The design of antennas for wireless personal communication systems is the subject of much research that is motivated by size, efficiency and health issues. In addition to maximizing the antenna radiated/accepted power of the handsets, the effects on the antenna performance from surrounding objects such as the human body must be considered. On the other hand the effect of radiation on the human body must be also considered. The closest human sensitive part to the handset in calling position is the human brain and ear in most mobile models or at least close enough to cause harmful effects. The tissues of these organs are mostly nerves plus liquid and hence, they carry electrical signals that might be affected by electromagnetic radiation from the wireless device [1] -[9] .

The RF energy is scattered and attenuated as it propagates through the tissues of the head, and maximum energy absorption is expected in the more absorptive high water-content tissues near the surface of the head. Inner ear (that contains high water-content) is just under the mobile phone and it will be subject to the strongest radiation from the mobile unit as shown in Figure 1.

The electromagnetic (EM) penetration into human head causes permanent damage to tissues that are exposed to high density EM energy. This could cause some organs to malfunction or at least a disturbance in their functionality. The amount of exposed energy that can be handled by human tissues is measured by the specific absorption rate (SAR) that is given by [10] -[15] :

where is the electric field intensity, is the tissue conductivity and is the tissue density. The dependency of on frequency is the result of interaction between the EM waves and the tissue material, such that the existence of ions will increase the conductivity and will change the permittivity of the tissue. The complex nature of the permittivity reflected into changing the conductivity of the tissue.

The effect of radiation in the inner ear has two folds: the effect on the neural tissues (hearing) and the effect on the filling liquid (balance). The radiation devices must be compliant to the SAR standard IEEE C95.1. The IEEE exposure criteria are based on a determination that potentially harmful biological effects can occur at an SAR level of 4 W/kg as averaged over the whole-body. Appropriate safety factors were then added to arrive at limits for both whole-body exposure (0.4 W/kg for “controlled” or “occupational” exposure and 0.08 W/kg for “uncontrolled” or “general population” exposure, respectively) and for partial-body (localized SAR), this might occur in the head of the user of a hand-held cellular telephone [9] .

The nature of the tissues in the inner ear makes its relative dielectric permittivity in the order of (41.5 + j17.98 at 900 MHz and 40.0 + j13.98 at 1.8 GHz) and its conductivity (0.97 at 900 MHz and 1.4 at 1.8 GHz). The problem with the inner ear arises from the fact that its inner liquid heat dissipation is not suited to dissipate heat generated from high radiation near the ear. This will maximize the risk of losing balance and/or changing the physical characteristics of the inner ear and hence, hearing impairment might occur [10] [12] .

This paper presents an antenna design to minimize radiation in the inner ear direction and at the same time produce an acceptable radiation pattern that can be used to communicate with base stations.

The proposed antenna system in this paper consists of ground plane and two H shaped PCB tracks on the other side that is using a coaxial feeder as shown in Figure 2. The radiation pattern for each antenna in the near field and the far field are shown in Figure 3 and Figure 4. The combination of the two antenna elements makes it possible to steer the radiation pattern toward the base station and creates a null toward the human head. This will

reduce the SAR in the human head and maintains the communication with the base station.

The two antenna elements proposed here will have an H shape each as shown in Figure 5. The near field radiation pattern for each element as seen from Figure 3 is close to Omni directional. Therefore, the electric field can be expressed in mathematical form as [16] -[18] :

where is the electric field radiated from the antenna in the near field and is constant in all directions.

To steer the radiation pattern, a variable delay element is introduced in the feeding circuit of one of the elements. Assuming that it is required to steer the radiation pattern main beam in direction and steer the null is

direction (that is usually in the normal direction to the front plane of the cellular phone) then the delay is found by:

where is the equivalent phase shift in radians and is the carrier period. To find the optimal that maximises the radiation pattern in the base station direction and at the same time minimize the radiation pattern in the human head direction to maintain acceptable SAR value, we solve the following equations:

And

The electric field to the base station direction is given by:

Then to find the optimal we maximize:

where is the received power from base station and is a constant. This equation is represented graphically as shown in Figure 6 and it can be maximized analytically.

For example if and in the y-z plane. Here the optimal has more than one optimal

value as shown in Figure 7. The radiation pattern in the near field for the two

elements at is shown in Figure 8.

The above example shows that there are several solutions for Equation (7). This is due to the existence of nulls in the dominator of the equation. As both and get close to each other the optimization becomes less efficient and the maximum value for becomes less for example for and the

optimal has more than one optimal value as shown in Figure 9.

Direct maximization of Equation (7) yields to solution where the SAR in the dominator of the equation is very small and hence any value for the electric field in the base station direction will maximize the equation. This happens when and any value of the will maximize. To solve this problem, we use a constraint optimization technique, such that we impose the constraint not to exceed a certain value of SAR and maximize the received power in the direction of the base station. Lagrange multiplier method can be used to find the optimal value of, such that we maximize the radiated energy in the base station direction under the constraint not to exceed a maximum value for the SAR. The cost function can be written as:

where is the Lagrange multiplier.

Solving for we find that:

And from the constraint:

From Equation (10) we find that:

The function is assumed here since analytical result is hard to get. A good approximation yields to:

Solving for as a function of and substituting in Equation (11). Then finding the value of from Equation (11) that satisfies the constraint and substituting it in Equation (10) to get the optimal value of.

And:

Note that the analytical solution is hard to get since Equations (10) and (11) are not linear. We need a numerical technique to find such that, the solution can be found fast and the mobile device can determine the optimal delay in real time. We propose to use an iterative technique based on simulated annealing (SA) method to solve for the optimal delay [19] -[22] . This technique will result in a sub-optimal value for but it should converge to a solution in real time. Equation (10) has more than one solution depending on the values of and, some of them are local optimal values. We need to find the global optimal value, and therefore, simulated annealing algorithm is selected since it converges to the global optimal point (or near optimal). Starting from the cost function defined as:

An approximation of this cost function is given by:

The devised system need to know the base station direction as well as the SAR direction, these angels should be known each optimization update. The SAR angle is easy to obtain since it is always normal to the speaker of the phone as shown in Figure 10. is usually unknown and need to be estimated on real time. To estimate the arrival angle many techniques may be used. Here we may use simple method to measure, such that, by using the received signal strength indicator (RSSI) of the device when on receiving mode and sweeping the delay between the elements to get maximum RSSI.

The simulated annealing algorithm does not require derivative information; it needs to be supplied with a cost function for each trial solution it generates. The algorithm simulates a small random displacement of an atom that results in a change in energy. If the change in energy is negative, the energy state of the new configuration is lower and the new configuration is accepted. If the change in energy is positive, the new configuration has a higher energy state; however, it may still be accepted according to the Boltzmann probability factor given by:

where is the Boltzmann constant, is the current temperature and is the change in energy (cost

function). The solution is started at a high “temperature”, where it has a high cost. Random perturbations are then made to the solution. If the cost is lower, the new solution is made the current solution; if it is higher, it may still be accepted according the probability given by the Boltzmann factor. The Boltzmann probability is compared to a random number drawn from a uniform distribution between 0 and 1; if the random number is smaller than the Boltzmann probability, the solution is accepted. This allows the algorithm to escape local minima. As the temperature is gradually lowered, the probability that a worse solution is accepted becomes smaller. Although the algorithm is not guaranteed to find the best optimum, it will often find near optimum and it is also a simple algorithm to implement.

The simulated annealing algorithm is given as in the following pseudo code:

In the following we use MatLab to calculate the optimal delay for the previous examples using the simulated annealing algorithm.

To demonstrate the performance of the devised system and to find the optimal delay value using simulated annealing algorithm we use MatLab software to find the optimal delay for the examples discussed in the previous section: In the first example where and. Figure 11 shows a numerical calculation of the cost function given in Equation (17). Here the optimal has more than one solution at the zero crossing points one of them is the global minimum cost solution.

Using simulated annealing we solve the same example as shown in Figure 12. Here the global optimal is found to be at 18.66˚ after 10 iterations.

In the second example for and. Figure 13 shows a numerical calculation of the cost function given in Equation (17). A gain, the optimal has more than one solution at the zero crossing points one of them is the global minimum cost solution.

Using simulated annealing we solve the same example as shown in Figure 14. Here the global optimal is found to be at −57.27˚ after 6 iterations.

The simulated annealing algorithm in both examples arrives in few iterations at the global optimal solution. Next we discuss the results obtained for the whole devised system.

The proposed system uses two H shaped patch antennas with delay element to steer the radiation pattern of the resultant array in a way that ensures the safety of the user and at the same time maintain the connectivity with

the cellular network. Maximizing the radiated power toward the base station while keeping the SAR level under the allowable maximum value is used as the optimization criteria. This problem is solved using Lagrange multiplier method and yields a numerically challenging solution; therefore, simulated annealing algorithm is used to find a sub-optimal solution that works fast in real time for the mobile unit. Numerical calculations showed good and efficient solutions for the optimal delay value when using the simulated annealing algorithm.

The design is simple and can be easily implemented on mobile units; it does not need large processing power from the mobile unit. It can be implemented in real time with minimum cost. Local field is also affects the user and needs to be investigated in future work.