In a K-pair-user two-way interference channel (TWIC), 2K messages and 2K transmitters receivers form a K-user IC in the forward direction (K messages) and another K-user IC in the backward direction which operate in full-duplex mode. All nodes may interact, or adapt inputs to past received signals. We derive a new outer bound to demonstrate that the optimal degrees of freedom (DoF, also known as the multiplexing gain) is K: full-duplex operation doubles the DoF, but interaction does not further increase the DoF. We next characterize the DoF of the K-pair-user TWIC with a MIMO, full-duplex relay. If the relay is non-causal instantaneous (at time k forwards a function of its received signals up to time k) and has 2K antennas, we demonstrate a one-shot scheme where the relay mitigates all interference to achieve the interference-free 2K DoF. In contrast, if the relay is causal (at time k forwards a function of its received signals up to time k 1), we show that a full-duplex MIMO relay cannot increase the DoF of the K-pair-user TWIC beyond K, as if no relay or interaction is present. We comment on reducing the number of antennas at the instantaneous relay.
The @math -user interference channel, as an extension of the 2-user interference channel, information theoretically models wireless communications in networks involving more than two-pairs of users. Using the idea of interference alignment @cite_13 @cite_33 @cite_20 , the DoF of the @math -user (one-way) IC for both time-varying channels and (almost all) The precise definition of almost all'' may be found in @cite_36 . constant channels has been shown to be @math in @cite_7 and @cite_36 respectively. The generalized DoF of the @math -user IC without and with feedback have been characterized in @cite_25 and @cite_27 (full feedback from receiver @math to transmitter @math ) respectively. Authors in @cite_3 showed that for almost all constant channel coefficients of fully connected two-hop wireless networks with @math sources, @math relays and @math destinations (source nodes are not destination nodes as they are here, i.e. the network is one-way), the DoF is @math .
@cite_33 @cite_7 @cite_36 @cite_3 @cite_27 @cite_13 @cite_25 @cite_20
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We study the degrees of freedom (DoF) of the @math -user interference channel with coordinated multipoint (CoMP) transmission and reception. Each message is jointly transmitted by @math successive transmitters, and is jointly received by @math successive receivers. We refer to this channel as the CoMP channel with a transmit cooperation order of @math and receive cooperation order of @math . Since the channel has a total of @math transmit antennas and @math receive antennas, the maximum possible DoF is equal to @math . We show that the CoMP channel has @math DoF if and only if @math . The key idea is that the zero forcing of the interference corresponding to the @math message at the decoder of the @math message, where @math , can be viewed as a shared responsibility between the @math transmitters carrying the @math message, and the @math receivers decoding the @math message. For the general case, we derive an outer bound that states that the DoF is bounded above by @math . For the special case with only CoMP transmission, i.e, @math , we propose a scheme that can achieve @math DoF for all @math K @math M_ t @math M_ t -1$ receivers, thereby allowing each of these receivers to enjoy 1 DoF, and asymptotic interference alignment is used to align the interfering signals at each other receiver to occupy half the signal space. The achievability proofs are based on the notion of algebraic independence from algebraic geometry. In this paper, we develop the machinery of real interference alignment. This machinery is extremely powerful in achieving the sum degrees of freedom (DoF) of single antenna systems. The scheme of real interference alignment is based on designing single-layer and multilayer constellations used for modulating information messages at the transmitters. We show that constellations can be aligned in a similar fashion as that of vectors in multiple antenna systems and space can be broken up into fractional dimensions. The performance analysis of the signaling scheme makes use of a recent result in the field of Diophantine approximation, which states that the convergence part of the Khintchine-Groshev theorem holds for points on nondegenerate manifolds. Using real interference alignment, we obtain the sum DoF of two model channels, namely the Gaussian interference channel (IC) and the X channel. It is proved that the sum DoF of the K-user IC is (K 2) for almost all channel parameters. We also prove that the sum DoF of the X-channel with K transmitters and M receivers is (K M K + M - 1) for almost all channel parameters. In this correspondence, we show that the exact number of spatial degrees of freedom (DOF) for a two user nondegenerate (full rank channel matrices) multiple-input-multiple-output (MIMO) Gaussian interference channel with M1, M2 antennas at transmitters 1, 2 and N1, N2 antennas at the corresponding receivers, and perfect channel knowledge at all transmitters and receivers, is min M1 + M2, N1 + M2, max(M1, N2), max(M2, N1) . A constructive achievability proof shows that zero forcing is sufficient to achieve all the available DOF on the two user MIMO interference channel. We also show through an example of a share-and-transmit scheme how the gains of transmitter cooperation may be entirely offset by the cost of enabling that cooperation so that the available DOF are not increased. We consider a system, comprising a library of @math files (e.g., movies) and a wireless network with a @math transmitters, each equipped with a local cache of size of @math files and a @math receivers, each equipped with a local cache of size of @math files. Each receiver will ask for one of the @math files in the library, which needs to be delivered. The objective is to design the cache placement (without prior knowledge of receivers’ future requests) and the communication scheme to maximize the throughput of the delivery. In this setting, we show that the sum degrees-of-freedom (sum-DoF) of @math is achievable, and this is within a factor of 2 of the optimum, under uncoded prefetching and one-shot linear delivery schemes. This result shows that (i) the one-shot sum-DoF scales linearly with the aggregate cache size in the network (i.e., the cumulative memory available at all nodes ), (ii) the transmitters’ caches and receivers’ caches contribute equally in the one-shot sum-DoF, and (iii) caching can offer a throughput gain that scales linearly with the size of the network. To prove the result, we propose an achievable scheme that exploits the redundancy of the content at transmitter’s caches to cooperatively zero-force some outgoing interference, and availability of the unintended content at the receiver’s caches to cancel (subtract) some of the incoming interference. We develop a particular pattern for cache placement that maximizes the overall gains of cache-aided transmit and receive interference cancellations. For the converse, we present an integer optimization problem which minimizes the number of communication blocks needed to deliver any set of requested files to the receivers. We then provide a lower bound on the value of this optimization problem, hence leading to an upper bound on the linear one-shot sum-DoF of the network, which is within a factor of 2 of the achievable sum-DoF.