Optimization of Training and Feedback Overhead for Beamforming over Block Fading Channels

We examine the capacity of beamforming over a single-user, multi-antenna link taking into account the overhead due to channel estimation and limited feedback of channel state information. Multi-input single-output (MISO) and multi-input multi-output (MIMO) channels are considered subject to block Rayleigh fading. Each coherence block contains $L$ symbols, and is spanned by $T$ training symbols, $B$ feedback bits, and the data symbols. The training symbols are used to obtain a Minimum Mean Squared Error estimate of the channel matrix. Given this estimate, the receiver selects a transmit beamforming vector from a codebook containing $2^B$ {\em i.i.d.} random vectors, and sends the corresponding $B$ bits back to the transmitter. We derive bounds on the beamforming capacity for MISO and MIMO channels and characterize the optimal (rate-maximizing) training and feedback overhead ($T$ and $B$) as $L$ and the number of transmit antennas $N_t$ both become large. The optimal $N_t$ is limited by the coherence time, and increases as $L/\log L$. For the MISO channel the optimal $T/L$ and $B/L$ (fractional overhead due to training and feedback) are asymptotically the same, and tend to zero at the rate $1/\log N_t$. For the MIMO channel the optimal feedback overhead $B/L$ tends to zero faster (as $1/\log^2 N_t$).Comment: accepted for IEEE Trans. Info. Theory, 201

Sharing of Unlicensed Spectrum by Strategic Operators

Facing the challenge of meeting ever-increasing demand for wireless data, the industry is striving to exploit large swaths of spectrum which anyone can use for free without having to obtain a license. Major standards bodies are currently considering a proposal to retool and deploy Long Term Evolution (LTE) technologies in unlicensed bands below 6 GHz. This paper studies the fundamental questions of whether and how the unlicensed spectrum can be shared by intrinsically strategic operators without suffering from the tragedy of the commons. A class of general utility functions is considered. The spectrum sharing problem is formulated as a repeated game over a sequence of time slots. It is first shown that a simple static sharing scheme allows a given set of operators to reach a subgame perfect Nash equilibrium for mutually beneficial sharing. The question of how many operators will choose to enter the market is also addressed by studying an entry game. A sharing scheme which allows dynamic spectrum borrowing and lending between operators is then proposed to address time-varying traffic and proved to achieve perfect Bayesian equilibrium. Numerical results show that the proposed dynamic sharing scheme outperforms static sharing, which in turn achieves much higher revenue than uncoordinated full-spectrum sharing. Implications of the results to the standardization and deployment of LTE in unlicensed bands (LTE-U) are also discussed.Comment: To appear in the IEEE Journal on Selected Areas in Communications, Special Issue on Game Theory for Network

Distributed Optimization of Multi-Cell Uplink Co-operation with Backhaul Constraints

We address the problem of uplink co-operative reception with constraints on both backhaul bandwidth and the receiver aperture, or number of antenna signals that can be processed. The problem is cast as a network utility (weighted sum rate) maximization subject to computational complexity and architectural bandwidth sharing constraints. We show that a relaxed version of the problem is convex, and can be solved via a dual-decomposition. The proposed solution is distributed in that each cell broadcasts a set of {\em demand prices} based on the data sharing requests they receive. Given the demand prices, the algorithm determines an antenna/cell ordering and antenna-selection for each scheduled user in a cell. This algorithm, referred to as {\em LiquidMAAS}, iterates between the preceding two steps. Simulations of realistic network scenarios show that the algorithm exhibits fast convergence even for systems with large number of cells.Comment: IEEE ICC Conference, 201

Scalable Spectrum Allocation for Large Networks Based on Sparse Optimization

Joint allocation of spectrum and user association is considered for a large cellular network. The objective is to optimize a network utility function such as average delay given traffic statistics collected over a slow timescale. A key challenge is scalability: given $n$ Access Points (APs), there are $O(2^n)$ ways in which the APs can share the spectrum. The number of variables is reduced from $O(2^n)$ to $O(nk)$, where $k$ is the number of users, by optimizing over local overlapping neighborhoods, defined by interference conditions, and by exploiting the existence of sparse solutions in which the spectrum is divided into $k+1$ segments. We reformulate the problem by optimizing the assignment of subsets of active APs to those segments. An $\ell_0$ constraint enforces a one-to-one mapping of subsets to spectrum, and an iterative (reweighted $\ell_1$) algorithm is used to find an approximate solution. Numerical results for a network with 100 APs serving several hundred users show the proposed method achieves a substantial increase in total throughput relative to benchmark schemes.Comment: Submitted to the IEEE International Symposium on Information Theory (ISIT), 201

An Example of Atomic Requirements - Login Screen

A simple example of what an atomic or individual or singular requirement statement should be. Using the example of the familiar login screen, shows the evolution from a low quality initial attempt at requirements to a complete atomic requirement statement. Introduces the idea of a system glossary to support the atomic requirement