"Concerning matter, we have been all wrong. What we have called the matter is energy, whose vibration has been so lowered as to be perceptible to the senses. There is no matter."
------Albert Einstein.
My philosophy and belief at this stage is that we are multi-dimensional being and so is the universe. We see and feel in a 3 dimensional sense externally because we are designed to feel and see in the three dimensional manner. Till date there are no scientific explanations or theories of the human life and the universe based on the multi-dimensional understanding. String theory explains the universe as being an eleven dimensional wave, which deals only with the universe and still carries many controversy among the scientific community.Since everything is part of the universe, each object, each phenomenon and each being in the universe is multi-dimensional.
Hence, this rises questions on what are the extra-dimensions beside those that we can observe and how many dimensions are possible. We have no idea and no scientific proof on these facts. However, in this article I am writing only my personal belief and my feelings without any rigorous scientific proof. The most important fact about the existence of the universe is the knowledge or information. We exist because we know we exist and existence is completely a relative concept. The fact that information is contained in all beings and the existence is linked with the information is completely forgotten when explaining the universe only based on the space and time. Thus, one of the must added dimensions besides space and time at this stage to the engineering and scientific principles and also to the human life is the dimension of the knowledge.
The dimension of knowledge actually determines how strong and how intelligent we are. This means we can measure the intelligence of any system based on the amount of information or the amount of the knowledge it possesses. So I have called this concept as adding an extra dimension to the physical phenomenon. I believe our thoughts are multi-dimensional. Since we think what we already know or what we have not seen or known but we have imagined, one of the dimension in the thoughts is obviously knowledge or the information. Imagination and dream are also multi-dimensional. It means the things which we cant see but that exists with us every time are multi-dimensional.
One of my greatest desires in life is to model thoughts, imagination and dreams. One of my greatest desires in life is to model the desire itself. It means I have to move towards the multi-dimensional spectra. Observing and seeing things in the lower dimension is not quite helpful for me to be successful in my goals. Thats why I am concerned about multi-dimensional universe and multi-dimensional human beings. When we can view things multi-dimensionally we can view thoughts, we can view dreams and we can view visualization. I think this was also the explanation of some of the eastern philosophers and gurus, who are believed to have reached in their higher dimensional states by meditating and arousing their inner self. Since they have achieved it, since they have shown to be internally and spiritually successful, why is science and engineering lacking in describing such a great magic that had existed in the world from ages.
The next generation research should go in this direction of taking the human invention to the higher dimension and one of the way that we can immediately take is to consider the dimension of knowledge and information available to the individual. This is also equally valid for the invention and the technology we are designing in the future. Adding up more and more dimensions to a problem makes it complicated and difficult to think but in real life a problem can have multiple dimensions and constraints that has to be looked into. The more the dimensionality of a problem can be exploited the more the benefit can be taken from it. So the motto is increase the dimensionality of thinking and vision as much as you can. To achieve more, it should be exploited more upto the achievable limit. This is the fundamental fact of the real life and so is the fundamental fact of research. Optimization and exploitation are the two facts that have to be considered while seeing the problem and analyzing the achievability.
So this has led to the assumptions that we can add some more dimensions in the communication systems and that dimension can be the dimension of the channel knowledge or it can also be considered as a constraint. The channel which is quite a random factor in wireless communication is not properly looked after or in other words there is very less knowledge about the channel at the transmitter. But likewise the channel is not also completely unknown. It can be statistically studied, it can be studied with error and it can be estimated in one way or the other. However how good we are in estimating the channel is a question.
The major drawback of the algorithms like interference alignment is that the channel should be perfectly known to the transmitter to design the precoder that would align the interference, which is often not true in real life. However, in real life we always do not talk about a fully connected channel or completely random channel whose CSI cant be estimated with some errors. How much error in the channel should the interference alignment allow is a question. The answer is earlier interference alignment requires perfect channel knowledge.
Is feedback the only way to improve the degrees of freedom of the interference channel? How has feedback played a role in the interference channel is the core of the talk by Dr. Vincent Poor on the conference,where he mentioned that the generalized degrees of freedom can be improved by the help of delayed feedback. One of the interesting concepts that is discussed is the concept of spatio-temporal variation of the feedback. By this we are exploiting the variability of feedback in the communication system.
Suppose a base station with $K$ antennas is transmitting to the $K$ users at the same time. Each user has a desired signal and remaining $K-1$ interference signals. Determining the capacity region of such an interference channel is an open problem since decades. However there has been an extensive study in determining the pre-log factor or the degrees of freedom of such channels where interference is the major limitation. Researchers have come up with the number of ideas to play with the interference. They have come up with the different view points of seeing the interference. Actually how harmful or useful is the interference is still an open issue. The good thing about interference is that it is a power and there should be a number of ways how this power can be useful.
Besides the number of approaches that have been mentioned in the literature about dealing with the interference like interference alignment and interference containment, interference cancellation, interference exploitation etc. We should also broaden our vision on how to take the good from the 'so called bad'. Is there a way to take the good out from the bad? Is there a way to view interference as a good friend rather than an enemy. Research should also focus towards this area. The area is still open and very few researchers have come up with the ideas that the interference power can be harvested and used to charge the number of systems without wire. So it has opened up one idea of thinking about the usefulness of the interference.
Efficient mitigation of interference is the other research area that many communication engineers are presently working. Interference alignment is one of the hottest topics among them. It is the generic idea to allow more degrees of freedom to the desired signal by restricting the interference signals to the lower dimensions.
In what case can the feasibility of interference alignment be determined in the absence of the channel knowledge? What approaches can be taken into consideration so that optimum benefit with less channel knowledge can be obtained.
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