We consider the problem of channel estimation for amplify-and-forward (AF) two-way relay networks (TWRNs). Most works on this problem focus on pilot-based approaches which impose a significant training overhead that reduces the spectral efficiency of the system. To avoid such losses, this work proposes blind channel estimation algorithms for AF TWRNs that employ constant-modulus (CM) signaling. Our main algorithm is based on the deterministic maximum likelihood (DML) approach.Assuming M-PSK modulation, we show that the resulting estimator is consistent and approaches the true channel with high probability at high SNR for modulation orders higher than 2. For BPSK, however, the DML performs poorly and we propose an alternative algorithm that performs much better by taking into account the BPSK structure of the data symbols. For comparative purposes, we also investigate the Gaussian maximum-likelihood (GML) approach which treats the data symbols as Gaussian-distributed nuisance parameters. We derive the Cramer-Rao bound and use Monte-Carlo simulations to investigate the mean squared error (MSE) performance of the proposed algorithms. We also compare the symbol-error rate (SER) performance of the DML algorithm with that of the training-based least-squares (LS) algorithm and demonstrate that the DML offers a superior tradeoff between accuracy and spectral efficiency.

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Heterogeneous networks that consist of densely deployed base stations of different (macro and small-cell) tiers are envisioned to be among the key technologies for providing the high data rates required in 5G systems. Moreover, interconnecting small-cell base stations via millimeter-wave (mm-wave) backhaul links is a flexible and cost-effective alternative to fiber optic backhauling. Given a set of mm-wave backhaul links, this paper addresses the problem of scheduling all links in the minimum number of time slots such that the subset of links scheduled to each time slot can be activated simultaneously. In particular, a set of links can be activated simultaneously if all link signal-to-interference-plus-noise-ratio (SINR) targets are satisfied, and the number of RF chains of every base station is not exceeded. We give a succinct optimization-based formulation of the problem, capturing both SINR constraints and number of RF chains limitations. Using reduction from the set-cover problem, we devise a provably good polynomial-time algorithm for the problem. Our numerical results further indicate the significant superiority of the presented approach. INDEX TERMS Backhaul network, greedy algorithms, link scheduling, millimeter wave.