In this paper, we investigate the channel estimation in massive multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. The recently proposed simplified information geometry (SIG) algorithm offers a promising solution for channel estimation with relatively low computational complexity. However, the damping factors used in the SIG algorithm are based on a heuristic strategy, which results in inconsistent performance. To address this issue, we propose a deep unfolding based SIG (DU-SIG) approach in this paper. Specifically, each iteration of the SIG algorithm is unfolded into a layer-wise structure resembling a neural network and the damping factors are optimized based on deep unfolding technique. Notably, the optimized damping factors can be directly integrated into the original SIG algorithm to improve the performance of channel estimation without increasing the computational complexity. Simulation results validate the effectiveness and superiority of our proposed algorithm.

With knowledge of statistical channel state information (CSI) at the base station (BS), one can reduce the pilot overhead and improve the channel estimation performance in massive multiple-input multiple-output (MIMO) systems by exploiting the non-orthogonal pilot sequences. However, due to the limited uplink (UL) training resources, it is challenging to acquire the high-accuracy statistical CSI in real-time. To tackle this problem, an emerging technique is to construct a channel knowledge map (CKM) based on the statistical CSI. In order to construct such a CKM, it is necessary to analyze the spatial and temporal correlations of statistical CSI. Specifically, this paper analyzes the spatial and temporal correlations of beam domain channel power matrices (BDCPMs), obtained from channel measurements in a massive MIMO testbed. Furthermore, to verify the effectiveness of the stored aged BDCPMs, we also simulate channel estimation performance using BDCPMs measured at different dates. Both measured and simulated results demonstrate the effectiveness of the CKM based on statistical CSI.

In this paper, we investigate the channel estimation in massive multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. Many channel estimation algorithms, such as the recently proposed original information geometry (OIG) and simplified information geometry (SIG) algorithms, require statistical channel state information (CSI) when performing instantaneous channel estimation. However, in practice, obtaining statistical CSI may require a substantial amount of additional overhead, especially when the number of users is large. To address this issue, we propose an expectation-maximization (EM) based IG approach for massive MIMO-OFDM channel estimation, which does not need to know the statistical CSI beforehand and can estimate the instantaneous channel and statistical CSI simultaneously. Specifically, the EM-based procedure is embedded within the IG algorithms’ iteration loop to learn the statistical CSI. Moreover, all of the quantities needed for the EM updates can be obtained by the IG procedure, making the overall process computationally efficient. Furthermore, we propose a low complexity implementation for the proposed EM-SIG algorithm with the adjustable phase shift pilots of multiple roots, which can significantly reduce the computational complexity of EM-SIG. Simulations confirm the excellent performance of the proposed EM-OIG and EM-SIG algorithms both in terms of channel estimation and statistical CSI estimation.

Accurate channel estimation is essential in massive multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. As the number of base station antennas further increases, high dimensional channel estimation becomes challenging. To tackle this problem, we first introduce window functions into received signal model to obtain the windowed received signal model. The channel estimation is formulated as obtaining the$\mit {a} \;\mit {posteriori}$distribution’s marginals of the beam domain channel within the information geometry (IG) framework. The calculation of the marginals is turned into an iterative projection process. We derive the windowed information geometry (WIG) approach by calculating an approximate solution of the projection in the presence of window functions. To reduce the computational complexity, we further propose a low-complexity calculation method for WIG. Specifically, by choosing suitable window functions, we can transform the original matrix multiplications into sparse matrix multiplications, which dramatically reduces the complexity. Furthermore, by adjusting the values of thresholds used in the low-complexity calculation method, we can make a superior trade-off between complexity and performance of WIG. Finally, complexity and performance of WIG are evaluated through simulations. Simulation results show that WIG can achieve similar performance to the simplified IG (SIG) while the complexity is much lower.

We theoretically study the issues for long-distance transmission of quantum key distribution (QKD) coexisting with classical signals. The recently proposed phase-matching QKD protocol can drastically improve the transmission distance of QKD. However, in the coexistence system, the noise generated by classical signals, especially spontaneous Raman scattering noise, is a big challenge. Moreover, the classical optical amplifier, which is necessary for the realistic long-distance classical communication, makes the noise more serious. In view of this, we establish the unified Raman noise model for three discrete-variable QKD protocols (BB84, measurement-device-independent and phase-matching QKD protocols) in the presence of classical optical amplifiers, which can be applied to both single-core single-mode fiber and multicore fiber. Then, we derive the key rate of the three QKD protocols coexisting with classical signals using the proposed unified Raman noise model. Finally, simulation results show that multicore fiber is promising for simultaneous long-distance transmission of QKD and the dense wavelength division multiplexing system.