This paper studies the degrees of freedom (DoFs) of full-duplex (FD) multicell networks that share the spectrum among multiple cells. In the considered network, we assume that FD base stations (BSs) with multiple transmit and receive antennas communicate with multiple single-antenna uplink (UL) and downlink (DL) mobile users. By spectrum sharing among multiple cells, and with FD radio, the network can utilize the spectrum more efficiently. However, since spectrum sharing and FD induce additional inter-cell and intra-cell interferences, interference management is crucial to take advantage of these features. In this paper, we propose novel interference management strategies which take into account the new sources of interferences caused by spectrum sharing and FD to establish a general achievability result on the sum DoFs. The key ideas in our proposed scheme are to minimize the dimension of UL inter-cell and user-to-user interferences using interference alignment at the UL users. On the BS side, we propose an interference management strategy to align or null out DL intra-cell and inter-cell interferences, and BS-to-BS interferences. We further establish an upper bound on the sum DoFs and show that our lower and upper bounds match under certain conditions. Several numerical evaluations are shown which demonstrate that spectrum sharing and FD can significantly improve the throughput over conventional cellular networks, especially for a network with large number of users and or cells.
To deal with the additional interference caused by spectrum sharing among multiple cells and FD, we propose signal space (IA) strategies that are optimized for multicell FD networks. The pioneering work of Maddah-Ali, Motahari, and Khandani @cite_1 and Cadambe and Jafar @cite_18 @cite_36 introduced IA as an effective coding technique that efficiently deals with interference. In particular, IA has been shown to achieve the optimal DoF for various interference networks @cite_27 @cite_38 @cite_24 @cite_11 @cite_19 @cite_2 @cite_20 @cite_21 @cite_33 @cite_37 @cite_22 @cite_39 .
@cite_38 @cite_18 @cite_37 @cite_33 @cite_22 @cite_36 @cite_21 @cite_1 @cite_39 @cite_24 @cite_19 @cite_27 @cite_2 @cite_20 @cite_11
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We develop an interference alignment (IA) technique for a downlink cellular system. In the uplink, IA schemes need channel-state-information exchange across base-stations of different cells, but our downlink IA technique requires feedback only within a cell. As a result, the proposed scheme can be implemented with a few changes to an existing cellular system where the feedback mechanism (within a cell) is already being considered for supporting multi-user MIMO. Not only is our proposed scheme implementable with little effort, it can in fact provide substantial gain especially when interference from a dominant interferer is significantly stronger than the remaining interference: it is shown that in the two-isolated cell layout, our scheme provides four-fold gain in throughput performance over a standard multi-user MIMO technique. We also show through simulations that our technique provides respectable gain under a more realistic scenario: it gives approximately 28 gain for a 19 hexagonal wrap-around-cell layout. Furthermore, we show that our scheme has the potential to provide substantial gain for macro-pico cellular networks where pico-users can be significantly interfered with by the nearby macro-BS. We provide achievability as well as converse results for the degrees of freedom region of a multiple-input multiple-output (MIMO) X channel, i.e., a system with two transmitters, two receivers, each equipped with multiple antennas, where independent messages need to be conveyed over fixed channels from each transmitter to each receiver. The inner and outer bounds on the degrees of freedom region are tight whenever integer degrees of freedom are optimal for each message. With M = 1 antennas at each node, we find that the total (sum rate) degrees of freedom are bounded above and below as 1 les eta*x les 4 3. If M > 1 and channel matrices are nondegenerate then the precise degrees of freedom eta*x = (4 3)M. Thus, the MIMO X channel has noninteger degrees of freedom when M is not a multiple of 3. Simple zero forcing without dirty paper encoding or successive decoding, suffices to achieve the (4 3)M degrees of freedom. If the channels vary with time frequency then the channel with single antennas (M = 1) at all nodes has exactly 4 3 degrees of freedom. The key idea for the achievability of the degrees of freedom is interference alignment-i.e., signal spaces are aligned at receivers where they constitute interference while they are separable at receivers where they are desired. We also explore the increase in degrees of freedom when some of the messages are made available to a transmitter or receiver in the manner of cognitive radio. An uplink–downlink two-cell cellular network is studied in which the first base station (BS) with @math antennas receives independent messages from its @math serving users, while the second BS with @math antennas transmits independent messages to its @math serving users. That is, the first and second cells operate as uplink and downlink, respectively. Each user is assumed to have a single antenna. Under this uplink–downlink setting, the sum degrees of freedom (DoFs) is completely characterized as the minimum of @math , @math , @math , and @math , where @math denotes @math . The result demonstrates that, for a broad class of network configurations, operating one of the two cells as uplink and the other cell as downlink can strictly improve the sum DoF compared with the conventional uplink or downlink operation, in which both cells operate as either uplink or downlink. The DoF gain from such uplink–downlink operation is further shown to be achievable for heterogeneous cellular networks having hotspots and with delayed channel state information. In recent years, there has been rapid progress on understanding Gaussian networks with multiple unicast connections, and new coding techniques have emerged. The essence of multi-source networks is how to efficiently manage interference that arises from the transmission of other sessions. Classically, interference is removed by orthogonalization (in time or frequency). This means that the rate per session drops inversely proportional to the number of sessions, suggesting that interference is a strong limiting factor in such networks. However, recently discovered interference management techniques have led to a paradigm shift that interference might not be quite as detrimental after all. The aim of this paper is to provide a review of these new coding techniques as they apply to the case of time-varying Gaussian networks with multiple unicast connections. Specifically, we review interference alignment and ergodic interference alignment for multi-source single-hop networks and interference neutralization and ergodic interference neutralization for multi-source multi-hop networks. We mainly focus on the “degrees of freedom” perspective and also discuss an approximate capacity characterization. Feasibility of full-duplex opens up the possibility of applying it to cellular networks to operate uplink and downlink simultaneously for multiple users. However, simultaneous operation of uplink and downlink poses a new challenge of intra-cell inter-node interference. In this paper, we identify scenarios where inter-node interference can be managed to provide significant gain in degrees of freedom over the conventional half-duplex cellular design. For the fully connected K user wireless interference channel where the channel coefficients are time-varying and are drawn from a continuous distribution, the sum capacity is characterized as C(SNR)=K 2log(SNR)+o(log(SNR)) . Thus, the K user time-varying interference channel almost surely has K 2 degrees of freedom. Achievability is based on the idea of interference alignment. Examples are also provided of fully connected K user interference channels with constant (not time-varying) coefficients where the capacity is exactly achieved by interference alignment at all SNR values. We show that the 2 × 2 × 2 interference network, i.e., the multihop interference network formed by concatenation of two two-user interference channels achieves the min-cut outer bound value of 2 DoF, for almost all values of channel coefficients, for both time-varying or fixed-channel coefficients. The key to this result is a new idea, called aligned interference neutralization, that provides a way to align interference terms over each hop in a manner that allows them to be canceled over the air at the last hop. In a multiple-antenna system with two transmitters and two receivers, a scenario of data communication, known as the X channel, is studied in which each receiver receives data from both transmitters. In this scenario, it is assumed that each transmitter is unaware of the other transmitter's data (noncooperative scenario). This system can be considered as a combination of two broadcast channels (from the transmitters' points of view) and two multiple-access channels (from the receivers' points of view). Taking advantage of both perspectives, two signaling schemes for such a scenario are developed. In these schemes, some linear filters are employed at the transmitters and at the receivers which decompose the system into either two noninterfering multiple-antenna broadcast subchannels or two noninterfering multiple-antenna multiple-access subchannels. The main objective in the design of the filters is to exploit the structure of the channel matrices to achieve the highest multiplexing gain (MG). It is shown that the proposed noncooperative signaling schemes outperform other known noncooperative schemes in terms of the achievable MG. In particular, it is shown that in some specific cases, the achieved MG is the same as the MG of the system if full cooperation is provided either between the transmitters or between the receivers. In the second part of the paper, it is shown that by using mixed design schemes, rather than decomposition schemes, and taking the statistical properties of the interference terms into account, the power offset of the system can be improved. The power offset represents the horizontal shift in the curve of the sum-rate versus the total power in decibels. This paper develops a new communication strategy, ergodic interference alignment, for the K-user interference channel with time-varying fading. At any particular time, each receiver will see a superposition of the transmitted signals plus noise. The standard approach to such a scenario results in each transmitter-receiver pair achieving a rate proportional to 1 K its interference-free ergodic capacity. However, given two well-chosen time indices, the channel coefficients from interfering users can be made to exactly cancel. By adding up these two observations, each receiver can obtain its desired signal without any interference. If the channel gains have independent, uniform phases, this technique allows each user to achieve at least 1 2 its interference-free ergodic capacity at any signal-to-noise ratio. Prior interference alignment techniques were only able to attain this performance as the signal-to-noise ratio tended to infinity. Extensions are given for the case where each receiver wants a message from more than one transmitter as well as the “X channel” case (with two receivers) where each transmitter has an independent message for each receiver. Finally, it is shown how to generalize this strategy beyond Gaussian channel models. For a class of finite field interference channels, this approach yields the ergodic capacity region. We find the degrees of freedom of a network with S source nodes, R relay nodes, and D destination nodes, with random time-varying frequency-selective channel coefficients and global channel knowledge at all nodes. We allow full-duplex operation at all nodes, as well as causal noise-free feedback of all received signals to all source and relay nodes. An outer bound to the capacity region of this network is obtained. Combining the outer bound with previous interference alignment based achievability results, we conclude that the techniques of relays, feedback, full-duplex operation and noisy cooperation do not increase the degrees of freedom of interference and X networks. As a second contribution, we show that for a network with K full-duplex nodes and K(K-1) independent messages with one message from every node to each of the other K-1 nodes, the total degrees of freedom are bounded above and below by [( K(K-1)) ( (2K-2))] and [( K(K-1)) ( (2K-3))], respectively. We provide inner bound and outer bound for the total number of degrees of freedom of the K user multiple-input multiple-output (MIMO) Gaussian interference channel with M antennas at each transmitter and N antennas at each receiver if the channel coefficients are time-varying and drawn from a continuous distribution. The bounds are tight when the ratio [(max(M,N)) (min(M,N))]=R is equal to an integer. For this case, we show that the total number of degrees of freedom is equal to min(M,N)K if K ≤ R and min(M,N)[(R) (R+1)]K if K > R. Achievability is based on interference alignment. We also provide examples where using interference alignment combined with zero forcing can achieve more degrees of freedom than merely zero forcing for some MIMO interference channels with constant channel coefficients. In this paper, we propose a new way of interference management for cellular networks. We develop the scheme that approaches to interference-free degree-of-freedom (dof) as the number K of users in each cell increases. Also we find the corresponding bandwidth scaling conditions for typical wireless channels: multi-path channels and single-path channels with propagation delay. The scheme is based on interference alignment. Especially for more-than-two-cell cases where there are multiple non-intended BSs, we propose a new version of interference alignment, namely subspace interference alignment. The idea is to align interferences into multi-dimensional subspace (instead of one dimension) for simultaneous alignments at multiple non-intended BSs. The proposed scheme requires finite dimensions growing linearly with K, i.e., O(K). 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. We consider a single-hop interference network with K transmitters and J receivers, all having M antennas. Each transmitter emits an independent message and each receiver requests an arbitrary subset of the messages. This generalizes the well-known K -user M-antenna interference channel, where each message is requested by a unique receiver. For our setup, we derive the degrees of freedom (DoF) region. The achievability scheme generalizes the interference alignment schemes proposed by Cadambe and Jafar. In particular, we achieve general points in the DoF region by using multiple base vectors and aligning all interferers at a given receiver to the interferer with the largest DoF. As a byproduct, we obtain the DoF region for the original interference channel. We also discuss extensions of our approach where the same region can be achieved by considering a reduced set of interference alignment constraints, thus reducing the time-expansion duration needed. The DoF region for the considered system depends only on a subset of receivers whose demands meet certain characteristics. The geometric shape of the DoF region is also discussed. We explore the degrees of freedom of M times N user wireless X networks, i.e., networks of M transmitters and N receivers where every transmitter has an independent message for every receiver. We derive a general outer bound on the degrees of freedom region of these networks. When all nodes have a single antenna and all channel coefficients vary in time or frequency, we show that the total number of degrees of freedom of the X network is equal to [(MN) (M+N-1)] per orthogonal time and frequency dimension. Achievability is proved by constructing interference alignment schemes for X networks that can come arbitrarily close to the outer bound on degrees of freedom. For the case where either M=2 or N=2 we find that the degrees of freedom characterization also provides a capacity approximation that is accurate to within O(1) . For these cases the degrees of freedom outer bound is exactly achievable.