**Smart Antenna?**

Smart Antenna is an antenna array aided by some “smart” algorithm to combine the signals, designed to adapt to different signal environments. The antenna can automatically adjust to a dynamic signal Environment. The gain of the antenna for a given direction of arrival is adjustable. In truth, antennas are not smart, antenna systems are smart. Generally collocated with a base station, a smart antenna system combines an antenna array with a digital signal-processing capability to transmit and receive in an adaptive, spatially sensitive manner. In other words, such a system can automatically change the directionality of its radiation patterns in response to its signal environment. This can dramatically increase the performance characteristics (such as capacity) of a wireless system.

**Types of Smart Antenna Systems**

The following are distinctions between the two major categories of smart antennas regarding the choices in transmit strategy:

*Switched Beam Antennas*

In Switched Beam Smart antenna, there are a finite number of fixed, predefined patterns or combining strategies (sectors).

Switched beam antenna systems form multiple fixed beams with heightened sensitivity in particular directions. These antenna systems detect signal strength, choose from one of several predetermined, fixed beams, and switch from one beam to another as the mobile moves throughout the sector. Instead of shaping the directional antenna pattern with the metallic properties and physical design of a single element (like a sectorized antenna), switched beam systems combine the outputs of multiple antennas in such a way as to form finely sectorized (directional) beams with more spatial selectivity than can be achieved with conventional, single-element approaches.

In the Switched Beam scheme, beams are created by choosing a particular set of antenna weights from a fixed “library” of beam weight vectors. The weight vector associated with maximum SNIR is chosen as the current weight vector. It follows that in order to continuously maintain maximum SNIR, the choice of weight vector must be continuously updated via ongoing SNIR measurements.Switched beam systems are simpler and less computationally intensive.

**Figure:** Switched Beam System Coverage Patterns (Sectors)

*Adaptive Array Antennas*

In Adaptive Array antenna there are an infinite number of patterns (scenario-based) that are adjusted in real time.

Adaptive antenna technology represents the most advanced smart antenna approach to date. Using a variety of new signal-processing algorithms, the adaptive system takes advantage of its ability to effectively locate and track various types of signals to dynamically minimize interference and maximize intended signal reception. Both systems attempt to increase gain according to the location of the user; however, only the adaptive system provides optimal gain while simultaneously identifying, tracking, and minimizing interfering signals.

**Figure:** Adaptive Array Coverage, A representative depiction of a Main Lobe extending toward a User with a Null directed toward a Co channel Interferer.

**Beamforming Algorithms**

In beamforming, both the amplitude and phase of each antenna element are controlled. Combined amplitude and phase control can be used to adjust side lobe levels and steer nulls better than can be achieved by phase control alone. The combined relative amplitude a_{k}** **and phase shift **q**_{k}** **for each antenna is called a “** complex weight**” and is represented by a complex constant

**w**

_{k }(for the kth antenna). These weights are calculated using different algorithms.

Beamforming is the term used to describe the application of weights to the inputs of an array of antennas to focus the reception of the antenna array in a certain direction, called the look direction or the main lobe. More importantly, other signals of the same carrier frequency from other directions can be rejected. These effects are all achieved electronically and no physical movement of the receiving antennas is necessary. In addition, multiple beamformers focused in different directions can share a single antenna array; one set of antennas can service multiple calls of the same carrier.

In Beamforming, we discriminate between signals according to their angles of arrival (AOA). Beam pattern is controlled by the complex weights.

*Least-Mean-Squares Algorithm*

The LMS algorithm can be considered to be the most common adaptive algorithm for continues adaptation. It uses the steepest-descent method and recursively computes and updates the weight vector.

Figure: LMS Algorithm

Due to the steepest-descend the updated vector will propagate to the vector which causes the least mean square error (MSE) between the beamformer output and the reference signal. The following derivation for the LMS algorithm is found in . The MSE is defined by:

is the complex conjugate of the desired signal. The signal is the received signal from the antenna elements, and is the output of the beamform antenna and is the Hermetian operator. The expected value of both sides leads to:

In this relation the ** r **and

**are defined by:**

*R*

** R **is referred to as the covariance matrix. If the gradient of the weight vector

**is zero, the MSE is at its**

*w*minimum. This leads to:

This solution is called the Wiener-Hopf equation for the optimum Wiener solution:

The LMS algorithm converges to this optimum Wiener solution. The basic iteration is based on the

following simple recursive relation:

And combining above two equations, gives:

The measurement of the gradient vector is not possible, and therefore the instantaneous estimate is used.

The LMS algorithm can be written in its final form.

One of the issues on the use of the instantaneous error is concerned with the gradient vector, which is not the true error gradient. The gradient is stochastic and therefore the estimated vector will never be the optimum solution. The steady state solution is noisy; it will fluctuate around the optimum solution. By decreasing µ the precision will improve but it will decrease the adaptation rate. An adaptive µ could solve this issue by starting with a large µ and decrease the factor when the vector converges. When an array of 4 antennas is used, there is a maximum of 3 nulls that can eliminate the interferer. Figure 7 shows the convergence of the array for 2 interferers. The minimum error is a result of the extra ‘system’ noise that is added to all antennas. The interference signals are Gaussian white noise, zero mean with a sigma of 1. The extra system noise to all antennas is white noise with zero mean and a sigma of 0.1. The received signals are MSK signals with an oversampling of 4 and have an amplitude of 1 in the simulations. The true array output *y(t) *is converging to the desired signal *d(t)*. After 40 samples the signal is at its minimum due to the system noise. The LMS cannot filter the system noise, as it is not correlated for all four antennas. The interferers are cancelled by placing nulls in the direction of the interferers. The received signal arrives at an angle of 25 degrees and the array response is 0 dB. The LMS algorithm clearly works sufficient as the strong interferers are reduced.