Achieving Global Optimality for Weighted Sum-Rate Maximization in the K-User Gaussian Interference Channel with Multiple Antennas

Characterizing the global maximum of weighted sum-rate (WSR) for the K-user Gaussian interference channel (GIC), with the interference treated as Gaussian noise, is a key problem in wireless communication. However, due to the users' mutual interference, this problem is in general non-convex and thus cannot be solved directly by conventional convex optimization techniques. In this paper, by jointly utilizing the monotonic optimization and rate profile techniques, we develop a new framework to obtain the globally optimal power control and/or beamforming solutions to the WSR maximization problems for the GICs with single-antenna transmitters and single-antenna receivers (SISO), single-antenna transmitters and multi-antenna receivers (SIMO), or multi-antenna transmitters and single-antenna receivers (MISO). Different from prior work, this paper proposes to maximize the WSR in the achievable rate region of the GIC directly by exploiting the facts that the achievable rate region is a "normal" set and the users' WSR is a "strictly increasing" function over the rate region. Consequently, the WSR maximization is shown to be in the form of monotonic optimization over a normal set and thus can be solved globally optimally by the existing outer polyblock approximation algorithm. However, an essential step in the algorithm hinges on how to efficiently characterize the intersection point on the Pareto boundary of the achievable rate region with any prescribed "rate profile" vector. This paper shows that such a problem can be transformed into a sequence of signal-to-interference-plus-noise ratio (SINR) feasibility problems, which can be solved efficiently by existing techniques. Numerical results validate that the proposed algorithms can achieve the global WSR maximum for the SISO, SIMO or MISO GIC.Comment: This is the longer version of a paper to appear in IEEE Transactions on Wireless Communication

Wireless Information Transfer with Opportunistic Energy Harvesting

Energy harvesting is a promising solution to prolong the operation of energy-constrained wireless networks. In particular, scavenging energy from ambient radio signals, namely wireless energy harvesting (WEH), has recently drawn significant attention. In this paper, we consider a point-to-point wireless link over the narrowband flat-fading channel subject to time-varying co-channel interference. It is assumed that the receiver has no fixed power supplies and thus needs to replenish energy opportunistically via WEH from the unintended interference and/or the intended signal sent by the transmitter. We further assume a single-antenna receiver that can only decode information or harvest energy at any time due to the practical circuit limitation. Therefore, it is important to investigate when the receiver should switch between the two modes of information decoding (ID) and energy harvesting (EH), based on the instantaneous channel and interference condition. In this paper, we derive the optimal mode switching rule at the receiver to achieve various trade-offs between wireless information transfer and energy harvesting. Specifically, we determine the minimum transmission outage probability for delay-limited information transfer and the maximum ergodic capacity for no-delay-limited information transfer versus the maximum average energy harvested at the receiver, which are characterized by the boundary of so-called "outage-energy" region and "rate-energy" region, respectively. Moreover, for the case when the channel state information (CSI) is known at the transmitter, we investigate the joint optimization of transmit power control, information and energy transfer scheduling, and the receiver's mode switching. Our results provide useful guidelines for the efficient design of emerging wireless communication systems powered by opportunistic WEH.Comment: to appear in IEEE Transactions on Wireless Communicatio

Modification and Characterisation of Vanadium Phosphorus Oxide Catalysts for Selective Oxidation of Propane to Acrylic Acid

Vanadium phosphate catalysts synthesized via VOPO4∙2H2O were further reduced in isobutanol to produce VOHPO4∙0.5H2O precursor. Calcination of this precursor in propane/air environment (1% propane in air) transformed into activated (VO)2P2O7 catalysts. The morphology, structure, oxidant’s nature and catalytic performance for propane oxidation to acrylic acid over this catalyst strongly depended on the duration of calcination. The catalyst calcined for 36 h (VPD36P) exhibits low surface area. However, prolonged calcination promoted a higher surface area with better crystallization. VIII and VV phases are detected in all catalysts. The SEM micrographs showed that all propane/air catalysts gave rosebud type agglomerates with various sizes but in a uniform shape. A comparison of effect of calcinations environments on the vanadium phosphate catalyst in flow of both propane/air and butane/air, the latter calcinations environment produced catalyst with more platelet and higher surface area. Chemical analysis also shows that VPDB catalyst consist of higher amount of VV (26%) and 74% of VIV phase whereas VPDP only contains 76 and 9.8% of VIV and VV phases, respectively. Interestingly, VPDP also showed 14.2% of VIII phase. For n-butane oxidation at 673 K, VPDB gave 83% of conversion and 63% of MA selectivity whereas VPDP gave 75% of conversion and 64% of MA selectivity. The n-butane/air calcined catalyst, VPDB showed better activity (14.1%) in propane oxidation than the propne/air calcined catalyst, VPDP (7.9%). The addition of 1, 2 and 5 mol % of Zr into (VO)2P2O7 catalysts produced a single vanadyl pyrophosphate phase in VOPO4∙2H2O method with different degree of crystallinity. The presence of lower percentage of Zr (1 and 2%) improved the surface area of the catalysts; however, the surface area of the catalyst with 5% of Zr added is decreased. The SEM micrograph for all Zr modified catalysts gave roughed rosebud agglomerates as compared to the unpromoted catalyst. VPDZr1 catalyst was found to be the most selective catalyst among all the Zr doped catalysts in propane oxidation

Secrecy Wireless Information and Power Transfer with MISO Beamforming

The dual use of radio signals for simultaneous wireless information and power transfer (SWIPT) has recently drawn significant attention. To meet the practical requirement that energy receivers (ERs) operate with significantly higher received power as compared to information receivers (IRs), ERs need to be deployed in more proximity to the transmitter than IRs. However, due to the broadcast nature of wireless channels, one critical issue arises that the messages sent to IRs can be eavesdropped by ERs, which possess better channels from the transmitter. In this paper, we address this new secrecy communication problem in a multiuser multiple-input single-output (MISO) SWIPT system where one multi-antenna transmitter sends information and energy simultaneously to an IR and multiple ERs, each with one single antenna. To optimally design transmit beamforming vectors and their power allocation, two problems are investigated with different aims: the first problem maximizes the secrecy rate for IR subject to individual harvested energy constraints of ERs, while the second problem maximizes the weighted sum-energy transferred to ERs subject to a secrecy rate constraint for IR. We solve these two non-convex problems optimally by reformulating each of them into a two-stage problem. First, by fixing the signal-to-interference-plus-noise ratio (SINR) target for ERs (for the first problem) or IR (for the second problem), we obtain the optimal beamforming and power allocation solution by applying the technique of semidefinite relaxation (SDR). Then, the original problems are solved by a one-dimension search over the optimal SINR target for ERs or IR. Furthermore, for each of the two studied problems, suboptimal solutions of lower complexity are also proposed in which the information and energy beamforming vectors are separately designed with their power allocation.Comment: accepted by IEEE Transactions on Signal Processing. Longer version of arXiv:1306.096