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Abstract
We investigate the asymptotic behavior for an overlooked aspect of spectrum-sharing systems when the number of transmit antennas $n_{t}$ at the secondary transmitter (ST) grows to infinity. Considering imperfect channel state information (CSI), we apply the transmit antenna selection and the maximal-ratio combining techniques at the ST and the secondary receiver (SR), respectively. First, we obtain the signal-to-noise ratio (SNR) distributions received by the SR under perfect and imperfect CSI conditions. Then we show that the SNR distributions are tail-equivalent in the sense that the right tails of the two distributions decay in the same rate as the number of transmit antennas $n_{t}$ grows to infinity. Based on the extreme value theory, when the transmit power of the ST is solely limited by the interference constraint, we show that the limiting SNR at the SR is Frechet-distributed and the limiting rate scales as $\log (n_{t})$ . When the transmit power of ST is determined by both the maximal transmit power and the interference power constraints, the limiting SNR is Gumbel-distributed and the limiting rate scales as $\log (\log (n_{t}))$ . We further show that the average rate can be estimated by the corresponding easier-to-obtain outage rate. Numerical results indicate that the derived asymptotic rate expressions represent accurate approximations even when $n_{t}$ is “not-so-large”. Finally, we study the robustness of the secondary transmissions by analyzing the corresponding average symbol error rates (SER) under general modulation and coding schemes. The findings indicate that the SER is Weibull distributed, when the maximal transmit power and interference power constraints are comparable.
Highlights
Spectrum sharing has been considered as a promising technology to efficiently utilize the radio spectrum, and significant progress has been achieved in developing spectrumsharing techniques, for instance, dynamic spectrum access and 5G heterogeneous networks [1], [2], licensed and
We adopt the same assumption for underlay spectrum sharing paradigm as in [7], [21], [28]–[31] that the interference from the primary transmitter (PT) is treated as Gaussian noise or via proper cooperative schemes [32] such that we can obtain analytic results with sufficient insights on the addressed problem
We show that the signalto-noise ratio (SNR) distributions with and without channel estimation errors are tailequivalent
Summary
Spectrum sharing has been considered as a promising technology to efficiently utilize the radio spectrum, and significant progress has been achieved in developing spectrumsharing techniques, for instance, dynamic spectrum access and 5G heterogeneous networks [1], [2], licensed and. To the best of our knowledge, when both the transmit power and the interference power constraints are active, the limiting SNR distribution and the corresponding asymptotic performance metrics of the TAS/MRC secondary systems, as functions of the number of transmit antennas, are unknown and are non-trivial to deduce such results on the existing works. CONTRIBUTIONS AND PAPER ORGANIZATION To address the above discussed issues, at generic SNR levels, the extreme value theory (EVT) is applied to analyze various performance metrics of the secondary spectrum-sharing systems subject to both the maximal transmit power constraint at ST and the maximal interference power constraint at PR The performance of such secondary system is evaluated via closed-form expressions for the limiting SNR distributions, the average rate, the outage rate, and the average symbol error rate (ASER) using general modulation and coding schemes. Proofs of key technical results are provided in the Appendices
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