Shlomo Shamai Shitz

Multi-Cell MIMO Cooperative Networks: A New Look at Interference

This paper presents an overview of the theory and currently known techniques for multi-cell MIMO (multiple input multiple output) cooperation in wireless networks. In dense networks where interference emerges as the key capacity-limiting factor, multi-cell cooperation can dramatically improve the system performance. Remarkably, such techniques literally exploit inter-cell interference by allowing the user data to be jointly processed by several interfering base stations, thus mimicking the benefits of a large virtual MIMO array. Multi-cell MIMO cooperation concepts are examined from different perspectives, including an examination of the fundamental information-theoretic limits, a review of the coding and signal processing algorithmic developments, and, going beyond that, consideration of very practical issues related to scalability and system-level integration. A few promising and quite fundamental research avenues are also suggested.

On the Synergistic Benefits of Alternating CSIT for the MISO Broadcast Channel

The degrees of freedom (DoFs) of the two-user multiple-input single-output (MISO) broadcast channel (BC) are studied under the assumption that the form, <i>Ii</i>, <i>i</i>=1, 2, of the channel state information at the transmitter (CSIT) for each users channel can be either perfect (<i>P</i>), delayed (<i>D</i>), or not available (<i>N</i>), i.e., <i>I</i>₁,<i>I</i>₂ ∈ {<i>P</i>,<i>N</i>,<i>D</i>} , and therefore, the overall CSIT can alternate between the nine resulting states <i>I</i>₁<i>I</i>₂. The fraction of time associated with CSIT state <i>I</i>₁<i>I</i>₂ is denoted by the parameter λ<i>I</i>₁<i>I</i>₂ and it is assumed throughout that λ<i>I</i>₁<i>I</i>₂ = λ<i>I</i>₂<i>I</i>₁, i.e., λ<i>PN</i> = λ<i>NP</i>, λ<i>PD</i>=λ<i>DP</i>, λ<i>DN</i>=λ<i>ND</i> . Under this assumption of symmetry, the main contribution of this paper is a complete characterization of the DoF region of the two-user MISO BC with alternating CSIT. Surprisingly, the DoF region is found to depend only on the marginal probabilities (λ<i>P</i>, λ<i>D</i>,λ<i>N</i>) = (Σ<i>I</i>₂ λ<i>PI</i>₂, Σ<i>I</i>₂ λ<i>DI</i>₂, Σ<i>I</i>₂ λ<i>NI</i>₂), <i>I</i>₂ ∈ {<i>P</i>, <i>D</i>, <i>N</i>}, which represent the fraction of time that any given user (e.g., user 1) is associated with perfect, delayed, or no CSIT, respectively. As a consequence, the DoF region with all nine CSIT states, <i>D</i>(λ<i>I</i>₁<i>I</i>₂:<i>I</i>₁,<i>I</i>₂ ∈ {<i>P</i>,<i>D</i>,<i>N</i>}) , is the same as the DoF region with only three CSIT states <i>D</i>(λ<i>PP</i>, λ<i>DD</i>, λ<i>NN</i>), under the same marginal distribution of CSIT states, i.e., (λ<i>PP</i>, λ<i>DD</i>,λ<i>NN</i>)=(λ<i>P</i>,λ<i>D</i>,λ<i>N</i>). The sum-DoF value can be expressed as DoF=min([(4+2λ<i>P</i>)/3], 1+λ<i>P</i>+λ<i>D</i>), from which one can uniquely identify the minimum required marginal CSIT fractions to achieve any target DoF value as (λ<i>P</i>,λ<i>D</i>)_min=([3/2] DoF-2,1- [1/2] DoF) when DoF ∈ [[4/3],2] and (λ<i>P</i>,λ<i>D</i>)_min=(0,(DoF-1)⁺) when DoF ∈ [0, [4/3]). The results highlight the synergistic benefits of alternating CSIT and the tradeoffs between various forms of CSIT for any given DoF value. Partial results are also presented for the multiuser MISO BC with <i>M</i> transmit antennas and <i>K</i> single antenna users. For this problem, the minimum amount of perfect CSIT required per user to achieve the maximum DoFs of min(<i>M</i>,<i>K</i>) is characterized. By the minimum amount of CSIT per user, we refer to the minimum fraction of time that the transmitter has access to perfect and instantaneous CSIT from a user. Through a novel converse proof and an achievable scheme, it is shown that the minimum fraction of time perfect CSIT is required per user in order to achieve the DoF of min(<i>M</i>,<i>K</i>) is given by min(<i>M</i>,<i>K</i>)/<i>K</i>.

Reconstruction of nonperiodic two-dimensional signals from zero crossings

In this correspondence, we present new results on the reconstruction of two-dimensional signals from zero crossing or threshold crossing information. Specifically, we develop new theoretical results which state conditions under which two-dimensional bandlimited signals are uniquely specified to within a scale factor with this information. Unlike previous results in this area, our new results do not constrain the signals to be periodic or bandpass.

Information Dimension and the Degrees of Freedom of the Interference Channel

The degrees of freedom (DoFs) of the K -user Gaussian interference channel determine the asymptotic growth of the maximal sum rate as a function of the signal-to-noise ratio. Subject to a very general sufficient condition on the cross-channel gains, we give a formula for the DoFs of the scalar interference channel as a function of the deterministic channel matrix, which involves maximization of a sum of information dimensions over K scalar input distributions. Known special cases are recovered, and even generalized in certain cases with unified proofs.

Cognitive Wyner Networks With Clustered Decoding

We study an interference network where equally numbered transmitters and receivers lie on two parallel lines, with each transmitter opposite its intended receiver. We consider two short-range interference models: the asymmetric network, where the signal sent by each transmitter is interfered only by the signal sent by its left neighbor (if present), and a symmetric network, where it is interfered by both its left and its right neighbors. Each transmitter is cognizant of its own message, the messages of the t_ℓ transmitters to its left, and the messages of the t_r transmitters to its right. Each receiver decodes its message based on the signals received at its own antenna, at the r_r receive antennas to its left, and at the r_r receive antennas to its right. For such networks, we provide upper and lower bounds on the multiplexing gain, i.e., on the high signal-to-noise ratio asymptotic logarithmic growth of the sum-rate capacity. In some cases, our bounds coincide, e.g., for the asymmetric network. Our results exhibit an equivalence between the transmitter sideinformation parameters t_ℓ, tr and the receiver side-information parameters r_ℓ, r_r in the sense that increasing/decreasing t_ℓ or t_r by a positive integer δ has the same effect on the multiplexing gain as increasing/decreasing r_ℓ or r_r by δ. Moreover-even in asymmetric networks-there is an equivalence between the left side-information parameters (t_ℓ, r_ℓ) and the right sideinformation parameters (t_r, r_r).

On the capacity region of Gaussian interference channels with state

The Gaussian interference channel with additive state at two receivers is investigated, in which the state information is noncausally known at both transmitters but not known at either receiver. For the very strong Gaussian interference channel with state, the capacity region is obtained under certain conditions on channel parameters. For the strong (but not very strong) Gaussian interference channel with state, points on the boundary of the capacity region are characterized under corresponding conditions on channel parameters. Finally, for the weak Gaussian interference channel with state, the sum capacity is obtained for certain channel parameters. All the above capacity-achieving rate points achieve the capacity for the corresponding channel without state.

State-dependent Gaussian Z-channel with mismatched side-information and interference

A state-dependent Gaussian Z-interference channel model is investigated in the regime of high state power, in which transmitters 1 and 2 communicate with receivers 1 and 2, and only receiver 2 is interfered by transmitter 1s signal and a random state sequence. The state sequence is known noncausally only to transmitter 1, not to the corresponding transmitter 2. A layered coding scheme is designed for transmitter 1 to help interference cancelation at receiver 2 (using a cognitive dirty paper coding) and to transmit its own message to receiver 1. Inner and outer bounds are derived, and are further analyzed to characterize the boundary of the capacity region either fully or partially for all Gaussian channel parameters. Our results imply that the capacity region of such a channel with mismatched transmitter-side state cognition and receiver-side state interference is strictly less than that of the corresponding channel without state, which is in contrast to Costa type of dirty channels, for which dirty paper coding achieves the capacity of the corresponding channels without state.

On Coded and Interleaved Noncoherent Multiple Symbol Detected MPSK

The performance of multiple symbol noncoherent detection of MPSK combined with coding and interleaving is examined in terms of the cut-off rate bound. It is shown that, within this approach, inner modulation coding improves on standard DPSK when both are combined with an external error correcting code, such as the industry standard, K = 7 R = 1/2 convolutional code. Some modulation codes over BPSK and QPSK are examined and a reduced complexity decoder is presented. The results and conclusions are verified by some simulations.

On the duality of time and frequency domain signal reconstruction from partial information

Certain results on one-dimensional signal representation and reconstruction from partial information in the frequency domain are related to and derived, using relevant results obtained in the time or positional information domain. In particular, we adopt Logans approach and apply his results concerning zero-crossing representation of certain bandpass signals. We also apply Voelckers results on demodulation of analytic SSB signals by an AM detector. Exploiting the duality of the Fourier-Stieltjes transform and its inverse, we rederive and extend to continuous one-dimensional signals some results concerning the representation of Fourier-transformed discrete time (finite) sequences by partial information such as one bit or complete Fourier phase, Fourier magnitude or signed-magnitude. The duality and interrelationship of characteristics and constraints attributed to time and frequency signal representation create further possibilities of drawing results and interpretations from one- to its counter-domain. In particular, we indicate possible extensions of certain results to problems of N-dimensional signals and to issues of stochastic signals. We also highlight basic issues concerning the structure of signals and their reconstruction from partial information.

On Broadcast Channels With Binary Inputs and Symmetric Outputs

We establish capacity regions for some classes of broadcast channels with binary inputs and symmetric outputs. We investigate the more capable partial order and establish that the binary erasure channel and the binary symmetric channel form the two extremes for channels having the same capacity. Further, we apply the results to identify a class of broadcast channels for which the best-known inner and outer bounds on the capacity region differ.