Adaptive Equalization in Wireless Communication

Adaptive equalization is a technique that can be used with either linear or non-linear equalizers to improve their performance in a changing channel environment. An adaptive equalizer is an equalizer that automatically adapts to the time-varying properties of the communication channel.

Adaptive Equalization assumes the channel is time-varying and tries to design an equalizer filter whose filter coefficients are varying in time according to the change of channel and tries to eliminate intersymbol interference and additive noise at each time. The implicit assumption of adaptive equalization is that the channel is varying slowly.

Adaptive equalization works by adjusting the equalization filter in real-time to compensate for the distortion introduced by the channel. The equalization filter can be adapted based on the received signal characteristics and feedback from the receiver.

Adaptive equalization uses algorithms to estimate the channel response and then adaptively adjusts the filter coefficients to minimize the error between the received signal and the transmitted signal.

The desired output signal received by the equalizer is given by: 

here , x(t) = original message

           f(t) = combined impulse response

           n(t) = baseband noise

if  the impulse responses of the equalizer h_eq(t) , then the output of the equalizer is:

Basic Steps of Adaptive Equalization

1. Receives distorted signal.
2. Estimates channel characteristics.
3. Calculates filter coefficients.
4. Applies a filter to the signal.
5. Updates filter coefficients.
6. Outputs equalized signal.
   

Adaptive Equalization in wireless communication

There are two operating modes of adaptive equalization:

1. Training Mode: In the training mode, the equalizer is trained to learn the characteristics of the channel by using a known training sequence. The training sequence is typically a predetermined sequence of symbols that is transmitted by the transmitter and known by the receiver. The receiver uses this known sequence to estimate the channel characteristics and adapt the equalizer coefficients accordingly.
2. Tracking mode: In the tracking mode, the equalizer coefficient is adjusted based on the decisions made on the received signal. The receiver makes the decision and uses that decision to update the equalization coefficient.  or we can say that the equalizer uses the received signal to estimate the channel characteristics and adjust the filter coefficients to compensate for any changes in the channel.

Advantages of Adaptive Equalization

• Improves signal quality
• Reduces interference
• Increases spectral efficiency
• Enables longer distances
• Reduces power consumption
• Adapts to different channel conditions
• Robustness to channel changes: Adaptive equalizers can adjust to changes in the channel, making them more robust to variations in the wireless environment.