Network pruning is a commonly used measure to alleviate the storage and computational burden of deep neural networks. However, the fundamental limit of network pruning is still lacking. To close the gap, in this work we'll take a first-principles approach, i.e. we'll directly impose the sparsity constraint on the loss function and leverage the framework of statistical dimension in convex geometry, thus enabling us to characterize the sharp phase transition point, which can be regarded as the fundamental limit of the pruning ratio. Through this limit, we're able to identify two key factors that determine the pruning ratio limit, namely, weight magnitude and network sharpness. Generally speaking, the flatter the loss landscape or the smaller the weight magnitude, the smaller pruning ratio. Moreover, we provide efficient countermeasures to address the challenges in the computation of the pruning limit, which mainly involves the accurate spectrum estimation of a large-scale and non-positive Hessian matrix. Moreover, through the lens of the pruning ratio threshold, we can also provide rigorous interpretations on several heuristics in existing pruning algorithms. Extensive experiments are performed which demonstrate that our theoretical pruning ratio threshold coincides very well with the experiments. All codes are available at: https://github.com/QiaozheZhang/Global-One-shot-Pruning

Interferences due to non-orthogonality of signals usually exist in wireless networks when the number of users is larger than the sequence length, such as non-orthogonality of the pilots in multi-cell systems and non-orthogonality of the signature sequences in overloaded code-division-multiple-access (CDMA) systems. We address this effect from the perspective of non-orthogonal sequence design in a two-cell multiple-antenna network. Specifically, we aim at designing pilot sequences to minimize the sum mean-squared-error (MSE) of channel estimation with a given sequence length$\tau $where$\tau \in [K,2K]$and$K$is the number of users per cell. Considering the strength disparity between channels originating from the home cell and the neighbor cell, this problem boils down to minimizing the sum of squares of weighted correlations among sequences, whose lower bound is obtained inclosed formand can be regarded as a generalization of the well-known Welch bound (Welch, 1974). We prove this extended Welch bound is achievable, and design an algorithm based on the Davies-Higham method to generate the interference-minimizing sequences. Three fundamental properties of the proposed sequences are presented. Finally, we derive closed-form expressions of the average signal-to-interference-plus-noise-ratio (SINR) and rate for data transmission, based on which the optimal training duration can be found.

Interferences due to non-orthogonality of training sequences usually exist in cellular networks when the number of all users is relatively large compared to the coherence time, such as the case in massive MIMO systems. In this paper, we address this effect from the perspective of non-orthogonal training sequence design in two-cell interference networks with K users per cell. We relax the general assumption in which the cross-correlations of sequences are restricted to be 0 or 1, and target at designing the training sequences to minimize training phase interference with a given pilot length τ, which is no larger than the total number of users, i.e., τ ∈ [K, 2K]. We note that when large scale fading between different cells β ≠ 1, the strengths of interferences arising from non-orthogonal training sequences within a cell or from the adjacent cell become asymmetric, and optimal design needs to treat the intra-cell sequence correlation and inter-cell correlation differently. To this end, by incorporating β into the design, we extend the Welch bound (Welch 1974 [1]) to the two-cell scenario with asymmetric intra-cell and inter-cell interference, and characterize the lower bound of the interference precisely. Specifically, we obtain the result that the sum of the squares of β -weighted cross-correlations of the training sequences is lower-bounded by [(2K2(1+β2))/(K+(τ-K)β2)], which can be achieved by the proposed training sequence design in closed-form. Particularly, when β = 1, this bound reduces to [((2K)2)/(τ)] which is exactly the Welch bound. This result is applicable for the uplink design of general interference networks such as the pilot design in massive MIMO and the signature sequence design in multicell CDMA systems.

In this study, the authors propose a low complexity detector for the generalised space shift keying (GSSK) in large‐scale multiple‐input–multiple‐output systems. To be concrete, they propose a sparse K ‐best (SK) detector based on the breadth‐first category of sphere detector (referred to K ‐best sphere decoding). The author's detector is inspired by the fact that the GSSK signal is naturally a sparse zero‐one vector since only a few antennas are activated at the transmitter. Different with the conventional K ‐best detector searching all the transmit antennas, their proposed SK detector investigates only a few promising candidates which are activated antennas at the transmitter. Overall, their proposed SK detector exploits not only the sparsity of the GSSK signal but also the constraint on its non‐zero values. Therefore the restricted isometry property‐based performance analysis shows that is effective in detecting the GSSK signal. Moreover, the empirical results show that their detector performs much better than the sparse algorithms‐based normalised compressive sensing (NCS) detectors while exhibits only slightly higher complexity than the latter (the low‐complexity orthogonal matching pursuit‐based NCS detector).

Equispaced pilot arrangement is the most popular scheme for pilot‐aided transmission in orthogonal frequency division multiplexing systems. In this study, the authors argue that a non‐equispaced pilot pattern may outperform its equispaced counterpart, if they fully take into account the sparsity of the channel impulse response which is inherent in wireless channels. More specifically, a sparsity‐aware pilot arrangement scheme based on the coherence criterion is investigated in this study. To address the resulting non‐deterministic polynomial (NP)‐hard combinatorial optimisation problem, they propose an efficient local search algorithm. For channel estimation, they convert it to a sparse recovery problem. To enhance the applicability of the authors scheme, that is, when there is no prior knowledge about the channel order, they propose to employ the Bayesian information criterion to estimate the channel order first and then recover the sparse channel vector via existing low‐complexity methods, for example, orthogonal matching pursuit. By combining the above pilot arrangement scheme with channel estimation, their scheme exhibits substantially better performance in comparison with the conventional equispaced schemes with linear (or spline) interpolation, in terms of total number of pilot symbols and bit error rate.

A subspace method for channel estimation has been recently proposed for tackling the pilot contamination effect, which is regarded by some researchers as a bottleneck in massive MIMO systems. It was shown in the literature that if the power ratio between the desired signal and interference is kept above a certain value, the received signal spectrum splits into signal and interference eigenvalues, namely, the “pilot contamination” effect can be completely eliminated. However, in the literature an independently distributed (i.d.) channel is assumed, which is actually not much the case in practice. Considering this, a more sensible finite-dimensional physical channel model (i.e., a finite scattering environment, where signals impinge on the base station (BS) from a finite number of angles of arrival (AoA)) is employed in this paper. Via asymptotic spectral analysis, it is demonstrated that, compared with the i.d. channel, the physical channel imposes a penalty in the form of an increased power ratio between the useful signal and the interference. Furthermore, we demonstrate an interesting “antenna saturation” effect, i.e., when the number of the BS antennas approaches infinity, the performance under the physical channel withPAoAs is limited by and nearly the same as the performance under the i.d. channel withPreceive antennas.

The two-user multiple-input multiple-output (MIMO) Gaussian Broadcast Channel (BC) with mixed CSIT (i.e., delayed CSIT plus estimated current CSIT) under general antenna configuration is considered in this paper. Unlike the MISO scenario, obtaining tight characterization of the Degrees of Freedom (DoF) region seems difficult for the general MIMO BC settings. Despite that, the inner bound we provide in this paper is believed to be the best achievable bound so far. One novel ingredient of our scheme is the rate-splitting of the interference-encoded symbols, which provides the possible benefit of DoF gain by accommodating the transmission to the asymmetric receivers. Moreover, the outer bound of DoF region is also presented, which coincides our proposed inner bound in some cases.

The graphical models have been proven to be a very powerful and potential framework for addressing the inference problems. In this paper, we propose a new graphical model based algorithm for the detection of MIMO systems. The main feature of the algorithm lies in that it is implemented as a MRF-like graph, when combined with the Gaussian approximation and vector-based inference, our algorithm can lead to very promising performance, especially when the constellation size is small, with just linear complexity per symbol and memory requirement increases linearly with the number of transmit antennas. Simulation results collaborate with the analytical results, hence verifying the appeal of the algorithm for practical applications.

In this paper, we consider the problem of the capacity limits of the cellular network, which is modeled as a network consisting of two mutually interfering multiple access channel with multiple antennas at each receiver (e.g. the Base Station). By developing a tight outerbound (in the sense of DoF) and an achievable scheme which exploits the idea of interference alignment, we are able to exactly characterize the degrees of freedom (DoF) of the network when the channel coefficients are time- or frequency-varying, which is, the DoF per cell is $\frac{{KM}}{{K + \min (M,K)}}$ (where $M$ and $K$ denotes the number of receiver antennas and number of users in a cell, respectively). From the DoF result, it can be observed that when the number of users is large, we can nearly achieve the interference-free DoF of a multi-antenna cell!