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Wireless Networks

Erschienen in:

18.03.2020

Fast node cardinality estimation and cognitive MAC protocol design for heterogeneous machine-to-machine networks

verfasst von: Sachin Kadam, Chaitanya S. Raut, Aman Deep Meena, Gaurav S. Kasbekar

Erschienen in: Wireless Networks | Ausgabe 6/2020

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Abstract

We design two estimation schemes, Method I and Method II, for rapidly obtaining separate estimates of the number of active nodes of each traffic type in a heterogeneous machine-to-machine (M2M) network with T types of nodes (e.g., those that send emergency, periodic, normal type data etc.), where \(T\ge 2\) is an arbitrary integer. Method I is a simple scheme, and Method II is more sophisticated and outperforms Method I. Also, we design a medium access control (MAC) protocol that supports multi-channel operation for a heterogeneous M2M network with T types of nodes, operating as a secondary network using Cognitive Radio technology. In every time frame, our Cognitive MAC protocol uses the proposed estimation schemes to rapidly estimate the active node cardinality of each type, and uses these estimates to find the optimal contention probabilities to be used. We compute a closed form expression for the expected number of time slots required by Method I to execute, and a simple upper bound on it. Also, we analytically obtain expressions for the expected number of successful contentions per frame and the expected amount of energy consumed. Finally, we evaluate the performances of our proposed estimation schemes and Cognitive MAC protocol using simulations.

Vorheriger Artikel RETRACTED ARTICLE: Throughput maximization of multichannel allocation mechanism under interference constraint for hybrid overlay/underlay cognitive radio networks with energy harvesting

Nächster Artikel Performance evaluation of a C-RAN supporting a mixture of random and quasi-random traffic

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For example, some M2M nodes need to transmit data (e.g., smart meter readings) periodically, some need to send emergency or alarm messages (e.g., in healthcare and security applications), some need to transmit normal data traffic and some need to reliably transmit data packets (e.g., in remote payment gateway systems) [3, 5, 6].

Specifically, Wi-Fi has high power consumption, due to which it is not suitable for battery operated M2M devices, and Bluetooth has high latency when the number of devices is large, as is the case in M2M networks [7]. ZigBee operates on unlicensed bands and is prone to interference from Wi-Fi networks and other equipment (e.g., microwave ovens) that use those bands [4, 7]. Due to the high demand for H2H communication services such as voice, video, emails etc, only a limited amount of radio spectrum is available with cellular operators to support M2M communications [4].

Note that for two nodes to be able to exchange data, both must have their wireless transceiver tuned to a common channel at a time.

Note that [19] is a technical report corresponding to [18], and it is available online.

Note that this would be the case in M2M networks in which the nodes are, e.g., sensors that occasionally transmit measurements or nodes that transmit alarms, emergency alerts and other infrequent messages.

A given node randomly chooses a preamble from a pool of preambles and transmits it on the random access channel (RACH).

|A| denotes the cardinality of set A.

If all the bits of the ID are 1, then its hash value is defined to be l.

See Lemma 4.1 and equation (6) on page 1446 of [21], which state that \({\hat{n}} = \frac{1}{\phi } 2^{\rho }\). The value 1.2897 is obtained by inverting \(\phi = 0.775351\), i.e., \(1/\phi = 1.2897\). In the computation of \({\hat{n}}\), \(1/\phi\) is used as a correction factor and it is introduced to improve the accuracy of the estimation [21].

\(\lceil x\rceil =\) The smallest integer greater than or equal to x.

Note that the block results (E, \(\alpha\)), (\(\alpha\), E), (\(\alpha\), \(\beta\)) and (\(\beta\), \(\alpha\)) cannot occur under the above protocol. The reason is as follows. Recall that active Type 1 nodes transmit symbol \(\alpha\) in both the slots, and Type 2 and Type 3 nodes do not use symbol \(\alpha\). So whenever one (respectively, two or more) node (respectively, nodes) of Type 1 transmits (respectively, transmit), then only the following results are possible: (\(\alpha\), \(\alpha\)), (\(\alpha\), C), and (C, \(\alpha\)) (respectively, (C, C)). Hence, whenever symbol \(\alpha\) is observed in one slot, the result of the other slot should be either \(\alpha\) or C.

For example: (i) If the outcome is (\(\alpha , \alpha , \ldots , \alpha\)), then it implies that exactly one node from \({\mathcal {N}}_1\) has transmitted and no nodes from \({\mathcal {N}}_2, \ldots , {\mathcal {N}}_T\) have transmitted. (ii) If the outcome is (\(\beta , \beta , \ldots , \beta\)), then it implies that exactly one node from each of \({\mathcal {N}}_2, \ldots , {\mathcal {N}}_T\) have transmitted and no node from \({\mathcal {N}}_1\) has transmitted. (iii) If the outcome is (\(\alpha , C, C, \ldots , C, C, \alpha\)), then it implies that exactly one node from \({\mathcal {N}}_1\), at least one node from \({\mathcal {N}}_3, {\mathcal {N}}_4, \ldots , {\mathcal {N}}_{T-2}, {\mathcal {N}}_{T-1}\) have transmitted and no node from \({\mathcal {N}}_2\) and \({\mathcal {N}}_T\) have transmitted. (iv) If the outcome is (\(\beta , C, E, \beta , E, E, \ldots , E\)), then it implies that exactly one node from each of \({\mathcal {N}}_2\) and \({\mathcal {N}}_5\), at least two nodes from \({\mathcal {N}}_3\) have transmitted, and no nodes from any of the remaining types have transmitted.

For example, \(S_W\) may be 5 [22].

For each \(j \in \{1, \dots , |C_{II}|\}\), the \(((j-1)(T-1)+1)^{th}\), …, \((j(T-1))^{th}\) slots of the third phase are used by nodes from \({\mathcal {N}}_2, \ldots , {\mathcal {N}}_T\) respectively. Specifically, for each \(j = 1, \dots , |C_{II}|\), in slot \(((j-1)(T-1)+1)\) (respectively, \(((j-1)(T-1)+2)\), …, \((j(T-1)\))) of the third phase, the active nodes from \({\mathcal {N}}_2\) (respectively, \({\mathcal {N}}_3\), …, \({\mathcal {N}}_T\)) whose hash value equals the first phase block number, say i, of the \(j^{th}\) element of \(C_{II}\) transmit. If slot \(((j-1)(T-1)+1)\) (respectively, \(((j-1)(T-1)+2)\), …, \((j(T-1)\))) is empty, then \(B(2,i) = 0\) (respectively, \(B(3,i) = 0\), …, \(B(T,i) = 0\)), else \(B(2,i) = 1\) (respectively, \(B(3, i) = 1\), …, \(B(T, i) = 1\)). Also, since \(B(1,i) = 1\), the above ambiguity is resolved in the third phase.

For example, each active node of Type 1 and hash value i transmits symbol \(\alpha\) in slot 1 and does not transmit in slots \(2, \ldots , \eta _T\) of block \(B_i\). Each active node of Type 2 and hash value i transmits symbol \(\alpha\) in slots 1 and 2 and does not transmit in slots \(3, \ldots , \eta _T\) of block \(B_i\). For T even, each active node of Type T and hash value i transmits symbol \(\beta\) in slots \(1, \ldots , \eta _T\) of block \(B_i\). For T odd, each active node of Type T and hash value i transmits symbol \(\beta\) in slot 1, symbol \(\alpha\) in slot \(\eta _T\), and does not transmit in slots \(2, \ldots , \eta _T -1\) of block \(B_i\).

For example: Let us consider the case \(T=4\). From Fig. 4, we get that the symbol combinations used are \((\alpha , 0)\), \((\alpha , \alpha )\), \((0, \beta )\), and \((\beta , \beta )\). If the slot results in the first phase of block \(B_i\) are (\(\alpha , \beta\)), it implies that exactly one node each from Type 1 (hence, \(B(1,i)=1\)), Type 3 (hence, \(B(3,i)=1\)), and no nodes from Type 2 (hence, \(B(2,i)=0\)), Type 4 (hence, \(B(4,i)=0\)) have transmitted.

We assume that the probabilities \(z_i\) are known to the base station; for example, they can be estimated using past observations of PU occupancies on different channels.

Recall that for \(T = 2\) and \(T = 3\), the same estimation scheme is used under Methods I and II described in Sect. 4. For \(T \ge 4\), either Method I or Method II can be used in the EW.

Note that although the value of \(R_s\) is not known in advance, after the first (respectively, second) phase of the estimation scheme, the BS can find the value of \(|C_I|\) (respectively, \(|C_{II}|\)) (see Sects. 4.1.1 and 4.1.2). So the information required to reserve \(R_s\) slots is available with the network.

\(\lfloor x\rfloor =\) The largest integer less than or equal to x.

All our simulations were done using the MATLAB software.

Let \(n_b\) (respectively, \({\hat{n}}_b\)) be the number of active nodes (respectively, estimate of the number of active nodes) of Type b. Let \(\epsilon\) and \(\delta\) denote the desired relative estimation error and estimation scheme failure probability respectively [25]. For the given accuracy requirements (\(\epsilon , \delta\)), under each estimation scheme, estimates \({\hat{n}}_b\) are obtained by independently running the scheme multiple times and averaging the results; the number of runs is selected such that \(Pr(|{\hat{n}}_b - n_b| \le \epsilon n_b) \ge 1 - \delta\). In our simulations, the parameter values \(\epsilon = 0.05\) and \(\delta = 0.01\) are used.

Note that for \(T = 2\) and \(T= 3\), we use the same scheme in both the methods. Hence, \(q^I_{threshold}= q^{II}_{threshold}\) for \(T = 2\) and \(T= 3\). Also, Fig. 10a shows that for odd values of \(T \ge 5\), \(q^{II}_{threshold}\) is higher than \(q^{II}_{threshold}\) for \(T-1\) (which is even). Intuitively, this is because in Method II, for even values of T, \((T/2)t_T\) slots are used in the first phase, whereas for odd values of T, only \(((T-1)/2)t_T\) slots are used in the first phase.

Note that the ideal protocol is not practically implementable and is considered only for comparison with the proposed protocol.

\(\left( \frac{1}{4}\right) ^{l_{n_r} + k} \le \left( \frac{1}{4}\right) ^{\log _2n_r} \le \left( \frac{1}{4}\right) ^k = \left( \frac{1}{4^k n_r^2}\right)\) for \(k = 0, 1, \dots , s -2\).

\(\left( \frac{1}{4^{T-1}}\right) ^{l_{n_r} + k} \le \left( \frac{1}{4^{T-1}}\right) ^{\log _2n_r} \left( \frac{1}{4^{T-1}}\right) ^k\) for \(k = 0, 1, 2, \dots , s-2\).

\(\left( \frac{1}{2^{T}}\right) ^{l_{n_r} + k} \le \left( \frac{1}{2^{T}}\right) ^{\log _2n_r} \left( \frac{1}{2^T}\right) ^k\) for \(k = 0, 1, 2, \dots , s-2\).

For example: If Slot 1 results in \(\alpha\) and Slot 2 results in \(\beta\), then the BS infers that in block \(B_i\), exactly one node each of Type 1 (hence, \(B(1,i) = 1\)) and Type 3 (hence, \(B(3,i) = 1\)) have transmitted, and no nodes of Type 2 (hence, \(B(2,i) = 0\)) and Type 4 (hence, \(B(4,i) = 0\)) have transmitted. Similarly, if Slot 1 results in E and Slot 2 results in \(\beta\), then the BS infers that in block \(B_i\), exactly one node of Type 3 (hence, \(B(3,i) = 1\)) has transmitted, and no nodes of Type 1 (hence, \(B(1,i) = 0\)), Type 2 (hence, \(B(2,i) = 0\)), and Type 4 (hence, \(B(4,i) = 0\)) have transmitted.

For example: If Slot 1 results in C and Slot 2 results in \(\alpha\), then the BS infers that at least one node of Type 1 and exactly one node of Type 2 are active, and all Type 3 and Type 4 nodes are inactive. Similarly, if Slot 1 results in C and Slot 2 results in \(\beta\), then the BS infers that at least one node of Type 1 is active, no node of Type 2 is active, and exactly one node of Type 3 or Type 4 is active.

For example– at least two nodes of Type 2 (second row) or exactly one node each of Types 2 and 4 (fourth row) or at least two nodes of each of Types 1 and 3 and none of Types 2 and 4 (last row).

For example (i) if the two bits in the \((2j-1)^{th}\) and \((2j)^{th}\) positions of the concatenated bit string are 00, then it implies that the activity or inactivity of nodes of all the types is known with certainty to the BS for the \(j^{th}\) block; hence all these nodes will be in silent mode during the second phase, (ii) if the two bits in the \((2j-1)^{th}\) and \((2j)^{th}\) positions of the concatenated bit string are 10, then it implies that ambiguity exists regarding the activity or inactivity of nodes of Types 1 and 2 and the activity or inactivity of nodes of Types 3 and 4 has been inferred with certainty for the \(j^{th}\) block. Hence, during the second phase, active nodes of Types 1 and 2 corresponding to the \(j^{th}\) block will participate to resolve the ambiguity and nodes of Types 3 and 4 will be in silent mode.

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Titel: Fast node cardinality estimation and cognitive MAC protocol design for heterogeneous machine-to-machine networks
verfasst von: Sachin Kadam
Chaitanya S. Raut
Aman Deep Meena
Gaurav S. Kasbekar
Publikationsdatum: 18.03.2020
Verlag: Springer US
Erschienen in: Wireless Networks / Ausgabe 6/2020
Print ISSN: 1022-0038
Elektronische ISSN: 1572-8196
DOI: https://doi.org/10.1007/s11276-020-02291-6

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