# Algorithms for Interference Sensing in Optical CDMA Networks

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3 After a window of time expires or on packet arrival, the state of the line is estimated. The estimated state of the line is used by the interference sensing algorithm to decide whether to transmit or not. E. Defer mode If the sensing algorithm is unable to determine a departure instant or if the detection operation detects interference, the node defers its transmission. The way the node defers is referred to as the defer mode. The purpose of the defer mechanism is to reduce the probability of multiple nodes which interfere with each other from accessing the medium at the same time. Conventional CSMA/CD protocols use several schemes to decide how to defer. These schemes can be used as defer modes in the interference sensing protocol. There are three defer modes which are explained in detail in [6]: Non-persistent mode p-persistent mode 1-persistent mode In this study two modes were examined: non-persistent mode with a fixed back off interval i.e. if interference was sensed, transmission was deferred for a fixed interval of time after which sensing was retried and 1-persistent. Both schemes used a fixed retry limit i.e. a limit on the number of retransmission attempts. V. ALGORITHMS FOR INTERFERENCE SENSING This section describes the three algorithms for Interference Sensing: Selfish sensing, Threshold based sensing and Codeword estimation based sensing A. Selfish sensing In selfish sensing, a node transmits if the state of the line will not cause interference with the codeword that it is transmitting. Otherwise the node defers until the state of the line allows transmission. The node does not check whether the transmission of its codeword would interfere with other codewords on the line. The state estimation algorithm is described in Section IV. The time required for estimating the state of the line depends on the sensing window. The selfish sensing algorithm is described above. The running time of this algorithm is O(N). B. Threshold based sensing Threshold based sensing limits the amount of interference caused to other users. Interference may be limited in two ways: By limiting the number of overlapping chips By limiting the magnitude of each overlap (i.e. how many chips overlap in a single chip time) Based on these limits, two thresholds may be defined: the overlap count limit, thresh c i.e. the maximum number of the overlaps between the codeword and the state of the line and overlap magnitude limit, thresh m i.e. the maximum magnitude of a single overlap between the codeword and the state of the line. C t Codeword to be transmitted Retry count rc Estimate the state of the line If (state & C t C t) then break The selfish interference sensing algorithm C t Codeword to be transmitted Retry count rc Estimate the state of the line If ((state & C t C t) AND (weight(state C t) thresh c) AND (maximum magnitude of all overlaps thresh m)) then break The threshold based interference sensing algorithm A node first performs the selfish test to determine whether the line state allows it to transmit without interfering with its own codeword. It then checks the overlap count and overlap magnitudes between its codeword and the state of the line. If the counts are below the thresholds, the node transmits its codeword. If not the node defers transmission. Decreasing thresh c and thresh m reduces the number of codewords on the line and thereby reduces interference. The state estimation algorithm is discussed in Section IV. The time required for estimating the state of the line depends on the sensing window. The threshold based sensing algorithm is described above. The running time of this algorithm is O(N). C. Codeword estimation Codeword estimation attempts to determine which codewords are on the line and what their relative phase shifts are. Given this information, a node can determine a departure instant that does not cause interference either with its code-

4 C t Codeword to be transmitted Retry count rc Estimate most likely codewords according to estimation algorithm For each most likely codeword C state All other most likely codewords + C t If (state & C == C) Continue the while loop Break from the while loop The codeword estimation interference sensing algorithm word or with any other node s codeword. The efficiency of this sensing algorithm depends on how accurate the codeword estimate is. This study used a window based estimation technique: A counter was maintained for every codeword in the codeset. The state of the line was sensed and the counter was incremented for every codeword that could be a part of the state. At the end of the window the counters were divided by the duration of the window. This gave an estimate of the probability of that codeword having been present. The codewords which had probabilities above a threshold were chosen as the most likely codewords. As sensing progresses the estimated codewords tended towards the actual codewords. Other estimation algorithms based on vector decomposition or maximum likelihood are also possible. The window based codeword estimation algorithm runs in O(NP) where P is the number of codewords in the codeset. (From the Johnson bound P = O(N κ ).) The total time required for estimating the state of the line also depends on the sensing window. The sensing algorithm to determine the departure instant is described above. The running time of the algorithm is O(NP). VI. SIMULATION RESULTS This section compares the three sensing algorithms and the effect of the algorithmic parameters on throughput and delay characteristics. A. Simulation parameters A simulator was designed to simulate an IS/ID based optical CDMA network. The chipping rate of the network was Mb/s. The codeset used was (N, w, κ) = (,3,2) giving a data rate of Mb/s. This allowed for interference sensing, given a network of maximum diameter m (propagation delay 5µs). Though the simulation used a chipping rate of Mb/s, the concept of interference sensing can be scaled to networks of higher speeds as long as the codelength is increased proportionately to allow interference sensing to be feasible [5]. The traffic used to drive the simulation had an offered load that varied from Mb/s to Mb/s. The packet lengths were chosen uniform randomly from between bytes and 15 bytes. The inter arrival times of packets were chosen uniform randomly to obtain the required offered load from to % of the chipping rate. The codeword used to transmit a specific packet was chosen randomly from the codeset. On-demand sensing was used for the selfish and the threshold based estimation and continuous sensing was used for the codeword estimation algorithm. Both 1-persistent and p-persistent defer algorithms were used. The retry limit was set to. The sensing window, unless specified otherwise, was settodatabits. B. Throughput and delay Figure 2 shows the effect of the three sensing algorithms on the throughput of the network. The throughput for an optical CDMA system which does not use any form of media access (called Aloha-CDMA) is also shown. The selfish sensing algorithm maintains throughput close to the offered load up to a normalized load of around %. Thereafter the throughput is maintained constant. The reason why the throughput is below the maximum possible throughput is that the selfish algorithm is greedy - a node checks interference with respect to its own codeword and not with respect to other nodes codewords. The selfish algorithm gives its maximum throughput when used in the on-demand sensing mode. The threshold based sensing algorithm controls of the amount of interference on the line providing better throughput. The throughput increases by approximately %. Threshold based sensing gave best results using a on-demand sensing mode. The codeword estimation technique gives a throughput that is worse than both selfish and threshold based sensing. This is because the state of the line when decomposed gives a large number of potential codewords, in turn giving a large number of false positives. The number of false positives can be reduced by increasing the sensing window. However packet arrivals and departures nullify these gains. Efficiency will reduce further as N increases. Codeword estimation needed a large window and hence continuous sensing was used. Figure 3 shows the channel access delay for the sensing algorithms. It is measured only for successful transmissions. The delay for all algorithms is kept within reasonable bounds i.e. in the order of µs. C. Effect of sensing window Figure 4 shows the effect of the sensing window on throughput. A window of around bits is required for accurate sensing using selfish and threshold based sensing. The optimal window size for the codeword estimation method is larger (around bits) to eliminate the false positives that the algorithm identifies.

5 Throughput (Mbps) Throughput v/s offered load for different Interference Sensing algorithms Offered load (Mbps) Aloha-CDMA Threshold based sensing Selfish sensing Code estimation Fig. 2. Throughput vs. offered load for different sensing algorithms for a (,3,2) code on a Mb/s network. A continuous sensing algorithm was used with a sensing window of bits for the selfish and threshold based algorithms and bits for codeword estimation. A 1-persistent defer algorithm was used with a retry limit of. Delay in milliseconds Delay v/s offered load (Is/Id) Threshold based sensing (bc=, bt=5us, t=4) Threshold based sensing (bc=, bt=5us, t=6) Threshold based sensing (bc=5, bt=5us, t=4) Threshold based sensing (bc =, 1-persistent sensing, t=2) Selfish sensing, (bc=, 1-persistent sensing) Code estimation, (bc=, 1-persistent sensing) 1e Offered load Fig. 3. Channel access delay vs. offered load for different sensing algorithms for a (,3,2) code on a Mb/s network. The results are shown for different values of the threshold settings (overlap count threshold (t)), different retry limits (bc). Two types of defer algorithms were used: a 1-persistent defer algorithm and a backoff based algorithm with backoff time (bt) = 5µs. Continuous sensing was used with a sensing window of bits for the selfish and threshold based algorithms and bits for codeword estimation. Throughput (Mbps) Throughput v/s sensing window duration (in data bits) for different Interference Sensing algorithms Selfish algorithm Threshold based algorithm Code estimation 5 15 Sensing window (data bits) Fig. 4. Throughput vs. sensing window for a (,3,2) code on a Mb/s network at % offered load. A on-demand sensing mode was used for selfish and threshold sensing and continuous sensing was used for codeword estimation to provide maximum throughput. A 1-persistent defer algorithm was used with a retry limit of. Throughput (Mbps) Throughput v/s offered load for different Threshold settings N= thresho=, threshm=1 N= thresho=, threshm=5 N= thresho=2, threshm=2 N= thresho=2, threshm= Offered load (Mbps) Fig. 5. Throughput vs. offered load for different values of threshold sensing parameters of (,3,2) code on a Mb/s network. On demand sensing and a 1-persistent defer mode were used. D. Effect of threshold settings Figure 5 shows the throughput values for different values of threshold settings. When thresh m is at its minimum value i.e. 1, no overlaps are allowed and the choice of thresh c does not affect the throughput and may be set to its maximum value of. To increase the number of codewords on the line, thresh m must be increased. However to ensure that the interference is limited, thresh c must be reduced. For the codeset used in the simulations, a setting of thresh o =2, thresh m =2, gave maximum throughput, around 5% more than the other threshold values and % more than selfish sensing. An incorrect selection of the threshold values renders the scheme no more effective than selfish sensing. VII. CONCLUSION Interference sensing is a media access mechanism that can improve the throughput of an Optical CDMA network under heavy load. Three algorithms for Interference Sensing were analyzed and it is shown that it is possible to operate an optical CDMA LAN at close to its maximum possible throughput at high loads. A judicious choice of the interference sensing parameters can ensure that the delay is kept within reasonable bounds. In particular, simple algorithms such as the selfish and threshold based algorithms can reduce interference levels significantly, increasing throughput by up to % over more complex codeword estimation algorithms. REFERENCES [1] P. Prucnal, M. Santoro, and T. Fan, Asynchronous multiplexing for an optical fiber local area network, IEEE Journal of Lightwave Technology, vol. 4, p. 547, [2] J. Salehi, Code division multiple-access techniques in optical fiber networks - Part 1: Fundamental principles, IEEE Transactions on Communications, vol. 37, no. 8, pp , Aug [3] J. Salehi and C. Brakett, Code division multiple-access techniques in optical fiber networks - Part 2: Systems performance analysis, IEEE Transactions on Communications, vol. 37, no. 8, pp , Aug [4] C. Lam, To spread or not to spread: The myths of optical CDMA, in IEEE Lasers and Electro-Optics Society Annual Meeting, vol. 2,, pp [5] P. Kamath, J. Touch, and J. Bannister, The need for media access control in Optical CDMA networks, in IEEE Infocom, 4. [6] F. Tobagi and V. Hunt, Performance analysis of carrier sense multiple access with collision detection, Computer Networks, vol. 4, no. 5, pp , Oct 198.

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