Remotely-sensed TOA interpretation of synthetic UWB based on neural networks
© Zhang et al.; licensee Springer. 2012
Received: 12 July 2011
Accepted: 2 August 2012
Published: 25 August 2012
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© Zhang et al.; licensee Springer. 2012
Received: 12 July 2011
Accepted: 2 August 2012
Published: 25 August 2012
Because of the good penetration into many common materials and inherent fine resolution, Ultra-Wideband (UWB) signals are widely used in remote sensing applications. Typically, accurate Time of Arrival (TOA) estimation of the UWB signals is very important. In order to improve the precision of the TOA estimation, a new threshold selection algorithm using Artificial Neural Networks (ANN) is proposed which is based on a joint metric of the skewness and maximum slope after Energy Detection (ED). The best threshold based on the signal-to-noise ratio (SNR) is investigated and the effects of the integration period and channel model are examined. Simulation results are presented which show that for the IEEE802.15.4a channel models CM1 and CM2, the proposed ANN algorithm provides better precision and robustness in both high and low SNR environments than other ED-based algorithms.
As a new wireless communications technology, Ultra-Wideband (UWB) has generated considerable research interest due to the many potential applications. One of the most promising areas is remote sensing [1, 2]. For example, Defense Research and Development Canada (DRDC) Ottawa has conducted numerous experiments on indoor through-wall imaging, snow penetration, stand-off remote sensing of human subjects, and mine detection using high-resolution UWB signals . In , UWB propagation channel characterization was performed to test the feasibility of using UWB technology in underground mining to monitor and communicate with remote sensors.
UWB technology offers many advantages for remote sensing . First, some frequency components may be able to penetrate obstacles to provide a Line-Of-Sight (LOS) signal. Second, the transmission of very short pulses makes high time resolution (sub-nanosecond to nanosecond) possible. Third, the wide signal bandwidth means a very low power spectral density, which reduces interference to other Radio Frequency systems.
Among the potential applications, precision ranging or Time of Arrival (TOA) estimation is the most important for remote sensing. However, this is a very challenging problem due to the severe environments encountered, e.g., thermal noise, multi-path fading, reflection interference, and inter-symbol interference. The TOA estimation problem has extensively been studied [3–6]. There are two approaches applicable to UWB technology, a Matched Filter (MF)  (such as a Rake or correlation receiver) with a high sampling rate and high-precision correlation, or an Energy Detector (ED) [4–6] with a lower sampling rate and low complexity. An MF is the optimal technique for TOA estimation, where a correlator template is matched exactly to the received signal. However, an UWB receiver operating at the Nyquist sampling rate makes it very difficult to align with the multipath components of the received signal . In addition, an MF requires a priori estimation of the channel, including the timing, amplitude, and phase of each multipath component of the impulse . Because of the high sampling rates and channel estimation, an MF may not be practical in many applications. As opposed to a more complex MF, an ED is a non-coherent approach to TOA estimation. It consists of a square-law device, followed by an integrator, sampler, and a decision mechanism. The TOA estimate is made by comparing the integrator output with a threshold and choosing the first sample to exceed the threshold. It is a practical solution as it directly yields an estimate of the start of the received signal. An ED is thus a low complexity, low sampling rate receiver that can be employed without the need for a priori channel estimation.
The major challenge with ED is the selection of an appropriate threshold based on the received signal samples. Threshold selection for different signal-to-noise ratios (SNRs) has been investigated via simulation. In , a normalized threshold selection technique for TOA estimation of UWB signals was proposed which uses exponential and linear curve fitting of the kurtosis of the received samples. In , an approach based on the minimum and maximum sample energy was introduced. These approaches have limited TOA precision, as the strongest path is not necessarily the first arriving path.
Neural networks (NNs) have extensively been used in signal processing applications. The weights between the input and output layers can be adjusted to minimize the error between the input and output. Because of the complexity of wireless environments, it is difficult to derive a closed-form expression to estimate the TOA. On the other hand, an artificial neural network (ANN) can provide a very flexible mapping based on the training input. The ANN here intends to solve a regression problem being J the input and optimal threshold the output.
In this article, we consider the relationship between the SNR and the statistics of the integrator output including skewness, maximum slope, kurtosis and standard deviation. A metric based on skewness and maximum slope is then used as the ANN input. A back propagation (BP) NN is used which is a feed forward NN. It approximates the relationship between the joint metric and the optimal threshold by using a nonlinear continuum rational function. Performance results are presented which show that in the IEEE 802.15.4a channel models CM1 and CM2, this ANN provides robust estimates with high precision for both high and low SNRs.
The remainder of this article is organized as follows. In the following section, the system model is presented. Section “TOA estimation based on ED” discusses TOA estimation algorithms based on ED. Section “Statistical characteristics of the signal energy” considers the statistical characteristics of the energy values, and a joint metric based on skewness and maximum slope is proposed. In Section “Optimal normalized threshold with respect to J”, the relationship between the joint metric and optimal normalized threshold is established. Section “Threshold selection using an ANN based on skewness and maximum slope” introduces a novel TOA estimation algorithm based on an ANN. Some performance results are presented in Section “Performance results and discussion”, and Section “Conclusions” concludes the article.
IEEE 802.15.4a  is the first international standard that specifies a wireless physical layer to enable precise TOA estimation and wireless ranging. It includes channel models for indoor residential, indoor office, industrial, outdoor, and open outdoor environments, usually with a distinction between LOS and non-LOS (NLOS) properties. In this article, a Pulse Position Modulation Time Hopping UWB (PPM-TH-UWB) signal  is employed for transmission between the transmitter and receiver.
where α is the shape factor and f(t) is the Gaussian pulse. A smaller value of α results in a shorter pulse duration and thus a larger bandwidth.
where X is a log-normal random variable representing the amplitude gain of the channel, N c is the number of observed clusters, K(n) is the number of multipath components received within the n th cluster, α nk is the coefficient of the k th component of the n th cluster, T n is the TOA of the n th cluster and τ nk is the delay of the k th component within the n th cluster.
respectively, where E n is the signal energy within the n th integration period and F is the number of degrees of freedom given by F = 2BT b + 1. B is the signal bandwidth.
The TOA estimate is then obtained using Equation (11). The problem in this case becomes one of how to set the threshold, i.e., how to establish the relationship between the received energy values and ξnorm. There are two main methods in the literature, curve fitting and fixed threshold (FT). In , a normalized threshold selection technique for TOA estimation of UWB signals was proposed which uses exponential and linear curve fitting of the kurtosis of the received samples. A simpler approach is the FT algorithm where the threshold is set to a fixed value, for example ξnorm = 0.4. If ξnorm is set to 1, the algorithm is the same as MES. In this article, an ANN algorithm is employed to obtain the normalized threshold based on the signal energy statistics.
where t n is the n th actual propagation time, is the n th TOA estimate, and N is the number of TOA estimates.
In this section, the skewness, maximum slope, kurtosis and standard deviation of the energy values are analyzed.
where is the mean, and σ is the standard deviation. The kurtosis for a standard normal distribution is three. For this reason, k is often redefined as K = k - 3 (referred to as excess kurtosis), so that the standard normal distribution has a kurtosis of zero. Positive kurtosis indicates a “peaked” distribution, while negative kurtosis indicates a “flat” distribution. For noise only (or for a low SNR) and sufficiently large F (degrees of freedom of the Chi-square distribution), z[n] has a Gaussian distribution and K = 0. On the other hand, as the SNR increases, K tends to increase.
The model coefficients were obtained using data from both the CM1 and CM2 channels.
where is the mean, and σ is the standard deviation of the energy values. The skewness for a normal distribution is zero, in fact any symmetric data will have a skewness of zero. Negative values of skewness indicate that the data are skewed left, while positive values indicate data that are skewed right. Skewed left indicates that the left tail is long relative to the right tail, while skewed right indicates the opposite. For noise only (or very low SNRs), and sufficiently large F, S ≈ 0. As the SNR increases, S tends to increase.
In order to examine the characteristics of the four statistical parameters (skewness, maximum slope, kurtosis, and standard deviation), the CM1 (residential LOS) and CM2 (residential NLOS) channel models from the IEEE802.15.4a standard are employed. For each SNR value, 1,000 channel realizations were generated and sampled at F c = 8 GHz. A second derivative Gaussian pulse is employed with T f = 200 ns, T c = 1 ns, T b = 4 ns, and N s = 1. Each realization has a TOA uniformly distributed within (0, T f ).
Standard Deviation of the Statistics
Generate a large number of channel realizations for each channel model, integration period, and SNR value in the range [4, 32] dB.
Calculate the average MAE value with respect to normalized threshold ξ norm for each J value, channel model, and integration period as shown in Section “Average MAE with respect to the normalized threshold”. In the simulation, because of the random signal, there are many MAE values with respect to one normalized threshold, so the average MAE should be calculated. At the same time, because J is a real value, J should be rounded to the nearest discrete value, for example integer value or half-integer value.
Select the normalized threshold with the lowest MAE as the best threshold ξ best with respect to J for each channel model and integration period, as shown in Section “Optimal thresholds”.
Calculate the average normalized thresholds of channels CM1 and CM2 for each J as the optimal normalized threshold ξ opt, as shown in Section “Optimal thresholds”.
To determine the optimal threshold ξopt based on J, the relationship between the average MAE and the normalized threshold ξnorm for different J, channel model and Tb was determined. ξ is the threshold which is compared to the energy values to find the first TC, as defined (12). When ξ is larger than the maximum energy value zmax, no value is found for τ, so in this case ξ is set to zmax, and ξnorm is set to 1.
The value of ξnorm ranges from 0 to 1, so the logsig function is selected as the transfer function for the neurons of both the hidden and output layers. This function is defind as logsig(x) = 1/(1 + exp(−x)). The Levenberg-Marquardt (LM) algorithm is used in the network training to update the weight and bias values according to LM optimization . Although this algorithm requires more memory than other algorithms, it is often the fastest BP algorithm. Because there is only one input and one output element in the proposed ANN, and only 39 ξnormJ pairs (J = −9 to 16 for T b =1 ns and J = −4 to 8 for T b =4 ns), the memory requirements are modest. The weight and bias values before training were set to random values uniformly distributed between −1 and 1.
In order to train the ANN, i.e., to determine the relationship between J and the normalized threshold ξnorm, 1,000 CM1 and CM2 channel realizations for each value of SNR from 4 to 32 dB were generated for both Tb = 1 ns and Tb = 4 ns. The integer J values in the range [−9, 16] and [−4, 8] for Tb =1 ns and Tb =4 ns, respectively, were used to train the ANN. Thus, there were 39 samples to train the ANN. On the other hand, the half-integer J values in the range [−0.85, 15.5] and [−3.5, 7.5] for Tb =1 ns and Tb =4 ns, respectively, were used to conduct the external validation for the trained ANN. To obtain the best ANN, 100 separate training iterations were conducted for each value of Tb, and the one with the lowest MSE was selected.
Validation Results of the ANN
Input of ANN (J)
Coefficient of Determination
[-9, -8, .., 15, 16]
[-8.5, -7.5, .. , 14.5, 15.5]
[-4, -3, .. , 7, 8]
[-3.5, -2.5, .. , 6.5, 7.5]
In this section, the MAE is examined for different ED based TOA estimation algorithms in the IEEE 802.15.4a channel model CM1 and CM2. As before, 1,000 channel realizations were generated for each case. A second derivative Gaussian pulse with a 1 ns pulse width was employed, and the received signal sampled at F c = 8 Ghz. The other system parameters were T f = 200 ns and N s =1. Each realization had a TOA uniformly distributed within (0, T f ).
MAE averaged over all the simulated realizations
The performance of the proposed algorithm is more robust than the other algorithms, as the difference between Tb = 1 ns and 4 ns is very small compared to the difference with the Kurtosis algorithm. For almost all SNR values the proposed algorithm is the best. Conversely, the performance of the Kurtosis algorithm varies greatly with respect to the other algorithms, and is very poor for low to moderate SNR values.
A low complexity ANN-based (TOA) estimation algorithm has been developed for UWB remote sensing applications. Four statistical parameters were investigated, and from the results obtained, a joint metric based on skewness and maximum slope was developed for TC TOA estimation. The optimal normalized threshold was determined using performance results for the CM1 and CM2 channels. The effects of the integration period and channel model were investigated. It was determined that the proposed threshold selection technique is largely independent of the channel model. The performance of the proposed algorithm is shown to be better than several well-known algorithms. In addition, the proposed algorithm is more robust to changes in the SNR and integration period.
This study was supported by the Nature Science Foundation of China under grant No. 60902005, the Outstanding Youth Foundation of Shandong Province under grant No. JQ200821, and the Program for New Century Excellent Talents of the Ministry of Education under grant No. NCET-08-0504.
1Department of Information Science and Engineering, Ocean University of China, Qing Dao, China. 2Department of Computer and Communication Engineering, China University of Petroleum (East Chinxa), Qing Dao, China.3Department of Electrical Computer Engineering, University of Victoria, Victoria, Canada.
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