The recursive least-squares algorithm with $ell_1$-norm regularization ($ell_1$-RLS) exhibits excellent performance in terms of convergence rate and steady-state error in identification of sparse systems. Nevertheless few works have studied its stochastic behavior, in particular its transient performance. In this letter, we derive analytical models of the transient behavior of the $ell_1$-RLS in the mean and mean-square sense. Simulation results illustrate the accuracy of these models.
The problem of assessing the performance of algorithms used for the minimization of an $ell_1$-penalized least-squares functional, for a range of penalty parameters, is investigated. A criterion that uses the idea of `approximation isochrones is introduced. Five different iterative minimization algorithms are tested and compared, as well as two warm-start strategies. Both well-conditioned and ill-conditioned problems are used in the comparison, and the contrast between these two categories is highlighted.
Aerial relays have been regarded as an alternative and promising solution to extend and improve satellite-terrestrial communications, as the probability of line-of-sight transmissions increases compared with adopting terrestrial relays. In this paper, a cooperative satellite-aerial-terrestrial system including a satellite transmitter (S), a group of terrestrial receivers (D), and an aerial relay (R) is considered. Specifically, considering the randomness of S and D and employing stochastic geometry, the coverage probability of R-D links in non-interference and interference scenarios is studied, and the outage performance of S-R link is investigated by deriving an approximated expression for the outage probability. Moreover, an optimization problem in terms of the transmit power and the transmission time over S-R and R-D links is formulated and solved to obtain the optimal end-to-end energy efficiency for the considered system. Finally, some numerical results are provided to validate our proposed analysis models, as well as to study the optimal energy efficiency performance of the considered system.
This paper presents a feasibility study for a novel positioning-communication integrated signal called Multi-Scale Non-Orthogonal Multiple Access (MS-NOMA) for 5G positioning. One of the main differences between the MS-NOMA and the traditional positioning signal is MS-NOMA supports configurable powers for different positioning users (P-Users) to obtain better ranging accuracy and signal coverage. Our major contributions are: Firstly, we present the MS-NOMA signal and analyze the Bit Error Rate (BER) and ranging accuracy by deriving their simple expressions. The results show the interaction between the communication and positioning signals is rather limited, and it is feasible to use the MS-NOMA signal to achieve high positioning accuracy. Secondly, for an optimal positioning accuracy and signal coverage, we model the power allocation problem for MS-NOMA signal as a convex optimization problem by satisfying the QoS (Quality of Services) requirement and other constraints. Then, we propose a novel Positioning-Communication Joint Power Allocation (PCJPA) algorithm which allocates the powers of all P-Users iteratively. The theoretical and numerical results show our proposed MS-NOMA signal has great improvements of ranging/positioning accuracy than traditional PRS (Positioning Reference Signal) in 5G, and improves the coverage dramatically which means more P-Users could locate their positions without suffering the near-far effect.
Hybrid free space optical (FSO)/radio frequency (RF) systems have been proved to be reliable links for high-data-rate wireless backhauls. In this paper, we present a unified performance analysis of the hybrid FSO/RF transmission system which transmits the identical data in both links and implements two popular diversity combining schemes, namely, selection combining (SC) and maximal ratio combining (MRC), in the receiver. Specially, for the FSO link, the Gamma-Gamma turbulence with pointing errors under heterodyne detection (HD) and intensity modulation/direction detection (IM/DD) is considered in our analysis while the general k{appa}-{mu} shadowed fading which unifies popular RF fading models is employed for the analysis of the RF link. As a result, unified closed-form expressions of outage probabilities and average bit error rates for different modulation schemes are derived. Analytical and Monte Carlo simulation results are provided to characterize the performance of the hybrid FSO/RF link which is compared to the single FSO link and the single RF link. The agreement between the analytical and simulation results confirms the unification of various FSO channels and RF fading scenarios into a single closed-form expression.
LoRa is a modulation technology for low power wide area networks (LPWAN) with enormous potential in 5G era. However, the performance of LoRa system deteriorates seriously in fading-channel environments. To tackle this problem, in this paper we introduce multiple-input-multiple-output (MIMO) configuration employing space-time block coding (STBC) schemes into the LoRa system to formulate an STBC-MIMO LoRa system. Then, we investigate the theoretical performance of the proposed system over Rayleigh fading channels. To this end, we derive the distribution of the decision metric for the demodulator in the proposed system. Based on the above distribution, we propose the closed-form approximated bit error rate (BER) expression of the proposed system when perfect and imperfect channel information states (CSIs) are considered. In addition, we analyze the diversity order of the proposed system. The result demonstrates that the diversity order of the system in the imperfect CSI scenario with fixed channel estimate error variance is zero. However, in the imperfect CSI scenario with a decreasing channel estimate error variance and the perfect CSI scenario, the system can achieve full diversity. Finally, experimental results verify the accuracy of the theoretical analysis and the excellent performance of the proposed system. Due to such superiority, the proposed STBC-MIMO LoRa system can be considered as a good scheme for LPWAN.