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The lack of effective techniques for estimation of shadow power in fading mobile wireless communication channels motivated the use of Kalman Filtering as an effective alternative. In this paper, linear second-order state space Kalman Filtering is further investigated and tested for applicability. This is important to optimize estimates of received power signals to improve control of handoffs. Simulation models were used extensively in the initial stage of this research to validate the proposed theory. Recently, we managed to further confirm validation of the concept through experiments supported by data from real scenarios. Our results have shown that the linear second-order state space Kalman Filter (KF) can be more accurate in predicting local shadow power profiles than the first-order Kalman Filter, even in channels with imposed non-Gaussian measurement noise.

In the fast growing field of wireless communication technology, accurate estimation of local mean shadow power at a mobile station (MS) is becoming a popular area of challenge for engineers in both industry and academia. There is an ever present need to continue to find ways to enhance device performance in power control and handoff, particularly to address mobility-induced fading.

Due to the motion of the mobile station (i.e. cellphone), the received signal strength fluctuates with two multiplicative forms of fading, shadowing (local mean, local power) and multipath [

Mobile communication shadowing plays a huge role in handoff decisions and power control. In [

Having an accurate estimate of shadowing will allow the mobile communication system to efficiently compensate for the signal degradation that will occur. In industry, several different types of windows-based estimators are utilized to filter multipath noise from the instantaneous received power signal in order to estimate the local mean shadow power. These windows-based estimators work well under the assumption that the shadowing component is relatively constant during the window period. In [

The lack of a consistent technique for calculating an optimized window period provides the motivation for finding an alternative method to windows-based estimation for estimating local mean shadow power. In our research, goal was to investigate an alternative method called Kalman Filtering. Kalman Filtering, introduced in [

In this paper, our contribution is to study and analyze output results of the first-order state space and to compare them to the second-order state space models while applying a Kalman Filter technique to determine shadow power signal in mobile communications from measurements that have impinged Rayleigh fast fading noise [

A model for instantaneous received power l(t) at a Mobile Station (MB) in a wireless communication is given in

fluctuation due to shadowing. It is customary to express power measurements in decibels as shown in

To solve this problem, we start with the multipath model shown in Equation (2),

where

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The Kalman Filter is a form of a linear algorithm for optimal recursive estimation of a system state with a specific set of output equations (

To build an estimation model in MATLAB, we started with Equations (3) and (4), with suitable entries to reflect the linear channel model [

where

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Assume initial values to be

Prediction States:

Equations (5) and (6) represent the “Time Update” state of the Kalman Filter, also known as “Prediction States.” Here, we project the current state estimate ahead (in time). Equation (5) projects the state ahead and equation (6) projects the error covariance ahead.

Correction States:

Equations (7), (8) and (9) belong to the “Measurement Update” state of the Kalman Filter, also known as the “Correction State.” Here, we adjust the projected estimate by an actual measurement. Equation (7) computes the Kalman Gain, Equation (8) adjusts the projected estimate by an actual measurement

If

The next step is to iterate through the estimates for a sufficient time. The output estimate in the previous step will be the input estimate in the next step. The main goal is to find an optimal value for

In this research, we assumed that the first-order order state space model can be used to model the Shadow Power.

To extend the first-order state space model equations [

Prediction States for Second-order Linear KF:

Equation (5) can be rewritten as Equation (14). Therefore, equation (14) in this section projects the state ahead, and equation (16) projects the error covariance ahead.

For second-order, matrices are defined as follows:

Parameter Q in Equation (16) represents the predicted process noise as shown in Equation (15).

Equation (6) can be then expressed in the following state space format:

Correction States for Second-order Linear KF:

Equation (17) was used to compute Kalman gain, where R represents the measurement noise due to multipath.

Equation (18) updates the estimate via

When the channel is nonlinear, the Unscented Kalman Filter also can be applied to the state space model to further improve and optimize the shadow power presented in this section. We may consider this optimization in the future.

In wireless cellular communications, accurate local mean (shadow) power estimation performed at a mobile station is important for use in power control, handoff and adaptive transmission [

The term soft handoff in mobile communications refers to the process of transferring a phone call currently in progress from one base station to another base station without any interruptions to the call.

The term hard handoff refers to the process of transferring a phone call where connection to one base station (named source cell) is broken before the connection to another base station (named target cell) is established.

Thus, an alternative name for this process is break-before-make and it is unique to cell phones that operate using the Global System for Mobile Communications. As depicted in

We propose a new adaptive handoff based on predictive function of the estimated part.

It is important to note that the land area supplied with radio service is divided into hexagonal cells. Each cell operates on a group of designated frequencies (f_{1}, f_{2}, f_{3}, f_{4}, f_{5}, f_{6}). The same group of frequencies cannot be used in an adjacent neighboring hexagonal cell, but it can be used in other nearby locations. See the illustration in

Previous reviewers on an earlier version of the manuscript suggested that we produce new results for estimation of local mean power by using the second-order state space Kalman Filter. Section 5.1 briefly explains Lab Setup used to conduct experiments and collect real data. Section 5.2 shows that we successfully validated our concept by using computer simulation. Section 5.3 presents results that show how we implemented idea in real scenarios where the fading model is unknown.

Current power measurement techniques are only able to provide a limited number of measurement schemes, which are not enough to asses such a complex phenomenon. There had been a great consideration and search in the area of measurements and modeling of the propagation effects in the indoor environments. However, such work only considered a specific environment explicitly stationary scenarios as reported in [

As part of this research, we were able to setup and conduct good experiments by utilizing an Electrical Engineering Laboratory at Georgia Tech University, shown in

Stationary Transmitter:

Signal generator: Generates a 2.43 GHz signal in order to transmit the signal at power levels-5 dBm and 15 dBm.

Omnidirectional transmitter antenna: Converts generated signal to produce radio waves.

Moving Receiver:

Omnidirectional receiver antenna: Captures the radio waves to receive the signal.

Receiver: The receiver is mounted on an extended arm of the linear positioner machine, which moves toward and away from the transmitter along the x-axis and y-axis. Therefore, in this experiment, the separation distance between the transmitter and receiver varied from 3 m to 3.45 m. The extended arm moves in a two-dimensional manner: 45.7 cm along the x-axis and 45.7 cm along the y-axis, with 2.5 cm step size (see

Additional Tools:

Spectrum analyzer: Collects the raw data (i.e., the received power level at a given position in x and y directions) and loads it into the computer.

Spectrum analyzer display: Displays results on the screen.

MATLAB Software: Reads the raw data from the spectrum analyzer. It was also used to load data into second-order Kalman Filter MATLAB Code for analysis purposes.

This section presents computer simulation results. Simulation models were created and used extensively in the initial stage of this research to validate the proposed theory.

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The second-order Kalman Filter shown in

Simulation was run to compare the system performance with the integrated second-order KF versus the same system with the first-order KF.

Changing parameter | Notation | 1^{st} test | 2^{nd} test | 3^{rd} test | Second-order KF performance |
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Mobile receiver velocity | (v) | 1 m/s | 10 m/s | 30 m/s | KF performed well when mobile receiver velocity was varied. |

Shadow variance | (σ_{s}) | 4 dB | 6 dB | 8 dB | KF performed well when shadow variance was varied. |

Effective correlation distance | (X_{c}) | 10 m | 200 m | 500 m | KF performed well when effective correlation distance was varied. |

Total power is the combination of multipath power and shadow power as illustrated in

performance of the first-order KF prediction for the total power. Similarly, the graph line marked in green illustrates performance of the second-order KF prediction for the total power. The results have been consistent in showing that the implementation of the second-order KF results in better estimation.

A previous reviewer of an earlier version of this manuscript suggested completing validation for this concept through lab experiments with data from a real scenario in addition to the MATLAB simulation. Experiments were conducted in the Laboratory at Georgia Tech University described in Section 5.1. In these experiments, we mainly explore how second-order KF compares to first-order KF. The experiment results supported by real data are shown in

Multipath is a Non-Gaussian disturbance in the power signal due to Doppler shifts along different signal paths. As mentioned earlier,

fluctuations due to multipath as well as fluctuations due to shadow power represent Rayleigh distribution. The total power pdf represents a combination of the multipath and shadow outputs.

Our contribution in this paper was to produce new results with second-order state space Kalman Filter to estimate local mean shadow power in mobile communications corrupted by multipath noise. At first, we generated a code to run simulations in order to evaluate the effectiveness of the proposed method by comparing an actual shadow power signal to estimate performance with the linear second-order Kalman Filtering method. Recently, we were able to validate this concept through experiments with an unknown fading model instead of relying on MATLAB simulation results only. Experiments with the real scenario data were conducted to compare the performance of the system with the integrated KF versus the same system without Kalman Filtering. Also, the performances of both the first order state space and the second order state space KF were compared. Experiment results show that the second-order Kalman Filter tracks the actual shadow power more accurately than the first- order Kalman Filter. Estimation of shadow power was good even when we varied parameters, such as effective

correlation distance, the number of paths used in the multipath or mobile receiver velocity. The second-order Kalman Filter output has less lag from the actual shadow power.

We also proposed a new adaptive handoff based on a balance of shadow signal strength and quality. Further study of this filter mode is being investigated together with nonlinear channels with imposed non Gaussian noise. We believe that there are opportunities for extending the scope of this study to multi-user and handoff in larger spaces such as parking lots or parks. For example, if there is more than one user in an area, we can create a cluster. The idea is to average roadside signals and clustering road signals as if they are one user.

The authors would like to express profound gratitude to Erica Yaharmatter from Autoliv Inc. for his initial contribution and thought on this subject. They would further like to thank Georgia Tech University for allowing them to use their laboratory facility. Comments and suggestions from two anonymous reviewers on an earlier version of the manuscript were also helpful in improving the presentation of this work.

The authors declare that they have no conflict of interest.

Azra Kapetanovic,Redhwan Mawari,Mohamed A. Zohdy, (2016) Second-Order Kalman Filtering Application to Fading Channels Supported by Real Data. Journal of Signal and Information Processing,07,61-74. doi: 10.4236/jsip.2016.72008