Andrea Zanella, Andrea Biral, Michele Zorzi

{zanella, biraland, zorzi}@dei.unipd.it

University of Padova (ITALY)

Asymptotic Throughput Analysis of Massive M2M Access

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.)4

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

j > b j-th signal is correctly decoded (capture)

j <= b j-th signal is collided (missed)

Aggregate

interference

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TX1

TX2

TX3

TXj

TXn

Pj

PnP1P2

P3

RX

Performance analysis

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)

System parameters

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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

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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

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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

PEnbI 10

10

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

1Pr~ hhhh IPIPnr

)()|( 11 hPhhPhh InFIPIFnn

•Residual interf.•Interf. from undecoded signals

11

1)1( hn nnhS

SIC+MPR throughput

b=0.02

Rayleigh fading

# of SIC iterations

High congestionLow congestion

optimal # of concurrent

transmissions

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ApproxSimulation

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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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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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

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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)

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

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