Performance Evaluation of CDMA-based Wireless Sensor Networks with Long-Thin Topologies
Ming-Wei Hsu and Hsin-Mu Tsai
Department of Computer Science and Information Engineering National Taiwan University, Taipei 10617, Taiwan
E-mail: {r98922118, hsinmu}@csie.ntu.edu.tw Abstract—In this paper, we evaluate the end-to-end throughput
of CDMA-based Wireless Sensor Networks (WSN) with long-thin topologies using theoretical models. In order to minimize the multiple access interference (MAI) and improve the throughput, a power allocation scheme is required. Instead of using sophisticated power allocation algorithms, which require the knowledge of path losses between all pairs of nodes in the network, a simple heuristic power allocation scheme is proposed and used in this paper. It has been found that in fading environments, our scheme results in better throughput performance and is easy and feasible to be implemented.
I. INTRODUCTION
Many specific scenarios are suitable for utilizing WSNs.
Examples include monitoring systems on the bridge, in the tunnel, and in the mine. The appearances or the interior structures of these locations are long, thin, and with few branches. In these examples, safety sensor network systems with long-thin topologies, i.e., topologies formed by a few chains of nodes, are a common and important case. These safety systems, when in urgent or critical situations, often need to report a much larger amount of sensor data to assist in the disaster recovery process, where the effective end-to-end throughput in the network should be maximized as opposed to minimizing the energy consumption as when they are in regular operation.
Most Media Access Control (MAC) protocols for WSNs are designed to maximize the network lifetime and would result in poor throughput in these urgent situations.
Conventionally, TDMA-based MAC protocols are considered more suitable for this type of scenario. However, if TDMA is used as the MAC protocol for wireless sensor networks, the transmission durations of adjacent wireless sensor nodes cannot overlap; otherwise, collisions would occur at the receiving nodes, i.e., the signal-to-interference-and-noise ratio (SINR) would be greatly reduced, and leads to lower overall network throughput.
When CDMA is used as the MAC protocol for WSNs, the original sent messages are modulated into broadband signals with a pseudo-noise code (PN code).With the characteristic of PN codes, interferences between transmitted signals would be greatly reduced, and, as a result, adjacent sensor nodes have the flexibility of transmitting the signals simultaneously, thus
having the opportunity to substantially increase the overall throughput.
In this paper, we investigate how to design the CDMA-based protocol in a dual-mode WSN system with long-thin topologies. The system would use a protocol optimized for energy saving during its regular operation, and use our CDMA-based protocol when switching to the emergency mode. The performance of the considered system with single-chain topologies is investigated and compared with that of the system using a TDMA-based protocol. We also propose an easy-to-implement heuristic power allocation scheme, which does not require the knowledge of the path losses between nodes.
II. SYSTEM MODEL
A. Radio Model
Our model is based on the DS-CDMA model in [4].
Assume there are nodes in the network. The data signal of the -th transmitting node, , can be modeled by a sequence of unit-amplitude, positive or negative, rectangular pulse of duration .
The pseudo-noise code sequence, , which consists of a periodic, repetitive sequence of unit-amplitude, positive or negative, rectangular pulse of duration , is assigned to the -th node. The “chip” bits, , …, , form a complete PN code sequence of a length of T/ =. Each bit of has a duration of . The received signal is then given by
=+ 2 − − cos +∅
!
"
, where is the signal power of link measured at a certain receiving node, is the propagation delay of link ,
is the Additive White Gaussian Noise (AWGN) with 2-sided power spectral density $/2 , is the carrier frequency, % is the initial phase of the carrier, and
∅=%− .
One of the path loss models we use is the log-distance path loss model with log-normal shadowing. The relationship of transmitted power and received power can be given by
978-1-4577-1767-3/12/$26.00 ©2012 IEEE
Figure 2. Power allocation of nodes in a 30-node chain when using ElBatt’s algorithm with SNR=30 dB
(a) CDMA
(b) TDMA
Figure 1. Scheduling in a single-chain network
&'()*=+,'()− -,'()
=&$+100log $*/*$+3, 1
where &'()* is the path loss at distance * in *4,
+,'() is the transmission power in *45, -,'() is the received power in *45, &$ is the path loss at the reference distance *$ in *4, 0 is the path loss exponent, and 3 is an optional normally-distributed random variable with zero mean to model the shadowing.
The other path loss model we use is Rician fading. In this model, each received signal is modeled as a line-of sight signal plus scattering signals. The movements of surrounding objects and the receiver itself would cause rapid changes in signal phase, and, in turn, rapid changes in the received signal power. In the analysis, we generate the path loss variable with a modified Clarke’s model according to [1], which is then added to the original path loss model shown in 1.
B. Single-Chain Topology and Scheduling
In this paper, we consider long-thin sensor networks with a “straight-line” topology, or a “chain” of nodes. The first node is the gateway, which relays collected sensor information to a remote server, and all other nodes are regular sensor nodes. Data collected by each sensor node are aggregated with the packet it has received from its down-stream neighboring node and forwarded to its up-stream neighboring node. The gateway node would eventually receive the packet containing the sensor information from all nodes in the chain.
We will now present the scheduling models for networks with the considered topologies using both CDMA-based and TDMA-based protocols. In Fig. 1(a), if Node B is sending a packet to Node A, Node C cannot send a packet to Node B in the same time slot since a sensor node cannot transmit and receive at the same time. However, Node D can send a packet to Node C in the same time slot. When using a CDMA-based MAC protocol, we assume that each transmitting node uses a unique transmitting PN code, so that the correlation between signals from different transmitting nodes would be small. For CDMA, a transmitting node must be located at least two hops away from another transmitting node. Therefore, it is sufficient to use two alternating time slots to schedule all transmissions in the single-chain network. For a TDMA-based protocol, as shown in Fig. 1(b), there can only exist one transmitting node in the receiving range of a node,
in order to prevent collisions. Therefore, for TDMA, it is required to use three alternating time slots to schedule all transmissions in the single-chain network. Comparing the two protocols, the transmission “speed” of a TDMA-based protocol is obviously slower than that of a CDMA-based protocol; the difference in the schedules leads to the performance difference, in terms of throughput, for these two protocols.
C. Power Allocation
We assume that the available transmission power setting of the radio in the sensor is continuous and ranges from -25 dBm to 0 dBm. In this paper, three different power allocation schemes are evaluated: (1) Full power allocation: all transmitting nodes use the maximum transmission power to send packets; (2) ElBatt’s algorithm [2]: the algorithm can find the optimal power allocation with the objective that the total transmission power of all transmitting nodes is minimized while the SINR of any transmitting link in a particular time slot is no less than a pre-specified threshold.
We revise ElBatt’s algorithm to find the power allocation with the maximum achievable SINR threshold under the transmission power constraint. The algorithm [2, 3, 5]
requires the knowledge of precise path losses between all pairs of nodes, which, in practice, need a great amount of bandwidth to obtain. Moreover, in an environment with rapid small-scale fading, it becomes impractical to track the changes of path losses between nodes, and the throughput performance also significantly degrades as the knowledge of the path losses becomes less accurate; (3) Heuristic power allocation: to address the problem of the second scheme, a heuristic scheme which does not require the knowledge of path losses between all pairs of nodes is proposed. We found that the power allocation results obtained by ElBatt’s algorithm in an environment with no fading can be closely approximated with linear functions, as shown in Fig. 2. The proposed heuristic scheme thus allocates the power to nodes using a linear function based on this observation. The performance of all three schemes is analyzed in Section III.
Figure 4. Effective throughput of CDMA and TDMA Figure 3. Route BER of CDMA and TDMA
D. Performance Metrics
SINR of a received packet in the CDMA network can be given by [4]
SINR:=;
<=∑B@=;?@?A
@≠A +SNRD;, 2
where is the number of active transmission links in a time slot, is the received signal power of link measured at the receiver of link E, is the number of chips in the PN code, and SNR is the received Signal-to-Noise Ratio. A TDMA network needs to periodically synchronize nodes in order to have a common time reference for precise scheduling, and, as a result, the difference in delays of transmissions from different nodes would be small. In addition, all transmitting nodes use the same PN code. These lead to large cross-correlation between transmissions, severe interference, and thus performance degradation. To reflect this in our model, we assume the differences in delays of transmissions of one node and all other nodes are uniformly distributed in F−4 , 4 G , 0 < 4 ≤ /2. The SINR of Node E in a TDMA network is then given by
SINR:=J=K+KLD;=M
;KL=K ∑ ?@
B ?A
@=;NOP +SNRD;. 3
With the closed-form expressions of SINR for CDMA-based and TDMA-based networks, we can now define a few performance metrics. Assuming that Binary Phase Shift Keying (BPSK) is used as the modulation format, the bit error rate (BER) of received packets is given by
BER=TJ√SINRM, 4
where Q-function is the tail probability of the standard normal distribution. Assuming that all packets have W bits in length and all bit errors in a packet are independent events, the packet error rate (PER) of received packets is given by
PER=1 − 1 − BERY. 5
Since the sensor data of a node is relayed to the gateway via all of its downlink nodes, we also need to consider the route BER and route PER, i.e., BER and PER observed by the source node and the gateway in an end-to-end sense. The route PER and BER are given by
BER[\]^_=1 − ∏! :" 1 − BER:, 5
and PER[\]^_=1 − ∏! :" 1 − PER:, 6
respectively, where is the number of nodes in the
single-chain network and BER: is the bit error rate of link E, and PER: is the packet error rate of link E. Last, we must compare the overall network throughputs of CDMA and TDMA networks. To this end, we define the effective throughput (ET) as the number of average successfully received packets at the gateway per unit time. It is influenced by both route PER and the duty cycle of a link, and is given by ET=1 − PER[\]^_∙Wcd_fdghi. 7
The duty cycles of TDMA and CDMA networks with the single-chain topology are 1 3⁄ and 1 2⁄ , respectively.
III. PERFORMANCE EVALUATION
We assume that nodes in the single-chain topology are placed equal distance apart. In the analysis, we assume that the length of the PN code =16, and the path loss exponent γ=2.
A. Perfomance of CDMA and TDMA with 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.
Fig. 3 compares route BER of CDMA and TDMA networks with different number of nodes in the chain. The SNR of the link between neighboring nodes (without considering the interference) is assumed to be 10 dB. One can observe that the performance degrades when the number of nodes increases in both cases. 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. In reality, it is reasonable to assume that the difference in delays of different transmissions, B, will be less than 3. Therefore, we can conclude that in realistic scenarios, CDMA outperforms TDMA in terms of route error performance.
In Fig. 4, we compare ET of CDMA and TDMA networks with random difference in delays of different transmissions, whose performance can be considered as the upper bound for all TDMA cases. One can observe that ET of CDMA outperforms that of TDMA when the SNR of the link
Figure 5. Route BER of CDMA with different power allocation scheme and TDMA in large-scale plus small-scale fading environment
between neighboring nodes is larger than 13 dB. As one can adjust the distance between neighboring nodes to change this SNR value, and 13 dB is a very reasonable setting, this implies that CDMA has the potential to greatly improve the throughput performance of networks with single-chain topologies over the conventional TDMA-based protocol.
B. Performance of CDMA with Different Power Allocation Schemes and TDMA in Fading Environments
In this subsection, we compare the performance of CDMA-based and TDMA-based networks under more realistic assumptions; instead of utilizing only the log-distance path loss model, we added both the large-scale fading (shadowing) and Rician small-scale fading to the path loss model. Fading parameters are configured to reflect those of an indoor fading environment, as shown in Fig. 5. Since with fading, the path loss is time-variant, with the power allocation scheme using ElBatt’s algorithm, the system needs to periodically measure the path losses between any two nodes – each node takes turn to broadcast a packet while other nodes measures the received power to estimate the path losses. We assume that, for the power allocation scheme using ElBatt’s algorithm, the interval between two path loss measurements is 1 second; this translates to about 4% of transmission overhead (no data can be transmitted during the measurements) when there are 30 nodes in the chain.
One can observe from Fig. 5 that in environments with fading, the error performance of TDMA is still inferior to that of CDMA when the number of nodes in the chain is more than 10. On the other hand, comparing the performance of CDMA when using different power allocation schemes, the heuristic scheme outperforms the other two when the number of nodes is more than 17. This can be explained as follows.
Although ElBatt’s algorithm tends to find an optimal solution when given accurate path loss information, in fading environments the path losses between nodes change rapidly with time; those given to the algorithm, measured a while ago, is very different from the actual experienced path loss at the time of transmission, and, as a result, the power allocation calculated by the algorithm is no longer accurate and would reduce the performance. The heuristic scheme, on the other
hand, derives the power allocation without the real-time path loss information, and thus does not have this limitation.
In summary, we believe that the heuristic power allocation scheme can further improve the error performance of the CDMA-based network over the simple full power allocation scheme in fading environments. The scheme is more scalable in terms of the number of nodes in the chain, and does not require the overhead of measuring the path losses between nodes.
IV. CONCLUSION AND FUTURE WORK
In this paper, we propose the use of a CDMA-based MAC protocol in dual-mode wireless sensor networks; the network would use an energy-efficient MAC protocol during its normal operation, and switches to use our CDMA-based MAC protocol in emergency, due to the need of higher network throughput. It has been shown that with the full power allocation scheme CDMA outperforms TDMA in terms of effective throughput in a non-fading environment.
We also proposed a heuristic power allocation scheme, which does not require the knowledge of path losses between nodes in the network, and compared its performance with the full power allocation scheme and the power allocation scheme using ElBatt’s algorithm. Results show that our proposed heuristic scheme outperforms the simple but naïve full power allocation scheme as well as the scheme using ElBatt’s algorithm by 14% in route BER performance in a 30-node single-chain network and an indoor environment with fading.
Moreover, the results also suggest that our protocol is more scalable in terms of the number of nodes in the chain. In summary, we believe that CDMA can greatly improve the throughput performance of networks with long-thin topologies formed by chains. Future works include detailed design and implementation of a prototype network utilizing off-the-shelf radios with configurable spreading sequence for performance evaluation.
ACKNOWLEDGMENT
This work is supported by National Science Council, National Taiwan University, and Intel Corporation under Grants NSC 100-2911-I-002-001 and 101R7501.
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