Interference Alignment — A New Look at Signal Dimensions in a Communication Network

Abstract

This monograph introduces to the reader the idea of interference alignment, traces its origins, reviews a variety of interference alignment schemes, summarizes the diverse settings where the idea of interference alignment is applicable and highlights the common principles that cut across these diverse applications. The focus is on theoretical aspects.1 To keep the discussion general as well as compact we do not specify if the symbols are from a finite field or if they are real/complex, as the same ideas apply in both cases. In the latter case, however, it is worth mentioning that as usual there are additive noise terms and power constraints present, that are not shown in these equations, but without which the communication problem would be trivial, i.e., the infinite resolution of a real/complex number will allow infinite information transfer in any signal dimension.

Cognitive Interference Alignment for Spectral Coexistence

“…Each receiver can then apply an interference removal filter to project the desired signal onto the interference free subspace. Due to this approach, the number of interference-free signalling dimensions of the network are substantially increased [27]. In Multiple Input Multiple Output (MIMO) networks, IA can be applied by using the spatial dimension offered by multiple antennas for alignment while in multicarrier systems, interference can be aligned along the carrier dimension.…”

“…It can also be defined as the number of signaling dimensions, each dimension corresponding to one interferencefree Additive White Gaussian Noise (AWGN) channel with Signal to Noise Ratio (SNR) that increases proportionally with the total transmit power P as P ! 1 [27]. The DoF also corresponds to the multiplexing gain, bandwidth, capacity prelog factor, or the number of signaling dimensions.…”

“…The above expression can be equivalently written as: R.P / D Álog.P / C O.log.P //, where the term O.log.P // is some function f .P / which satisfies the following relation [27] lim P !1 f .P / log.P / D 0:…”

“…Let˛denote the ratio of the cross channel strength to the direct channel strength in dB scale and R.P;˛/ denote the sumcapacity. Then the total GDoF metric, Á.˛/ can be defined as [27]:…”

“…Let us consider an interference network with K transmitters, each trying to send one information symbol. To resolve the 1 symbol desired by a particular receiver, K signalling dimensions are generally required [27]. If there are K number of receivers, each with access to a different set of K linear equations formed by its linear channel to the transmitters and interested in a different symbol, a total number of K signalling dimensions will be sufficient to recover the desired symbol by all the K receivers.…”