Single-Chain Topology

First, we compare the performance of CDMA and TDMA networks in the case that they have the single-chain topology. We suppose that the distance between one node and its neighbors is set to be a constant. Thus, with the SINR expression, the path loss

model, and schedules for CDMA and TDMA, we can obtain the SINR of the link of the 𝑖-th node in the network with the single-chain topology:

CDMA: SINR_𝑖 =

In the following, we consider some simulation parameter settings. We set the PN code length 𝑁 = 16, the transmission power which can be used on a node has a continuous range from -25 dBm to 0 dBm. We first discuss the route BER performance given different SNR values and different path loss exponents for TDMA networks with different upper bound in delay difference and CDMA networks. Through adjusting the distance between adjacent nodes, we can determine the received SNR of packets via

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each link. Practically, it is reasonable to ensure the received SNR using the minimum transmission power is no less than 10 dB in order to overcome the fading environment.

Thus, the range of the received SNR is set from 10 dB to 35 dB according to the transmission power setting.

(a) Performance of CDMA and TDMA using the full power allocation scheme

In this subsection, we compare the route BER of TDMA and CDMA networks. As described previously, TDMA networks usually perform synchronization, and, as a result, the difference in delays between different transmissions is small. In the analysis, we configure 𝐵 , the maximum delay difference, to a few values, and observe the performance difference.

From Figure 4-1 to Figure 4-4, the x-coordinate represents the length of single chain, that is, the number of nodes, including the gateway, and the y-coordinate represents the value of the route BER in log scale. In Figure 4-1, with path loss exponent γ = 2 and the received SNR = 10dB, the route BER curve of TDMA with random delay time (𝐵 = 8) outperforms the curve of CDMA, but one can also see that the curve of CDMA nearly matches the curve of TDMA with 𝐵 = 3, and all other TDMA curves with smaller 𝐵 values show worse route BER performance. As previously mentioned, all signals have very short delay with each other in the TDMA

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network since the transmitting nodes in the same time slot are synchronized. Therefore, the most realistic curve of TDMA is the one of TDMA with a small 𝐵 value, and it is obvious that CDMA outperforms TDMA in a realistic situation under our assumptions.

We can also find a similar phenomenon in Figure 4-2 with path loss exponent γ = 3. At the first glance, the curve of CDMA performs not so well, compared to the curves of TDMA. One of the reasons is the larger path loss exponent. If the path loss exponent is larger, the radio attenuation is more severe. Under the same received SNR but a larger path loss exponent, the interference is less significant. Therefore, the anti-interference capability of CDMA is not fully utilized. Nevertheless, as pointed out earlier, the realistic TDMA network is more likely to be the upper curve, then CDMA is still a good choice under the circumstance that the path loss exponent is large.

In Figure 4-3 and Figure 4-4, the received SNR is set to be 15 dB. We can also observe similar phenomena to the one shown in Figure 4-1 and Figure 4-2. Even though we claim that CDMA is better than TDMA in realistic cases from the route BER performance curve, the situation when the route BER curve of realistic TDMA is the lower curve in these figures should be considered. In that case, we compare the effective throughput of CDMA and TDMA networks with random difference in the delays of different transmissions, whose performance can be considered as the upper bound for all TDMA cases. The ratio of the duty cycles of the links in TDMA to that in CDMA is 2/3,

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and thus the effective throughput of CDMA could outperform that of TDMA. In Figure 4-5 and Figure 4-6, one can observe that the effective throughput of CDMA outperforms that of TDMA when the received SNR of each link is more than 13 dB with no error correction code. On the other hand, it decreases so fast as the number of nodes in the chain increases or the received SNR decreases, it is exceeded by the effective throughput of TDMA in the case that the number of nodes in the chain is less than 10 and the received SNR under 10 dB. Consider the case that an error correction code which can correct one bit of error per packet is used, as shown in Figure 4-7. We can find that the curve of CDMA is greatly improved and it outperforms the curve of TDMA

when the received SNR is more than 10 dB. In Figure 4-8, when the path loss exponent γ = 3, a similar phenomenon can be observed. This means that when we choose a good

error correction code technique, we can have a much higher overall throughput in a CDMA network with single-chain topologies.

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Figure 4-1 Route BER of CDMA and TDMA with SNR= 10dB and γ = 2

Figure 4-2 Route BER of CDMA and TDMA with SNR= 10dB and γ = 3

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Figure 4-3 Route BER of CDMA and TDMA with SNR= 15dB and γ = 2

Figure 4-4 Route BER of CDMA and TDMA with SNR= 15dB and γ = 3

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Figure 4-5 Effective throughput of CDMA and TDMA with γ = 2

Figure 4-6 Effective throughput of CDMA and TDMA with γ = 3

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Figure 4-7 Effective throughput of CDMA and TDMA with γ = 2 (1-bit error recoverable)

Figure 4-8 Effective throughput of CDMA and TDMA with γ = 3 (1-bit error recoverable)

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(b) Performance comparison in non-fading environments

Here we compare the performance of the full power allocation scheme, our heuristic power allocation scheme, and ElBatt’s algorithm in a CDMA network with single-chain topologies. In the analysis in this subsection, we assume that there is no fading in the environment. According to the range of transmission power of the sensor node in our assumption, ranging from -25 dBm to 0 dBm, the range of the received SNR is from 10 dB to 35 dB. Since the deployment of sensor networks with a specific topology is usually made by human, it is reasonable to choose the between-nodes distance and make the received SNR larger than 10dB when using the minimum transmission power.

In Figure 4-9, one can observe that the route BER of ElBatt’s algorithm and that of the heuristic power allocation scheme outperform that route BER of the full power allocation scheme in the environment with the path loss exponent γ = 2, and one can also observe that the curve of the heuristic power allocation scheme is very close to the curve of ElBatt’s algorithm. Figure 4-10 shows a similar phenomenon. Therefore, we can expect that our heuristic scheme can be well applied in CDMA networks with single-chain topologies. The original ElBatt’s algorithm takes pairwise path losses between nodes into consideration, and our revised version of the ElBatt’s algorithm further improves the error performance. Thus, the error performance of the ElBatt’s

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algorithm is usually better than that of the full power allocation scheme. In our evaluation, it can improve more error performance than the full power allocation scheme with the received SNR ranging from 10 dB to 35 dB we assume, as well as our heuristic power allocation scheme which is based on ElBatt’s algorithm.

Figure 4-9 Route BER of CDMA using different power allocation schemes with γ = 2

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Figure 4-10 Route BER of CDMA using different power allocation schemes with γ = 3

(c) Performance comparison in fading environments

In this subsection, we compare the performance of CDMA and TDMA networks under more realistic assumptions. Instead of utilizing only the log-distance path loss model, we add both the large-scale fading (shadowing) and the Rician small-scale fading to the path loss model. Fading parameters are configured to reflect those of an indoor fading environment. First, consider a large-scale fading environment whose standard deviation is 7 dB and whose path loss exponent is 2, as shown in Figure 4-11.

One can observe that CDMA with the heuristic power allocation scheme outperforms CDMA and TDMA with the full power allocation scheme, but much worse than CDMA with ElBatt’s algorithm. Since we assume that the system can have the knowledge of

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path losses between any two nodes in the network at any given time, ElBatt’s algorithm can perform much better than the heuristic power allocation scheme because the heuristic power allocation scheme does not take this knowledge into account. Then, we consider a fading environment with both shadowing and Rician fading, as shown in Figure 4-12. Since the wireless channel small-scale fading changes rapidly, the interval between measurements to obtain the path loss information should be small to accurately capture the states of the channel and use them in ElBatt’s algorithm. However, the smaller this interval is, the more overhead the system has. In the analysis, we assume that the interval is one second, which already results in at least 1.5%¹ of overhead. All other parameters are presented in Figure 4-11. We find that CDMA with the heuristic power allocation scheme still performs better than CDMA and TDMA with the full power allocation scheme in the cases that the length of the chain is longer than 7 nodes, but now ElBatt’s algorithm performs worse than in the large-scale fading environment, since it is exceeded by the heuristic power allocation scheme in the cases that the chain length is more than 17 nodes. ElBatt’s algorithm requires precise information of the path losses between any two nodes in the network, but with small-scale fading, the

channel changes rapidly. The path loss between the transmitter and the receiver at the

1 We take CC2520 as an example. Assuming there are 30 nodes in the network, and they takes turns to send a packet with 128 bits in non-overlapped manners. The maximum data rate of CC2520 is 250 kbit/s, so the overhead of once measurement of the pairwise path losses over one second is 30 ∙ 128/(250 ∗ 1000) ≈ 0.0153

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time of transmission can be different from that at the time of the measurements of path losses (each node takes turn to transmit a dummy packet for other nodes to measure the path losses). This results in the performance degradation of ElBatt’s algorithm. On the other hand, the full power allocation and the heuristic power allocation schemes do not require the knowledge of path losses, so they are not affected by the rapid changes of the channel. To sum up, it seems the heuristic power allocation scheme is realistic; that is, it does not need a surplus overhead to train the information of path losses between nodes, so the overall throughput is improved. This is good when the system changes to the high speed mode we propose in this work. In a small-scale fading environment, when the length of the chain is long, for example, when it is longer than 17 nodes, it is very suitable to use the heuristic power allocation scheme. When the chain length is short, the heuristic power allocation scheme can still be a good choice since it does not need the overhead to obtain the information of path losses between nodes.

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Figure 4-11 Route BER of CDMA with different power allocation schemes and TDMA in a large-scale fading environment

Figure 4-12 Route BER of CDMA with different power allocation schemes and TDMA in large-scale plus small-scale fading environment

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