Uncoordinated Rate Division Multiple Access with Prime Mod 60 Algorithm Anish Prasad Shrestha1 and Kyung Sup Kwak2 UWB Wireless Communication Research Center Inha University 253 Yonghyun-dong, Nam-gu, Incheon 402-751, Korea Email:
[email protected],
[email protected] On the other hand, rate-division multiple access (RDMA) is an alternative multiple-access schemes in which each sensor node transmits with an individual pulse rate keeping the duty cycle very low. Different pulse rate between different sensors make the transmitted signals distinguishable at the receiving side. It is apparent that pulse rate is simply reciprocal of pulse period. Hence, each sensor node will also have individual pulse period in RDMA. It should be noted that deterministic approach of RDMA results in a regular signal structure unlike time hopping pulse-position modulation (TH-PPM) signals where pulses have pseudorandom pulse positions.
Abstract— Pulse-based communication systems have emerged as a promising candidate in the deployment of short-range wireless networks compare to carrier-based system. The unique properties of pulse communication allow to design interesting medium access schemes where pulse streams transmitted by multiple nodes can be interleaved. Rate division multiple access (RDMA) is one of such schemes where each node is assigned different pulse period. The pulse period for each node in RDMA is required to be derived from relative prime numbers to minimize collision probability. In this paper, we propose a scheme to generate unique prime number using Prime Mod 60 algorithm from which pulse period for each node can be derived. Our scheme enables the implementation of RDMA in a truly uncoordinated fashion. We further investigate the statistical results of computed prime numbers to confirm its feasibility in RDMA.
An asynchronous multiple access scheme for pulsed ultrawide band (UWB) multiuser system based on RDMA is proposed in [2] and [3]. The authors verified that pulse period of each sensor node is required to be derived from relative prime numbers i.e. greatest common divisor had to be unity; so that upper bound of collision probability could be minimized. As such, the authors proposed to maintain a list of prime factors (LPF). In order to determine the pulse period, node has to select a random number and determine if the prime factor of that number already exists in LPF. If the common prime factor does not exist in LPF, the selected number is used to compute pulse period, otherwise the random number increased by one and the comparison process is repeated. This solution requires each user to have access to LPF which creates complexity in implementation. A similar approach is proposed [4] for Terahertz electromagnetic (EM) nanonetworks using handshake process between sensor and access point. However, the sensors randomly choose a pulse rate from pool of pairwise coprime rate codes in the order of 1000 (e.g., 1009, 1013, 1019,...). This creates the possibility of two or more sensors picking same pulse rate resulting catastrophic collision of pulses. The authors in [5] also proposed to use RDMA for transmit only UWB-WBAN. But, the method for user period selection is not clearly explained in the paper. The case is same for other works [6]–[8] in existing literature.
Keywords— Multiple access, RDMA, prime number generation, short range wireless networks.
I.
INTRODUCTION
Short-range wireless technologies such as wireless body area network (WBAN) and wireless nanosensor network (WNSN) are expected to play a key role in providing ubiquitous network where everybody and everything will be connected. These systems assume deployment of multiple sensor nodes in a star topology competing to access a single channel. In a practical scenario, coordination among these tiny sensors are anticipated to be very complex unlike other traditional wireless networks. Moreover, very short pulses are preferred instead of high power carrier signal due to its simple hardware, size and robustness to multipath and interference. Therefore, conventional medium access control (MAC) scheme based on carrier sense multiple access (CSMA) and all its variations cannot be used as there is no carrier signal to sense. A common MAC scheme that can be used under such circumstances is ALOHA [1]. The basic working principle of the ALOHA scheme is to transmit the data whenever a node has something to send. Since the transmission begins at random instant, collision occurs if another node also transmits before the transmission of previous node is completed. Consequently, retransmission is frequently required with increase in number of sensors resulting drastic decrease in throughput.
In this paper, we propose a simple yet novel algorithm to generate a set of prime numbers which can be used to compute distinct pulse rates. The algorithm is designed considering the computational and energy constraint of small sensor nodes. This scheme is based on random channel access time and the sensor nodes do not require to coordinate. We achieve this goal by implementing prime mod 60 algorithm. A unique integer associated to individual sensor node and a common integer
This research was supported by the MSIP(Ministry of Science, ICT and Future Planning), Korea, under the ITRC (Information Technology Research Center) support program (IITP-2015-H8501-15-1019) supervised by the IITP(Institute for Information & communications Technology Promotion) and by National Research Foundation of Korea-Grant funded by the Korean Government (Ministry of Science, ICT and Future Planning)NRF-2014K1A3A1A20034987).
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value share by all the sensor nodes are used as input to generate prime numbers from the prime mod 60 algortihm.
[10]. The users do not require to coordinate with each other to compute their corresponding user period. We explain prime
The remainder of the paper is organized as follows. In section II, the system model is discussed. Section III presents the brief description about prime mod 60 algorithm followed by explanation of the proposed scheme. Performance evaluation in terms of statistical result obtained from computed prime numbers are presented in section IV. Finally, we summarize the conclusion of this paper in section V. II.
SYSTEM MODEL
We consider an access point (AP) and M sensor nodes which transmit very short pulses. The sensor nodes are referred as users from herein and pulse period is interchanged by the term ―user period‖ as it is user specific. The users are indexed as * +. The user period of user m is denoted by Tm. Likewise, the pulse duration is denoted by Tp which is same for all users such that Tp
