
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16. Approx asymptotic throughput
We can also prove that n* is the optimal number of transmissions, i.e.,
In fact:
Which is true since
ITA

17. 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)
A BS capable of performing perfect SIC and MPR can theoretically decode an arbitrary large number of simultaneous transmissions by proportionally reducing the per-user data rate, in such a way that the aggregate system capacity remains almost constant. Furthermore, the capacity of the cell depends on the statistical distribution of the signal powers: generally, the higher the variance, the more effective the SIC and, then, the larger the asymptotic aggregate capacity.
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18. 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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19. 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
ITA