Large System Analysis of Game-Theoretic Power Control in UWB Wireless Networks with Rake Receivers

This paper studies the performance of partial-Rake (PRake) receivers in impulse-radio ultrawideband wireless networks when an energy-efficient power control scheme is adopted. Due to the large bandwidth of the system, the multipath channel is assumed to be frequency-selective. By using noncooperative game-theoretic models and large system analysis, explicit expressions are derived in terms of network parameters to measure the effects of self- and multiple-access interference at a receiving access point. Performance of the PRake is compared in terms of achieved utilities and loss to that of the all-Rake receiver.Comment: To appear in the Proceedings of the 8th IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), Helsinki, Finland, June 17-20, 200

A Learning-Based Approach to Caching in Heterogenous Small Cell Networks

A heterogenous network with base stations (BSs), small base stations (SBSs) and users distributed according to independent Poisson point processes is considered. SBS nodes are assumed to possess high storage capacity and to form a distributed caching network. Popular files are stored in local caches of SBSs, so that a user can download the desired files from one of the SBSs in its vicinity. The offloading-loss is captured via a cost function that depends on the random caching strategy proposed here. The popularity profile of cached content is unknown and estimated using instantaneous demands from users within a specified time interval. An estimate of the cost function is obtained from which an optimal random caching strategy is devised. The training time to achieve an $\epsilon>0$ difference between the achieved and optimal costs is finite provided the user density is greater than a predefined threshold, and scales as $N^2$, where $N$ is the support of the popularity profile. A transfer learning-based approach to improve this estimate is proposed. The training time is reduced when the popularity profile is modeled using a parametric family of distributions; the delay is independent of $N$ and scales linearly with the dimension of the distribution parameter.Comment: 12 pages, 5 figures, published in IEEE Transactions on Communications, 2016. arXiv admin note: text overlap with arXiv:1504.0363

Sequential joint signal detection and signal-to-noise ratio estimation

The sequential analysis of the problem of joint signal detection and signal-to-noise ratio (SNR) estimation for a linear Gaussian observation model is considered. The problem is posed as an optimization setup where the goal is to minimize the number of samples required to achieve the desired (i) type I and type II error probabilities and (ii) mean squared error performance. This optimization problem is reduced to a more tractable formulation by transforming the observed signal and noise sequences to a single sequence of Bernoulli random variables; joint detection and estimation is then performed on the Bernoulli sequence. This transformation renders the problem easily solvable, and results in a computationally simpler sufficient statistic compared to the one based on the (untransformed) observation sequences. Experimental results demonstrate the advantages of the proposed method, making it feasible for applications having strict constraints on data storage and computation.Comment: 5 pages, Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 201

Privacy-cost trade-offs in smart electricity metering systems

Trade-offs between privacy and cost are studied for a smart grid consumer, whose electricity consumption is monitoredin almost real time by the utility provider (UP) through smart meter (SM) readings. It is assumed that an electrical battery isavailable to the consumer, which can be utilized both to achieve privacy and to reduce the energy cost by demand shaping.Privacy is measured via the mean squared distance between the SM readings and a target load profile, while time-of-use (ToU)pricing is considered to compute the cost incurred. The consumer can also sell electricity back to the UP to further improve theprivacy-cost trade-off. Two privacy-preserving energy management policies (EMPs) are proposed, which differ in the way the targetload profile is characterized. A more practical EMP, which optimizes the energy management less frequently, is also considered.Numerical results are presented to compare the privacy-cost trade-off of these EMPs, considering various privacy indicators

Formal proofs of operator identities by a single formal computation

A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials.Comment: 22 page

Modified Partition Functions, Consistent Anomalies and Consistent Schwinger Terms

A gauge invariant partition function is defined for gauge theories which leads to the standard quantization. It is shown that the descent equations and consequently the consistent anomalies and Schwinger terms can be extracted from this modified partition function naturally.Comment: 25 page

Sample, Quantize and Encode: Timely Estimation Over Noisy Channels

The effects of quantization and coding on the estimation quality of Gauss-Markov processes are considered, with a special attention to the Ornstein-Uhlenbeck process. Samples are acquired from the process, quantized, and then encoded for transmission using either infinite incremental redundancy (IIR) or fixed redundancy (FR) coding schemes. A fixed processing time is consumed at the receiver for decoding and sending feedback to the transmitter. Decoded messages are used to construct a minimum mean square error (MMSE) estimate of the process as a function of time. This is shown to be an increasing functional of the age-of-information (AoI), defined as the time elapsed since the sampling time pertaining to the latest successfully decoded message. Such functional depends on the quantization bits, codewords lengths and receiver processing time. The goal, for each coding scheme, is to optimize sampling times such that the long-term average MMSE is minimized. This is then characterized in the setting of general increasing functionals of AoI, not necessarily corresponding to MMSE, which may be of independent interest in other contexts. We first show that the optimal sampling policy for IIR is such that a new sample is generated only if the AoI exceeds a certain threshold, while for FR it is such that a new sample is delivered just-in-time as the receiver finishes processing the previous one. Enhanced transmissions schemes are then developed in order to exploit the processing times to make new data available at the receiver sooner. For both IIR and FR, it is shown that there exists an optimal number of quantization bits that balances AoI and quantization errors, and hence minimizes the MMSE. It is also shown that for longer receiver processing times, the relatively simpler FR scheme outperforms IIR.Comment: Accepted for publication in the IEEE Transactions on Communications. arXiv admin note: substantial text overlap with arXiv:2004.1298