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Abstract
In practical massive multiple-input–multiple-output (MIMO) system, limited transmitted antennas installed at the base station (BS) cannot guarantee the ideal orthogonality and the theoretical channel rate cannot thus be achieved. In this paper, we consider the approximation of channel rate for the configuration of large but finite number of antennas at BS in a massive MIMO system. A perturbation matrix is introduced to model the non-ideal orthogonality. And then, Taylor expansion of determinant is utilized to derive the closed form of the achievable channel rate. The convergence of the Taylor expansion is theoretically proved and simulated. Numerical results show that our calculation of channel rate can get a better approximation compared with the practical rate, especially in the case of high expansion order and large number of antennas.
Highlights
Massive MIMO is a promising technology for 5G wireless networks that has recently received significant attention to potentially provide significant improvement in spectrum and energy efficiency in [1]–[3]
Yao et al.: Analytical Approximation of the Channel Rate for Massive MIMO System derivation is with a bigger mathematical calculation and more complexity; it can improve the approximation for different configuration of the number of base station (BS)’ antennas and users
We can find that, when the number of antennas installed at BS is large but finite, there is a rate loss compared to the ideal channel rate due to non-orthogonality of the channels for different user; even compared to the numerical one, the approximation error will be emerged for both the second- and third-order approximation
Summary
Massive MIMO is a promising technology for 5G wireless networks that has recently received significant attention to potentially provide significant improvement in spectrum and energy efficiency in [1]–[3]. A large number of works on massive MIMO assume that massive MIMO systems are equipped with infinite antennas at base station (BS) In this case, the channel vectors for different users will be asymptotically orthogonal [4], [5]. When system parameters are changed, especially with large number of users, the channel rate with the second-order expansion have no longer good approximation performance compared to the numerical one. To get a better approximation for a massive MIMO system with large but finite number of antennas at BS, in this paper, we carefully derive a closed-form of ergodic channel rate using the third-order Taylor expansion. R. Yao et al.: Analytical Approximation of the Channel Rate for Massive MIMO System derivation is with a bigger mathematical calculation and more complexity; it can improve the approximation for different configuration of the number of BS’ antennas and users.
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