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1325 results in Communications, Information Theory and Security

Page 24 of 67

  • 4 - Power Allocation in MIMO Systems

  • Rakhesh Singh Kshetrimayum, Indian Institute of Technology, Guwahati
  • Book:
    Fundamentals of MIMO Wireless Communications
    Published online:
    23 July 2017
    Print publication:
    17 April 2017, pp 70-79

  • Summary

    Introduction

    Since using SVD, we can decompose a MIMO channel into RH parallel Gaussian channels, where RH is the rank of the MIMO channel matrix, we will use the knowledge on the capacity of the parallel Gaussian channel (see Appendix C) to find the capacity of a MIMO channel for uniform and adaptive power allocation scheme. Uniform power allocation is employed when the channel state information (CSI) is available at the receiver but not at the transmitter (open loop MIMO system). We can use adaptive power allocation based on Water-filling algorithm when CSI is available at the receiver as well as the transmitter (closed loop MIMO system). We will also discuss near optimal power allocation for high and low SNR cases.

    Note that power allocation plays a significant role in deciding MIMO capacity. Power allocation was not an important issue in SISO since only single antenna was employed at the transmitter and receiver. Usually we allocate all the power to the single transmit antenna. But for MIMO it is one of the most important factors for increasing capacity. We have numerous antennas at the transmitter and receiver for MIMO case. The fundamental question is how much power we allocate to each transmit antennas. Hence if we allot power equally to all transmit antennas or unequally to each transmit antenna, capacity of the MIMO channel will be definitely different. If this is the case, then how we optimally allocate power to MIMO channels can be considered as an optimization problem to maximize capacity. To allocate power adaptively we need the CSI at the transmitter, also since power allocation is done at the transmitter. Intuitively we will allocate more power to better channels than the bad channels. We may not allocate any power at all to some of the worst channels. We will discuss these in detail in the following sections. In practical scenarios, we can allocate power near optimally for MIMO channels for two cases: high and low SNR regimes.

    Uniform power allocation

    The capacity indicates the best viable transmission data rate over the channel for miniscule probability of error. Shanon provided the expression of the achievable communication rate of a channel with noise (C. E. Shanon, 1948).

  • Appendix G - An Introduction to Game Theory

  • Rakhesh Singh Kshetrimayum, Indian Institute of Technology, Guwahati
  • Book:
    Fundamentals of MIMO Wireless Communications
    Published online:
    23 July 2017
    Print publication:
    17 April 2017, pp 342-346

  • Summary

    Introduction

    Game theory presents a formal analysis of interaction among a group of players in a game. In game theory, the action of player directly affects the other players. There are two types of games:

  • (a) Cooperative game: Player form alliance to bring the result of the game in his/her favour.

  • (b) Non-cooperative game: Optimal strategy for such game is that leads to Nash equilibrium, a term coined after the Nobel Laureate John Nash. Any player cannot gain from varying un-alterably his/her strategy if the strategy of all other players is fixed. An action profile is a vector of player's actions. A Nash equilibrium is an action profile in which each action is the best response to the actions of all the other players. Nash equilibrium is a stable operating or equilibrium point. It means that there is no payoff for any player in a finite game to vary strategy when all the other players pursue the equilibrium policy. The learning process can be cast as a repeated stochastic game (i.e., recast version of a one-shot game). Every player gets or knows the past behavior of the other players, which may influence the present decision to be made. The job of a player is to choose the best mixed strategy, having the knowledge of mixed strategies of all other players in the game. The mixed strategy of a player is a RV whose values are the pure strategies of that player.

    • An example from wireless sensor network:

    For instance, in wireless sensor network, a game needs three components (S. K. Das et al., 2004):

  • (a) Players (sensor nodes in the network)

  • (b) Strategy (criteria for selection of actions of players)

  • (c) Utility (payoff) function is the performance metric.

    • Let us assume a packet is sent from a source node (SN) to a destination node (DN) through an intermediate node (IN). IN may forward the packet to the DN by using the following criteria:

  • (a) Reputation: Have IN and DN made enough reputation to trust and co-operate each other to forward the packet?

  • (b) Distance: The farther are the two nodes, the more they don't trust each other.

  • (c) Traffic: Have IN and DN a joint operation history? Can they trust each other?

Fundamentals of MIMO Wireless Communications
  • Rakhesh Singh Kshetrimayum
  • Published online:
    23 July 2017
    Print publication:
    17 April 2017
  • Written in an easy-to-follow, tutorial style, this complete guide will allow students to quickly understand the key principles, techniques and applications of MIMO wireless communications. Important concepts such as MIMO channel models, power allocation and channel capacity, space-time codes, MIMO detection and antenna selection are covered in detail, providing practical insights into the world of modern telecommunication systems. The most up-to-date techniques are explained, with examples including spatial modulation, MIMO-based cooperative communications, large-scale MIMO systems, massive MIMO and space-time block coded spatial modulation. Supported by numerous solved examples, review questions, MATLAB problems and lecture slides, and including all the necessary mathematical background, this is an ideal text for students taking graduate, single-semester courses in wireless communications.

  • 11 - Antenna Selection and Spatial Modulation

  • Rakhesh Singh Kshetrimayum, Indian Institute of Technology, Guwahati
  • Book:
    Fundamentals of MIMO Wireless Communications
    Published online:
    23 July 2017
    Print publication:
    17 April 2017, pp 245-269

  • Summary

    Introduction

    Multiple-input multiple-output (MIMO) systems’ capacity increases and the bit error rate minimizes with the number of antennas as compared to single-input single-output (SISO) system. But, they have higher fabrication cost and energy consumption due to multiple radio frequency (RF) chains. An RF chain usually has low noise amplifier, frequency converters, analog–digital and digital–analog converters, filters, etc. A dedicated RF chain is needed for every antenna which makes implementation cost and hardware complexity higher. Antenna selection minimizes this by using lesser number of RF chains and by connecting selected antennas with RF chains with the help of switches. Select the best set of antennas at the transmitter or receiver so as to maximize the channel capacity or received signal-to-noise ratio (SNR). In the next section, we will discuss about the transmit antenna selection (also called as hard antenna selection) over fading channels. Then we will discuss about the soft antenna selection for closely spaced antennas. Then we will briefly discuss about spatial modulation and combine spatial modulation with antenna selection. In spatial modulation, there are two information bearing units: (a) Transmit antenna index and (b) Symbol from signal constellation, which is transmitted from antenna corresponding to the selected transmit antenna index. It is a relatively new MIMO technique, which was proposed R. Mesleh et al. (2008). Some of the advantages are (a) higher capacity (b) reduced hardware complexity and (c) avoidance of transmit antenna synchronization. One of the problems with spatial modulation is that the link for the selected antenna may be down, and then the performance of the spatial modulation is worst. In order to overcome this, one can do antenna selection before applying spatial modulation. Select a subset of antenna with the best links and apply spatial modulation on those selected antennas. As reported by B. Kumbhani et al., (2014), there is significant performance improvement in MIMO systems which combine antenna selection with spatial modulation.

    Transmit antenna selection (TAS) over fading channels

    We have considered a MIMO system with only one RF chain at the transmitter as depicted in Fig. 11.1. This kind of antenna selection is also called as hard antenna selection.

Page 24 of 67