Asymptotic Throughput Analysis of Massive M2M Access Andrea Zanella, Andrea Biral, Michele Zorzi {zanella, biraland, zorzi}@dei.unipd.it University of Padova (ITALY)

Outline The challenge of massive M2M access Random access with MPR and SIC Approximate throughput model Asymptotic analysis Conclusions ITA - 2015

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 - 2015

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.)

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 - 2015

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 - 2015

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 - 2015

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 - 2015

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 - 2015

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

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

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? ITA - 2015

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: ITA - 2015

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: ITA - 2015

Minimizing the fixed-point solution of recursive eq. ITA - 2015

Approx asymptotic throughput We can also prove that n* is the optimal number of transmissions, i.e., In fact: Which is true since ITA - 2015

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. ITA - 2015

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 ITA - 2015

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 - 2015