Luca Sanguinetti

Optimal Design of Energy-Efficient Multi-User MIMO Systems: Is Massive MIMO the Answer?

Assume that a multi-user multiple-input multiple-output (MIMO) system is designed from scratch to uniformly cover a given area with maximal energy efficiency (EE). What are the optimal number of antennas, active users, and transmit power? The aim of this paper is to answer this fundamental question. We consider jointly the uplink and downlink with different processing schemes at the base station and propose a new realistic power consumption model that reveals how the above parameters affect the EE. Closed-form expressions for the EE-optimal value of each parameter, when the other two are fixed, are provided for zero-forcing (ZF) processing in single-cell scenarios. These expressions prove how the parameters interact. For example, in sharp contrast to common belief, the transmit power is found to increase (not to decrease) with the number of antennas. This implies that energy-efficient systems can operate in high signal-to-noise ratio regimes in which interference-suppressing signal processing is mandatory. Numerical and analytical results show that the maximal EE is achieved by a massive MIMO setup wherein hundreds of antennas are deployed to serve a relatively large number of users using ZF processing. The numerical results show the same behavior under imperfect channel state information and in symmetric multi-cell scenarios.

A Tutorial on the Optimization of Amplify-and-Forward MIMO Relay Systems

The remarkable promise of multiple-input multiple-output (MIMO) wireless channels has motivated an intense research activity to characterize the theoretical and practical issues associated with the design of transmit (source) and receive (destination) processing matrices under different operating conditions. This activity was primarily focused on point-to-point (single-hop) communications but more recently there has been an extensive work on two-hop or multi-hop settings in which single or multiple relays are used to deliver the information from the source to the destination. The aim of this tutorial is to provide an up-to-date overview of the fundamental results and practical implementation issues in designing amplify-and-forward MIMO relay systems.

Channel estimation for adaptive frequency-domain equalization

Frequency-domain equalization (FDE) is an effective technique for high-rate wireless communications because of its reduced complexity compared to conventional time-domain equalization (TDE). In this paper, we consider adaptive FDE for single-carrier (SC) systems with explicit channel and noise-power estimation. The channel response is estimated in the frequency domain following two different approaches. The first operates independently on each frequency bin while the second exploits the fading correlation across the signal bandwidth. Least-mean-square (LMS) and recursive-least-square (RLS) algorithms are employed to update the channel estimates. The noise power is estimated using a low-complexity algorithm based on ad hoc reasoning. Compared to other existing receivers employing adaptive FDE, the proposed schemes have better error-rate performance and can be used even in the presence of relatively fast fading.

Energy-Efficient Power Control: A Look at 5G Wireless Technologies

This paper develops power control algorithms for energy efficiency (EE) maximization (measured in bit/Joule) in wireless networks. Unlike previous related works, minimum-rate constraints are imposed and the signal-to-interference-plus-noise ratio takes a more general expression, which allows one to encompass some of the most promising 5G candidate technologies. Both network-centric and user-centric EE maximizations are considered. In the network-centric scenario, the maximization of the global EE and the minimum EE of the network is performed. Unlike previous contributions, we develop centralized algorithms that are guaranteed to converge, with affordable computational complexity, to a Karush-Kuhn-Tucker point of the considered non-convex optimization problems. Moreover, closed-form feasibility conditions are derived. In the user-centric scenario, game theory is used to study the equilibria of the network and to derive convergent power control algorithms, which can be implemented in a fully decentralized fashion. Both scenarios above are studied under the assumption that single or multiple resource blocks are employed for data transmission. Numerical results assess the performance of the proposed solutions, analyzing the impact of minimum-rate constraints, and comparing the network-centric and user-centric approaches.

Deploying Dense Networks for Maximal Energy Efficiency: Small Cells Meet Massive MIMO

What would a cellular network designed for maximal energy efficiency look like? To answer this fundamental question, tools from stochastic geometry are used in this paper to model future cellular networks and obtain a new lower bound on the average uplink spectral efficiency. This enables us to formulate a tractable uplink energy efficiency (EE) maximization problem and solve it analytically with respect to the density of base stations (BSs), the transmit power levels, the number of BS antennas and users per cell, and the pilot reuse factor. The closed-form expressions obtained from this general EE maximization framework provide valuable insights on the interplay between the optimization variables, hardware characteristics, and propagation environment. Small cells are proved to give high EE, but the EE improvement saturates quickly with the BS density. Interestingly, the maximal EE is achieved by also equipping the BSs with multiple antennas and operate in a “massive MIMO” fashion, where the array gain from coherent detection mitigates interference and the multiplexing of many users reduces the energy cost per user.

Interference Management in 5G Reverse TDD HetNets With Wireless Backhaul: A Large System Analysis

This work analyzes a heterogeneous network (HetNet), which comprises a macro base station (BS) equipped with a large number of antennas and an overlaid dense tier of small cell access points (SCAs) using a wireless backhaul for data traffic. The static and low mobility user equipment terminals (UEs) are associated with the SCAs while those with medium-to-high mobility are served by the macro BS. A reverse time division duplexing (TDD) protocol is used by the two tiers, which allows the BS to locally estimate both the intra-tier and inter-tier channels. This knowledge is then used at the BS either in the uplink (UL) or in the downlink (DL) to simultaneously serve the macro UEs (MUEs) and to provide the wireless backhaul to SCAs. A concatenated linear precoding technique employing either zero-forcing (ZF) or regularized ZF is used at the BS to simultaneously serve MUEs and SCAs in DL while nulling interference toward those SCAs in UL. We evaluate and characterize the performance of the system through the power consumption of UL and DL transmissions under the assumption that target rates must be satisfied and imperfect channel state information is available for MUEs. The analysis is conducted in the asymptotic regime where the number of BS antennas and the network size (MUEs and SCAs) grow large with fixed ratios. Results from large system analysis are used to provide concise formulae for the asymptotic UL and DL transmit powers and precoding vectors under the above assumptions. Numerical results are used to validate the analysis in different settings and to make comparisons with alternative network architectures.

Game Theory for Networks: A tutorial on game-theoretic tools for emerging signal processing applications

The aim of this tutorial is to provide an overview, although necessarily incomplete, of game theory (GT) for signal processing (SP) in networks. One of the main features of this contribution is to gather in a single article some fundamental game-theoretic notions and tools that, over the past few years, have become widespread in the SP literature. In particular, both strategic-form and coalition-form games are described in detail, and the key connections and differences between them are outlined. Moreover, particular attention is also devoted to clarifying the connections between strategic-form games and distributed optimization and learning algorithms. Beyond an introduction to the basic concepts and main solution approaches, several carefully designed examples are provided to allow a better understanding of how to apply the described tools.

Power Allocation in Two-Hop Amplify-and-Forward MIMO Relay Systems With QoS Requirements

The problem of minimizing the total power consumption while satisfying different quality-of-service (QoS) requirements in a two-hop multiple-input multiple-output (MIMO) network with a single nonregenerative relay is considered. As shown by Y. Rong [“Multihop nonregenerative MIMO relays: QoS considerations,” IEEE Trans. Signal Process., vol. 59, no. 1, pp. 209-303, 2011] in [1], the optimal processing matrices for both linear and nonlinear transceiver architectures lead to the diagonalization of the source-relay-destination channel so that the power minimization problem reduces to properly allocating the available power over the established links. Unfortunately, finding the solution of this problem is numerically difficult as it is not in a convex form. To overcome this difficulty, existing solutions rely on the computation of upper- and lower-bounds that are hard to obtain or require the relaxation of the QoS constraints. In this work, a novel approach is devised for both linear and nonlinear transceiver architectures, which allows to closely approximate the solutions of the nonconvex power allocation problems with those of convex ones easy to compute in closed-form by means of multistep procedures of reduced complexity. Computer simulations are used to assess the performance of the proposed approach and to make comparisons with alternatives.

A novel prefiltering technique for downlink transmissions in TDD MC-CDMA systems

We discuss a prefiltering technique for interference mitigation in the downlink of a time division duplex (TDD) multicarrier code-division multiple access (MC-CDMA) system. The base station (BS) is equipped with multiple transmit antennas, and channel state information (CSI) is obtained at the transmitter side by exploiting the channel reciprocity between uplink and downlink transmissions. The prefiltering coefficients are designed so as to minimize a proper cost function that depends on the signal-to-interference-plus-noise ratios (SINRs) at the mobile terminals (MTs). The resulting scheme allows using a simple despreading receiver, thereby eliminating the need for channel estimation and equalization. Numerical results show the advantages of the proposed scheme over some existing solutions.

Energy-Aware Competitive Power Allocation for Heterogeneous Networks Under QoS Constraints

This work proposes a distributed power allocation scheme for maximizing energy efficiency in the uplink of OFDMA-based HetNets where a macro-tier is augmented with small cell access points. Each user equipment (UE) in the network is modeled as a rational agent that engages in a non-cooperative game and allocates its available transmit power over the set of assigned subcarriers to maximize its individual utility (defined as the users throughput per Watt of transmit power) subject to a target rate requirement. In this framework, the relevant solution concept is that of Debreu equilibrium, a generalization of the concept of Nash equilibrium. Using techniques from fractional programming, we provide a characterization of equilibrial power allocation profiles. In particular, Debreu equilibria are found to be the fixed points of a water-filling best response operator whose water level is a function of rate constraints and circuit power. Moreover, we also describe a set of sufficient conditions for the existence and uniqueness of Debreu equilibria exploiting the contraction properties of the best response operator. This analysis provides the necessary tools to derive a power allocation scheme that steers the network to equilibrium in an iterative and distributed manner without the need for any centralized processing. Numerical simulations are used to validate the analysis and assess the performance of the proposed algorithm as a function of the system parameters.