get node collects the coordinate information of reference nodes, , anddenoted by dots, and their corresponding signal strength, by which to calculate the ranges between itself and the four reference nodes, , , and. Afterward, the target node derives its own coordinate, and sends to a sink, denoted by the square in Figure 1.

In order to enable communication between the target and reference nodes in the network, we assume that each and every node in the WSN is able to communicate through U-BOTH, proposed in this paper.

For convenience, the notation used in this paper is summarized in Table 1.

3.  Physical Layer Model

3.1.  UWB Signal Spreading and Modulation

First of all to achieve accurate localization in wireless communication, we need a reliable physical layer communication technique that reduces bit error rate (BER), while mitigating the multi-users-interference (MUI) and Gaussian noise interference. Our physical layer is a UWB system based on time-hopping (TH) signal transmission as well as OVSF (orthogonal variable spread factor) for spreading out the symbols.

OVSF (Orthogonal Variable Spread Factor) was extensively used in CDMA systems to provide variable spreading codes [19]. Shorter OVSF code lengths are usually optimized for short distance, high data rate transmission in less crowed environments due to its smaller spreading factor. On the other hand, time hopping (TH) is one of many signal modulation methods used by UWB. We will apply the time-hopping pulse position modulation (TH-PPM) algorithm to encode UWB pulse streams, and OVSF direct sequence to spread the user data bit stream, called U-BOTH (UWB modulation Based on OVSF and Time Hopping).

Figure 2 illustrates the utilization of time hopping (TH) pulse position modulation and OVSF spreading to encode a single bit in the user data stream. First, U-BOTH sends each bit in the bit time, denoted by. Then it modulates the bit 1 using a TH code, 12110021, in which each digit denotes a chip slot position within a frame time, , to send a broadband radio pulse. The number of pulses is denoted by. Therefore, each bit duration is. Each chip slot lasts for, sufficient to send a short UWB pulse signal.

After the initial pulse position modulation using UWB signals, the pulse sequence is again applied with OVSF code so that the phases are shifted byto provide orthogonality between multiple users. The length of the

OVSF code is called the spread factor SF, which is equal to.

In our system, the TH code is a pseudo-random sequence generated from foreknown seeds, such as node IDs. And the OVSF codes are selected from a welldefined set of orthogonal spreading codes.

To formally analyze the system in this paper, we represent the transmitted signal by the nth transmitter in Equation (1):

, (1)

in which, is the OVSF code with the period, is the energy of the n-th transmitter, is the energy normalized pulse waveform, is the TH code with periodandindicates the data stream bit. If the data bit is 1,. Otherwise,.

At the receiver side, the received signal consists of three source of information:

in which, is the desired user signal, is co-channel interference from multiple users, andis the additive white Gaussian noise (AWGN).

Denote the pulse energy of the n-th transmitter as.

Without loss of generality, we assume that the first user’s transmission is the desired signal at the receiver for simplicity, then Equation (2) provides the desired signal function at the receiver:

. (2)

We define the correlation template of the receiver:

;. (3)

3.2.  Single User System Analysis

As the first step, we assume that the channel is the AWGN multipath-free channel, and that the transmitter and the receiver are synchronized. In a single user signal processing system, the input of the receiver has two parts: and, and the output of the receiver in time interval [0, T_b] is represented by:

. (4)

In Equation (4), the useful output signal is:

where.

Because, is the energy normalized pulse waveform, we have

   

.

In Equation (4), the output noise signal is:

whereis Gaussian random variable with mean 0 and variance. Becauseis not a random variable, the variance ofis:

,

.

Suppose that the statistical probabilities of data bit b = 0 and b = 1 are equal, we obtain the BER (bit error rate) of the single user system in AWGN channel as follows:

.

Becauseif b = 0, then the useful output is. Using Equation (4), the BER become:

.

It can be rewritten by complementary error function as follow:

.

where.

Because U-BOTH is a rate variable system using OVSF, we analyze the relation between BER and the bit rate. Suppose the system’s OVSF code is a code tree of 6 layers [20], and the spreading factor is 2, 4, 8, 16, 32, 64, respectively. Further suppose the basic rate of our system is, then the corresponding bit rate of U-BOTH is (i = 32, 16, 8, 4, 2, 1, respectively).

Denote the bit rate as, where, i = 1, 2…32, we can get the relation between BER and the bit rate:

, (5)

Equation (5) shows that the BER decrease when the spreading factor SF increases or when the bit rate decreases. Therefore, we can adjust SF to adapt different environments with various noise levels while maintaining the same bandwidth of the signal. This is the main reason we adjust OVSF codes in our system.

3.3.  Multi-User Interference Analysis

In multi-user communication system, the received signal includes multi-user interferenceand noises. The part is the same as Equation (4), but the multi-user interferenceis additional. Because the phase and delay _ of interfering pulses is random as shown in Figure 3, we have to compute the interference’s variance.

Suppose thatis uniformly distributed over [0,), then the interference variance of the desired signal, i.e. the signal from the 1st user, caused by transmitter n is [14]:

.

Therefore, the total interference variancefrom all other transmitters is:

.

Because the delayfor all transmitters has the same distribution, we get the following formula:

in which,

.

According to [14], and noticing that and ==, Equation (6) gives the BER in multi-user interference environments.

    .

(6)

4.  Network Protocol Operations

4.1.  Protocol Operation

Our localization algorithms depend on a two-step process—the first step is for the target node to acquire the coordinate and signal strength information from reference nodes in the network using U-BOTH based communication protocols, and the second step is for the target node to calculate the distances to the reference nodes, and infer its own coordinate.

In order to get the necessary coordinate information from adjacent reference nodes, the following protocol steps are taken:

1) The mobile node broadcasts a location request message.

2) All the reference nodes send back packet with their own coordinates. During each short sampling period, a moving node can receive tens of responses from each of the reference nodes.

In wireless sensor networks, code assignments are categorized into transmitter-oriented, receiver-oriented or a per-link-oriented code assignment schemes (also known as TOCA, ROCA and POCA, respectively) [21, 22]. Depending on the ways of assigning the OVSF-TH codes and encoding the MAC data frames for transmissions, we propose two different ways to implement multiple access protocols using U-BOTH.

a) ROCA-Based Protocol Operations: The first approach is based on the receiver-oriented code assignment (ROCA), in which case the data packet transmissions are encoded using the unique OVSF-TH code assigned to the receiver. Beside ROCA, there is a common OVSF-TH code for bootstrapping and coordination purposes.

In ROCA scheme, when a target node needs to find out its coordinate, it sends a location request message using the common OVSF-TH code to the reference nodes. The request message includes the request command, and the receiver’s OVSF-TH code. Upon receiving the request message, each reference nodes sends back a response message using the receiver’s OVSF-TH code using a random backoff mechanism.

The response message includes each reference node’s identification information, and their coordinates.

b) TOCA-Based Protocol Operations: The second approach is based on transmitter-oriented code assignment

(TOCA), in which case each packet transmission is encoded using two OVSF-TH codes — one is a common OVSF-TH code to encode the common physical layer frame header, and the other transmitter-specific code is to encode the physical layer frame payload. The frame head includes the transmitter-oriented OVSF-TH code for encoding the frame payload.

Because the physical layer headers are sent on a common OVSF-TH code, the physical layer header transmissions resemble those of ALOHA networks with regard to packet collision. Because the headers are usually short, the collision probability is low.

On the other hand, because the data frame payload is transmitted on unique OVSF-TH codes, the interference between the payload and other frame headers and payloads is dramatically reduced.

In both ROCAand TOCA-based systems, packets from the reference nodes can be lost. However, this does not affect the overall performance of our localization algorithms because they tolerate such losses.

4.2.  Location Calculation Algorithms

We make use of our OVSF-TH-UWB system and provide a UWB sensor localization network for mining applications to monitor environment and mineworker. We suppose moving nodes and other monitored nodes are the target nodes and every reference node knows its location. Suppose target node has a UWB RFID Tag equipped with transmitter and receiver to assist distributed localization with reference nodes. Data sink collect all the real-time localization information and send out to the monitoring center outside the mining area, as shown in Figure 1.

There are two steps in order to estimate the coordinate of the mobile node:

a) Ranging: Ranging is to estimate the approximate distance between the target node and the reference nodes. Target node estimates the distance from it to each reference node according to the RSSI values, using maximum likelihood estimation.

In this paper, we take ROCA scheme during ranging, target node broadcasts range-initiate (RI) packets for range estimates, and neighbor reference nodes reply with range-response (RR) packets, which include their coordinate and signal strength. To collect ranging and location information as much as possible in a short time, we take a dual-channel mechanism joint with common code and receiver code provided by OVSF-TH code. The receiver OVSF-TH code is generated by the unique MAC ID of receiver. Suppose target node i broadcast a RI packet via common channel code C₀ at t = t₁, and begin to listen the RR packets sent to its unique OVSF-TH code. This process initiate a window of time from t = t₁ to t = t₁ + Tw. The window-length Tw is much larger than RR duration T_RR, which allows multiple RR gathered within window duration from adjacent reference nodes.

Following are the ranging and localization algorithm:

1) Target node i broadcasts RI packet at t = t₁ on common code C₀. This RI includes node i’s MAC ID and OVSFTH code Ci. When there is no interference, the RI arrives at a reference node j.

2) Reference node j delaysafter receiving the RI, and then reply a RR packet transmitted on the OVSF-TH code Ci. The RR packet includes node j’s MAC ID, transmitted signal strength and node i’s MAC ID. Where n is a random positive integer belong to [1, K], K is the average number of reference nodes in the transmitted range of target node. The delayis used to avoid interference between RR packets.

3) If t₁ < t < t₁ +Tw, node j continue to delayand then transmit RR packet via Ci.

4) Other reference nodes in the transmitted range of node i send RR packets by the same ways as node j in step 2 and 3.

5) If t = t₁ + Tw, node i stop receiving RR packets.]

6) When t = t₁ + Tw, node i received multiple RR packets from different reference nodes and several RR packets from the same reference node. It uses all the recorded information of PLi to estimates the distances to different reference nodes by MLE based RSSI ranging indicated in Equation (14) in Section 5.

b) Localization: Coordinate calculation, which is to determine the coordinate of the mobile node according to the coordinate information of the reference nodes and the corresponding distance from the target node to the reference nodes. Using the coordinates of the reference nodes and the estimated distance information, calculate the coordinate of the target node. It is implemented as follows:

1) When node i estimated all the distances to different reference nodes in its transmitted range, it applies these ranging results to Equation (15) in Section 6 and then computes its location based on the least squares algorithm.

2) When node i estimated its coordinate, it broadcasts ACK packet via its common channel code C0, informing finish of ranging. Its newest location is aware to neighbor nodes by the ACK and will arrive at the data sink through the localization routing.

According to above procedures of network protocol operations, after getting the reference coordinates and the respective signal strength information, a target node calculates its coordinate in two steps — ranging and localization. In order to fully take advantage of U-BOTH physical model in Section 3, we also design specific ranging algorithm and localization algorithm for U-BOTH in following sections.

5.  Ranging Algorithm

Ranging is to estimate the approximate distance between the target node and the reference nodes. We use the maximum likelihood estimation for such calculations. First of all, we need to establish the path loss model of the UWB channel in order to inversely derive the distance information from received signal qualities.

5.1.  The Path Loss Model

It is well-known that the path loss model can be expressed by the log-distance path loss law in many indoor or outdoor environments, as shown by Equation (7).

;, (7)

in which

•  d0 is the reference distance (e.g. 1 meter in UWB medium)

•  PL0 means the path loss in dB at d0

•  d is the distance between the transmitter (Tx) and receiver (Rx)

•  refers to the path loss exponent which depends on channel and environment

•  S is the log-normal shadow fading in dB. Usually, S is a Gaussian-distributed random variable with zero mean and standard deviation.

The tunnel’s environment in coal mine can be regarded as a special type of indoor environments, considering various kinds of concrete environmental factors in coal mine [17]. Thus, we adopt the UWB path loss model in coal mine based on residential indoor propagation model.

According to the residential indoor models, the values of, and S in Equation (7) are specific in each propagation environment, and could be treated as random variables [16].

Accordingly, the UWB path loss is commonly modeled as:

, (8)

in whichis the mean value of shadow fading’s standard deviation.

The probability density function (pdf) is:

. (9)

However, an unknown distance variable d appears in both the denominator and the exponent’s denominator in Equation (9), so it is hard to develop further statistical analysis. In addition, the path loss exponentin the aforementioned model is a random variable, and requires sufficient measurements on the spot in various residential environments before effectively being applied in generic scenarios. Especially, the standard deviationof the log-normal shadow fading S usually changes from locations to locations. Even if at the same location, it may change because of the time-varying channel. Thus, we need practical method to estimate S, especially for moving targets.

Therefore, in order to apply above path loss model, IEEE 802.15.4a Task Group provided Channel Model 1-9 by taking limited real measurements to determine the values of, and other variables in different situations. When deploying real UWB networks, people could approximately choose the corresponding channel model with the parameters specified in IEEE 802.15.4a.

We propose a UWB coal mine propagation model based on many other modeling methods for the application of ranging and localization. In this model, the mean value of the path loss exponentis given for different tunnel environments, and the log-normal shadow fading S is represented through a random variable as follows:

     .

Then, the indoor UWB path loss could be expressed as:

, (10)

according to Equation (7).

In Equation (10), andare zero-mean Gaussian variables of unit standard deviation,. (PL0+10 log10 d) is the median path loss, andrepresents the random variation about the median path loss. According to the “3 principle” in Gaussian distribution, the probability of a Gaussian variable lying in the rangeis 99.73%, even though the range of Gaussian random variable is. That is, 99.73% value of variablesandis within the range of (-3, +3). Furthermore, it dramatically simplifies computation if we use truncated Gaussian distributions forandso as to keepand from taking on impractical values. According to [16], we confine, and.

In aforementioned model, is not exactly Gaussian becauseis not Gaussian variable. However, the product is very small with respect to whole expression of path loss. Thus, the path loss PL(d) is approximately a Gaussian-distributed random variable with:

,

.

The probability density function (pdf) of the path loss PL(d) is:

. (11)

Compared with the model in [16], our UWB coal mine propagation model given by Equation (11) is more convenient to carry out parameter estimation and statistic analysis because it simplifies the statistics and PDF. What is more, when considering the random influence of the log-normal shadow fading, this model is generic than current models in IEEE 802.15.4a.

5.2.  Ranging Algorithm Based on Maximum Likelihood Estimation

The distance between the transmitter Tx and the receiver Rx in Equation (10) can be calculated by the general ranging method between two nodes using the RSSI information:

Receiver computes the distance between the transmitter Tx and the receiver Rx using random valuesand in the truncated range. This method takes into account the influence of real log-normal shadow fading on raning and decreases the ranging error compared to the models in IEEE 802.15.4a.

However, the random variablesandselected by the transmitter Tx are not exactly those in the real time-variant channel. In order to avoid the ranging errors caused by the large deviation between the simulated andvalues and the realandvalues in each round of ranging estimation, we propose an iterative ranging based on MLE (maximum likelihood estimation) in UWB wireless sensor networks.

Suppose PLi is the ith observation value, we get the joint conditional pdf using Equation (12).

. (12)

The necessary condition to compute the MLE of d is:

. (13)

We solve Equation (13) and have:

.

Therefore, the MLE based RSSI UWB ranging is:

. (14)

6.  Localization Algorithm

When computing the location of a wireless sensor node, there are two types of nodes, the reference node and the target node. Suppose that we have three reference nodes with coordinates, and, respectively. The target node computes its coordinateusing trilateration method with the coordinates of reference nodes and their ranges, to the target node using the following equations:

In practical situations, three reference nodes are usually insufficient to accurately derive the target coordinate due to ranging errors from thermal noise and other interferences. The least squares algorithm uses multiple reference nodes and the corresponding ranges to improve accuracy in the presence of error. It first creates following equations:

(15)

whereand (i = 1,2,…,n)are the coordinate of the reference nodes, and the distances to the target node.

These equations can be linearized by subtracting the last low and performing some minor arithmetic shuffling, resulting in the following relations AI = b:

,

,

.

This work employs the following solution:

. (16)

Although the least squares algorithm could reduce the localization error, it requires a large amount of reference nodes within the communication radius of target node. Therefore, in the mining application of UWB wireless sensor networks, it is necessary to balance the cost and the accuracy.

In the following, we explore the relation between localization error and ranging error and then propose a modified algorithm based on the least squares algorithm.

Assume that the estimated distance between the target node and the ith reference node is, where is the ranging error,. From Equation (16), we have, where

                                                        

,

.

Denote, we get the coordinate of target node:

        .               

(17)

. (18)

Usually, , and are mutually independent. Therefore,

. (19)

. (20)

From above deduction, it is shown that localization error could be reduced proportionally to the reduction in the ranging error. According to the relation, if we guarantee the accuracy ofin every equation, the trilateration and the least squares algorithm could be kept similarly accurate even if the number of equations is limited. The proposed ranging solution using MLE based on RSSI in this paper improves the ranging accuracy between target node and every reference node through iterative ranging, and reduces the ranging error caused by ranging based on a single round sampling. Furthermore, it reduces the influence of fixed value ofgiven in our path loss model on ranging and localization in timevariant channel. Hence, our localization algorithm can provide accurate ranging and localization with less UWB reference nodes.

7.  Simulation Results

In order to verify our localization algorithms based on U-BOTH system for WSNs, we carried out simulation in the following scenarios:

1) With regard to the BER (bit error rate), we evaluate U-BOTH system performance in single and multi-user scenarios.

2) Using the sample network deployment as shown in Figure 4, we evaluate the ranging accuracy by comparing the results with the Cramer-Rao lower bounds.

3) Using the same sample network as shown in Figure 4, we evaluate the impact of the number of itera-

tions in calculating the coordinate of a specific target node, indicated by the triangle in the diagram.

7.1.  U-BOTH System Performance

We assume the channel is AWGN multipath-free single user channel; the transmitter and the receiver are synchronized perfectly. Then we randomly generate 2000 bits, every bit uses 4 pulses to repeat coding (Ns = 4).

Figure 5 illustrates the BER of the received signal using U-BOTH system, in contrast to DS-UWB that only uses direct sequence spreading, and TH-UWB that uses time-hopping pulse position modulation alone for UWB transmissions. We can see that the BER of U-BOTH and the DS-UWB system which use the-phase shift keying modulation are lower than TH-UWB. This is because the distance of two signals in binary phase shift keying (BPSK) modulation is, but in THUWB [23].

Secondly, we let E_b = N₀ = 0 dB, Ns = 4 and generated 2000 bits randomly. Figure 6 shows the relative performance of U-BOTH, TH-UWB and DS-UWB systems in multiple access scenarios. In this case, the received signal includes by noise and co-channel interference. In Figure 6, although both the BER and the variance of error bits increase as the number of users increases, the performance of our U-BOTH system is still better than DS-UWB and TH-UWB, proving that the UWB coding based OVSF-TH effectively handle the burst errors.

7.2.  Evaluation of the Ranging Algorithms

In order to evaluate the performance of the ranging algorithms, we compare the parameter estimation errors against the Cramer-Rao lower bound (CRLB).

Denoteas the unbiased estimation of the parameter d from Equation (13), then the mean square error (MSE) ofis

. (21)

Hence in unbiased condition, the MSE ofis equal to the variance. The lower bound of the MSE based on UWB RSSI ranging could be represented by the CRLB:

.

From Equation (13), we know thatcan

not be expressed in the form. So, the lower bound of MSE can not reach the CRLB. However, we can use the MLE based RSSI ranging to enable the MSE to approach the CRLB. The MSE of UWB ranging is:

. (22)

As PLi are mutually independent, we take Equation (12) and Equation (14) into Equation (22), and get the MSE of MLE based ranging using RSSI information:

.

(23)

Therefore, the MSE of estimated distanceis the function of real distance d and the number of iterations N.

Based on the data in [7,11,16], we set n₁, n₂ Î [-2, 2], n₁n₂Î [-4, 4] and adopt values of UWB path loss model for simulations as shown in Table 2.

Figure 7 illustrates the relation between d and the CRLB, and the relation between d and the MSE. On one hand, it shows that the CRLB and the MSE increase when d increases, on the other, the MSE of ranging and the CRLB are always very close. When d is very small, they even overlap with one another. The more iterations we have for ranging, the smaller difference between the CRLB and the MSE (When d = 4m, N = 20, the CRLB is 0.0412m², the corresponding MSE is 0.0414m². When d = 20m, N = 20, the CRLB is 1.0310 m², the corresponding MSE is 1.0357 m²).

In Figure 7, we can see that when N = 20, d > 20m, the MSE of ranging estimation grows higher than 1m². Therefore, it is necessary to filter out large d values in order to achieve higher ranging accuracy.

In the MLE based ranging using the RSSI values, the number of iterations N is an important parameter. Figure 8 gives the relation between N and the CRLB and the MSE, respectively. When N increases, the CRLB and the MSE decrease rapidly. The MSE of ranging approximates the CRLB when N is large enough (e.g. when d = 5m, N = 10, the CRLB is 0.1289 m², the corresponding MSE is 0.1300 m²). Accordingly, we validate Equation (23), and prove the validity of our MLE method.

Figure 9 compares the MLE based ranging errors when the numbers of iterations N are 1, 5, and 20. Even if thermal noises and other interferences cause the error to fluctuate randomly, we can see that higher numbers of iterations dramatically increase the accuracy of ranging computations.

Figure 10 analyzes the CRLB, which reflects the MSE of unbiased estimation, in LOS (line of sight) and NLOS (non-line of sight) environments. When N increases, the CRLB in LOS and NLOS decrease correspondingly. For the same distance d situations, the CRLB in NLOS is even smaller than the CRLB in LOS through our channel model and ranging method. Therefore, precise ranging and localization estimation also could be achieved in NLOS environment. This is especially attractive in coal mine environments.

7.3.  Evaluation of the Localization Algorithms

From the analysis of Cramer-Rao low bound in Equation (21), the variance of ranging error can be shown in Equation (23). Similarly, the localization error can be expressed by the estimated coordinates and the real coordinates as.

Figure 11 shows the relation between ranging error and localization error in Equation (19) and Equation (20). It is obvious that the ranging error and localization error decrease when N increases. The localization error when N = 2 is about 2/3 of that when N = 1. When N = 20, we could get the least localization error, which is 0.3009m.

Secondly, we choose some nodes in Figure 4 to examine the impact of the number of iterations to the accuracy of localization computations as shown in Figure 12, Figure 13 and Figure 14. The triangle is the target node, the squares are reference nodes in the communication radius of the target node, the star is the estimated location of target node and the hollow circles are other nodes. We set the communication radius in Figure 4 to be 20m, and the average number of reference nodes in this range to be K = 5. Therefore, allocating about 40 reference nodes in themining area should be enough to monitor target node. As the location calculation algorithms described in Section 4-B, when Tw = 1s, T_RR = 10ms and = 10ms, we can ensure 20 to 100 rangings between target node and every reference node. Figure 12, 13, 14 display the special deviation between estimated location and real location when N = 1, N = 20 and N = 100. Table 3 shows the localization error between the target node and a reference node that is d = 14.9430m away, which shows that the impact of N increments decreases when N is greater than a few dozen.

8.  Conclusions

We proposed a group of communication protocols and localization algorithms for wireless sensor networks in coal mine environments, namely a new UWB coding method, called U-BOTH (UWB based on Orthogonal Variable Spreading Factor and Time Hopping), an ALOHA-type channel access method and a message exchange protocol to collect location information. Then we derived the corresponding UWB path loss model in order to apply the maximum likelihood estimation (MLE) method to compute the distances to the reference sensors using the RSSI information, and provided least squares (LS) method to estimate the coordinate of the moving target. The performance of U-BOTH communication system and the localization algorithms are analyzed using communication theories and simulations. Results show that UBOTH transmission technique can effectively reduce the bit error rate under the path loss model, and the corresponding ranging and localization algorithms can accurately compute moving object locations in coal mine environments.

9.  Acknowledgment

We would like to express our sincere appreciation to Prof. Fanzi Zeng, and Prof. Juan Luo for their insightful feedbacks during the preparation of this manuscript, and of the anonymous reviewers for their helpful comments. This work has been generously sponsored in parts by the National Natural Science Foundation of China under Grant No. 60673061 and the Raytheon Company under Grant No. RC-42621.

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NOTES

* This work was sponsored in parts by the National Natural Science Foundation of China under Grant No. 60673061 and the Raytheon Company under Grant No. RC-42621.