Virgilio Rodriguez

Auction driven dynamic spectrum allocation: optimal bidding, pricing and service priorities for multi-rate, multi-class CDMA

Dynamic spectrum allocation (DSA) seeks to exploit the variations in the loads of various radio-access networks to allocate the spectrum efficiently. Here, a spectrum manager implements DSA by periodically auctioning short-term spectrum licenses. We solve analytically the problem of the operator of a CDMA cell populated by delay-tolerant terminals operating at various data rates, on the downlink, and representing users with dissimilar willingness to pay (WtP). WtP is the most a user would pay for a correctly transferred information bit. The operator finds a revenue-maximising internal pricing and a service priority policy, along with a bid for spectrum. Our clear and specific analytical results apply to a wide variety of physical layer configurations. The optimal operating point can be easily obtained from the frame-success rate function. At the optimum, (with a convenient time scale) a terminals contribution to revenues is the product of its WtP by its data rate; and the product of its WtP by its channel gain determines its service priority (revenue per Hertz). Assuming a second-price auction, the operators optimal bid for a certain spectrum band equals the sum of the individual revenue contributions of the additional terminals that could be served, if the band is won

Robust modeling and analysis for wireless data resource management

Recent publications recognize that decentralized algorithms useful in wireless data applications can be obtained via microeconomics and game theory. In these studies, each agent maximizes, under appropriate rules and constraints, a quality-of-service (QoS) index. A key solution is a Nash equilibrium; i.e., an allocation from which no agent is better off by unilaterally deviating. The actual maximization may be made by software which may not be directly controllable by a human user. The model and, especially, the chosen QoS index should be as general as possible, so that the derived results be applicable to a wide variety of channel conditions, modulation schemes, and other physical-layer characteristics. Likewise, the chosen index should exhibit predictable and reliable technical behavior, without exacting a high complexity cost. This note describes a model, and particularly, a QoS index which can accommodate a wide variety of physical layer situations. The proposed index is shown to exhibit solid technical behavior, be physically significant, intuitively appealing, and applicable to a wide variety of physical layer situations. A game in which terminals carrying multi-rate traffic seek to maximize this index is analyzed, and closed-form equilibrium conditions and power levels are derived from first principles. All terminals want the same signal-to-interference ratio (SIR), but some cannot reach the necessary power level. At equilibrium, a number of terminals transmit full power, and others achieve the same optimal SIR. A basic rationale to search for these equilibria is provided.

Market driven dynamic spectrum allocation over space and time among radio-access networks: DVB-T and B3G CDMA with heterogeneous terminals

The radio frequency spectrum is a naturally limited resource of extraordinary value, as the key to the provision of important communication and information services. Traditionally, spectrum has been allocated first to specific access technologies, and then sub-allocated to specific access networks, on very long term basis (up to decades). The traditional scheme can be very inefficient when demand patterns (“loads”) exhibit high temporal and spatial variations. Dynamic spectrum allocation (DSA) improves radio spectrum efficiency by adjusting the allocation as demand changes in time and/or space. In previous work, we introduced a DSA scheme in which a spectrum manager periodically auctions short-term spectrum licenses. The scheme can be supported by a realistic “pooling” business model, and can work with many radio-access technologies. But our previous analysis only considers a code-division multiple access (CDMA) technology; and DSA provides the greatest benefits with the participation of networks having complementary “busy hours,” such as video entertainment services and cellular telephony. Here, a digital video broadcast (DVB) terrestrial network joins the scheme. A typical DVB terrestrial cell is (much) larger than a UMTS cell. This brings to the forefront inter-cell interference, and inter-related auctions in different cells. To capture the essence of these issues we focus first on a situation where one DVB terrestrial cell overlays two adjacent CDMA cells. Subsequently we discuss extensions to richer scenarios. The contributions of the present work over our previous publications include to : (i) address the impact of inter-cell interference among several CDMA cells, (ii) introduce the DVB access technology into the DSA scheme, (iii) modify the auction scheme to consider that a DVB cell overlays several CDMA cells, (iv) characterise analytically the marketing and bidding behaviour of the DVB network.

Power and data rate assignment for maximal weighted throughput in 3G CDMA

Relevant to the uplink of a VSG-CDMA system, a technique part of 3G standards, this work investigates power and data rate allocations that maximize the network weighted throughput. Each terminal has one of 2 possible weights, which admit various practical interpretations. Earlier works of ours tell us that at least one terminal should operate at the highest available data rate, and that terminals not operating at this rate should operate at the same signal-to-interference ratio (SIR). We have also learned that when only two terminals of dissimilar weights operate at maximal data rate, the optimal SIR values for these terminals is obtained as an intersection point between an X-shaped graph arising from optimality conditions, and a U-shaped graph arising from the feasibility condition on power ratios. In the present work, we introduce a general procedure to seek an allocation that is a global optimizer. The analysis is based on classical optimization theory, and should accommodate a wide variety of physical layer configurations.Relevant to the uplink of a VSG-CDMA system, a technique part of 3G standards, this work seeks power and data rate allocation for each of the N terminals, so that the network weighted throughput is maximized. The weights admit various interpretations, including levels of importance, utility, and price. We have learned that at least one terminal should operate at the highest available data rate. Our analysis leads to allocations in which terminals not operating at the highest data rate operate at the same signal-to-interference ratio (SIR). This value is determined by the physical layer through the function that gives, in terms of the received SIR, the probability that a data packet is received correctly. Other factors held constant, lowering the highest available data rate increases the number of terminals which should operate at maximum data rate. This analysis conforms to classical optimization theory. Our model should accommodate a wide variety of physical layer.

Maximizing the throughput of CDMA data communications

We analyze aggregate throughput as a function of the transmitter power levels and the number of terminals sending data to a CDMA base station. We find that when noise and out-of-cell interference are negligible, received power balancing maximizes the aggregate throughout of the base station, provided the population of active terminals does not exceed an optimum size. The optimum number of active terminals depends on the CDMA processing gain and the details of the physical layer and data link layer. These details are summarized in a univariate frame success function. When noise is present, power balancing is suboptimal mathematically but attractive for practical implementation.

Optimal coding rate and power allocation for the streaming of scalably encoded video over a wireless link

Scalably encoded information results in files which can be truncated at an arbitrary point and decoded, as supported by the JPEG-2000 (image) and MPEG-4 (video) standards. This work introduces a tractable, yet flexible analytical model for resource management involving scalably encoded video. Each segment of video of a predetermined length yields a file that can be truncated and decoded independently of other segments. The problem is set up as a joint optimization of transmission power, and coding rate (where to truncate?). The analysis reveals that any one of these variables uniquely determines the other. The terminal should truncate the file at the point that maximizes quality per unit of power employed.

Power and data rate assignment for maximal weighted throughput in 3G CDMA: a global solution with two classes of users

Relevant to the uplink of a VSG-CDMA system, a technique part of 3G standards, this work investigates power and data rate allocations that maximize the network weighted throughput. Each terminal has one of 2 possible weights, which admit various practical interpretations. Earlier works of ours tell us that at least one terminal should operate at the highest available data rate, and that terminals not operating at this rate should operate at the same signal-to-interference ratio (SIR). We have also learned that when only two terminals of dissimilar weights operate at maximal data rate, the optimal SIR values for these terminals is obtained as an intersection point between an X-shaped graph arising from optimality conditions, and a U-shaped graph arising from the feasibility condition on power ratios. In the present work, we introduce a general procedure to seek an allocation that is a global optimizer. The analysis is based on classical optimization theory, and should accommodate a wide variety of physical layer configurations.

Resource management for scalably encoded information: the case of image transmission over wireless networks

Scalable encoded information, as in the JPEG 2000 standard, results in files, which can be truncated at an arbitrary point and decoded. This work introduces a tractable, yet flexible model appropriate for resource management involving scalably encoded information. At its core is a function yielding a measure of quality of the decoded information as a function of the number of bits chosen for decoding. It is assumed that all that is known about this function is that its graph yields an S-curve. An energy-efficient policy for the transmission over a wireless network of scalably- encoded images is sought. Two variables are jointly optimized: transmission power, and the number of bits of each file to be decoded (coding rate). The single-user case is fully analyzed, and a closed-form solution given, which can be clearly identified, graphically. The analysis indicates that both variables can be decoupled, and their optimal values found independently of each other.

Power and data rate assignment for maximal weighted throughput: a dual-class 3G CDMA scenario

Relevant to the uplink of a VSG-CDMA system, a technique part of 3G standards, this work investigates power and data rate allocations that maximize the network weighted throughput. Each terminal has one of 2 possible weights, which admit various practical interpretations. Earlier works of ours tell us that at least one terminal should operate at the highest available data rate, and that terminals not operating at this rate should operate at the same signal-to-interference ratio (SIR). This value is determined by the physical layer through the function that gives, in terms of the received SIR, the probability that a data packet is received correctly. In this work, we provide a more specific description of the optimal allocations. The key to the solution is an intersection point between an X-shaped graph arising from optimally conditions, and a U-shaped graph arising from the feasibility condition on power ratios. Our analysis is based on classical optimization theory, and should accommodate a wide variety of physical layer configurations.

An optimal architecture for a multi-standard reconfigurable radio: A network theory re-formulation

We provide a procedure for identifying an architecture for a multistandard reconfigurable radio that is optimal in view of cost and performance (latency) considerations. We examine the trade-off between installing complex self-contained components providing high performance at a high cost (as well as size and weight), versus invoking simpler, reusable low level modules, which reduces cost but increases system latency. In the present work, we show that the problem of finding an optimal design for a multistandard reconfigurable radio can be reformulated as a network design problem. This reformulation provides a wealth of results, algorithms, and experience already available in the scientific literature. We explain the reformulation, give a simple but realistic design example, and discuss some algorithms available in the network design literature