How do you design adaptive equalizers for wireless systems with time-varying channels?

2 Adaptive filter algorithms

Once you have an estimate of the channel characteristics, you can use an adaptive filter algorithm to update the equalizer coefficients based on the error signal, which is the difference between the desired and the actual output. There are many adaptive filter algorithms, such as least mean square (LMS), normalized LMS (NLMS), recursive least squares (RLS), and Kalman filter. The choice of algorithm depends on the convergence speed, stability, complexity, and tracking ability of the equalizer.

3 Equalizer structures

The structure of the equalizer determines how the filter coefficients are applied to the input signal. There are two main types of equalizer structures: linear and nonlinear. Linear equalizers, such as zero-forcing (ZF) and minimum mean square error (MMSE), use a linear filter to cancel or minimize the ISI. Nonlinear equalizers, such as decision feedback (DFE) and maximum likelihood sequence estimation (MLSE), use a nonlinear function or a feedback loop to reduce the error probability. The trade-off between linear and nonlinear equalizers is between complexity and performance.

4 Equalizer adaptation modes

The adaptation mode of the equalizer refers to how often and how much the filter coefficients are updated. There are three main adaptation modes: batch, block, and sample-by-sample. Batch mode updates the coefficients once for a large set of data, block mode updates them periodically for smaller subsets of data, and sample-by-sample mode updates them continuously for every incoming sample. The trade-off between adaptation modes is between latency and tracking.

5 Equalizer performance metrics

To evaluate the performance of an adaptive equalizer, you need to use some metrics that reflect the quality of the output signal and the efficiency of the adaptation process. Some common metrics are bit error rate (BER), mean square error (MSE), signal-to-noise ratio (SNR), convergence speed, misadjustment, and complexity. The optimal performance of an adaptive equalizer depends on the trade-off between these metrics and the requirements of the application.

6 Equalizer design steps

To design an adaptive equalizer for a wireless system with a time-varying channel, you need to consider several parameters and components. Firstly, you must define the system model and the channel characteristics, such as bandwidth, delay spread, fading, and noise. Then, you need to select the channel estimation method and the adaptive filter algorithm based on accuracy, overhead, and complexity. Additionally, you should choose the equalizer structure and the adaptation mode based on performance, complexity, and latency. Furthermore, you must determine the filter length, step size, initialization, and regularization factors based on convergence, stability, and tracking criteria. Finally, you should test and optimize the equalizer performance using metrics such as BER, MSE, SNR, and complexity.

7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?