Tomlinson-Harashima Precoding

Tomlinson-Harashima Precoding is an equalization method done at the transmitter side. Consider a decision feedback equalizer (DFE) at the receiver. It usually consists of two filters: a feed forward filter and a feedback filter. These are usually implemented as FIR filters. The structure of a DFE is shown here:

This equalizer works very well if there is not an error correction coding with a significant coding gain in the system. If there is a need to such an error correction coding system, this means that there are many errors at the decision block output that need correction. The feedback filter part of a DFE only works correctly if the decision block output does not have many errors. The FBF actually tries to cancel what is called post-cursor ISI (inter symbol interference). This means that it assumes that previous decisions have been correct and uses those to remove the post cursor ISI. If many of the decisions of the decision block are erroneous, then the FBF not only cannot cancel the post cursor ISI, but it ads extra noise to the system. Which in turns causes more errors, and in this way the error at the output of decision block grows. This is called error propagation. To combat this one can move the FBF part of a DFE to the transmitter, as the result the system will look like this:

  

The "Modulo-M" block shown in the above figure makes sure that the output of THP stays in the range of (-M, +M] by adding appropriate integer multiple of 2M to the summation output. The reason that this block is there is to limit the signal level transmitted into the channel. Without it there will be some FBF coefficients that can make the output of summation point to large, which in many practical cases are not acceptable.

What do you think about THP? If you have any question or suggestion we would love to hear from you so leave a comment for us.

Minutify: A new excellent weblog for electrical engineers

Our friends have recently informed us that they have started building a weblog for electrical engineers. The weblog is called Minutify.

The purpose of this weblog is to publish blog posts from experts in the electrical engineering field, both from industry and academia. The blog posts are going to be short so that a reader can read them in minutes (hence the name Minutify), and also the purpose of each post is to teach an important electrical engineering concept in an easy way.

As of now we can see that there are five categories that post will be published on, and they are: Analog, ASIC, Communications, DSP, and RF.

So far there are four post on the weblog, which are:

• SNR and ENOB in Analog-to-Digital Converters: This blog post explains the relationship between the signal-to-noise ratio and effective-number of bits in an ADC. It also shows that in practice the relationship is also a function of peak-to-average power ratio of the input signal.
• Symbol error rate calculations for PAM and QAM: This post takes a look at the relation between SNR and symbol error rate, it also explains what rate-normalized SNR is and how to use it for calculation of PAM and QAM symbol error rate.
• Genetic Algorithm for search and optimization: This posts in a very simple language explains what the Genetic algorithm is, and how it is used in search and optimization, It also explains the concept with a simple example and MATLAB code.
• 36 great Electrical Engineering books: This is a list of essential electrical engineering books from the best authors. It covers a vast area of electrical engineering, from communication systems, to coding theory, to microelectronics. 

By reading these posts so far it looks like this is a great weblog for electrical engineering students and also engineers working in this field, we highly recommend this website, and we wish the best of luck for our friends who are trying to put together what looks to be a fantastic resource for all electrical engineers.