Abstract-In this paper, a free deterministic equivalent is proposed for the capacity analysis of the multi-input multi-output (MIMO) multiple access channel (MAC) with a more general channel model compared to previous works. Specifically, a MIMO MAC with one base station (BS) equipped with several distributed antenna sets is considered. Each link between a user and a BS antenna set forms a jointly correlated Rician fading channel. The analysis is based on operator-valued free probability theory, which broadens the range of applicability of free probability techniques tremendously. By replacing independent Gaussian random matrices with operator-valued random variables satisfying certain operator-valued freeness relations, the free deterministic equivalent of the considered channel Gram matrix is obtained. The Shannon transform of the free deterministic equivalent is derived, which provides an approximate expression for the ergodic input-output mutual information of the channel. The sum-rate capacity achieving input covariance matrices are also derived based on the approximate ergodic input-output mutual information. The free deterministic equivalent results are easy to compute, and simulation results show that these approximations are numerically accurate and computationally efficient.Index Terms-Operator-valued free probability, deterministic equivalent, massive multi-input multi-output (MIMO), multiple access channel (MAC).

In this paper, we propose an information geometry approach (IGA) for signal detection (SD) in ultra-massive multiple-input multiple-output (MIMO) systems. We formulate the signal detection as obtaining the marginals of the a posteriori probability distribution of the transmitted symbol vector. Then, a maximization of the a posteriori marginals (MPM) for signal detection can be performed. With the information geometry theory, we calculate the approximations of the a posteriori marginals. It is formulated as an iterative m-projection process between submanifolds with different constraints. We then apply the central-limit-theorem (CLT) to simplify the calculation of the m-projection since the direct calculation of the m-projection is of exponential-complexity. With the CLT, we obtain an approximate solution of the m-projection, which is asymptotically accurate. Simulation results demonstrate that the proposed IGA-SD emerges as a promising and efficient method to implement the signal detector in ultra-massive MIMO systems.

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The integration of satellite and terrestrial 5G networks aims to provide ubiquitous coverage, improve service reliability, and enable the network scalability. However, the inherent characteristics of satellite channels bring challenges on the air interface design of integrated terrestrial-satellite networks. For example, for low earth orbits (LEO) mobile satellite communication (SatCom) system, it is unclear so far whether the 5G new radio (5G-NR) synchronization signals could meet the requirement of timing and frequency offset estimation in the presence of large Doppler shifts. In this paper, we investigate time and frequency synchronization for the downlink transmission of 5G-NR signals over LEO satellite channels. Starting from the maximum log-likelihood criterion for timing offset estimation given the observation of the received primary synchronization signals (PSS), we derive an upper bound of the objective function for simplicity. With a priori information that the maximum Doppler shift of LEO satellite-ground link is within a specific range, we construct the local synchronization sequence via using the modulated discrete prolate spheroidal sequences (DPSS) vectors. Then the timing offset estimation can be recast into a one-dimensional peak search problem. Moreover, the cyclic prefix (CP) structure of orthogonal frequency division multiplexing (OFDM) can be utilized to improve the estimation performance further. Once the timing and frequency offset are captured in the above initial synchronization phase, the tracking synchronization can be much simplified as the variation of both the timing and frequency offset is very small between two adjacent synchronization blocks. Simulation results show that by using the proposed algorithms, the 5G-NR signals can achieve near optimal downlink time and frequency synchronization in typical LEO SatCom systems.INDEX TERMS LEO satellite, 5G integrated network, time and frequency synchronization, Doppler shift.WENJIN WANG (M'14) received the Ph.D. degree in communication and information sys-

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