Analysis of Energy Efficiency and Area Throughput in Large Scale MIMO Systems with MRT and ZF Precoding

Abstract

The large-scale multiple input multiple output (LS-MIMO) systems are equipped with a large number of antennas at the base station. These systems are capable of serving a larger number of user terminals, with massive gains in the form of energy and bandwidth efficiency. The energy efficiency of LS-MIMO system depends on the overall power consumption and data rate. In this paper, we have improved the energy efficiency of the LS-MIMO system by using maximum ratio transmission/combining and zero forced linear pre-coding schemes in single and multi-cell scenarios. We have jointly considered the uplink and downlink communications to propose an improved, more practical and more realistic power consumption model. The proposed model deliberates the power required for the power amplifier, linear processing and the circuit components at the base stations and user terminals. The outcome of this work provides a significant improvement in terms of energy efficiency and area throughput. The analytical results illustrate that the LS-MIMO systems achieve the maximum energy efficiency and area throughput wherein larger number of transmit antennas are installed at the base station to serve comparatively greater number of users terminals. The mathematical results depict the similar performance for imperfect channel state information in multi-cell setups. All aspects of power consumption during bidirectional communication are considered to provide precise results. Hence, the improvements in simulations results support the accuracy of the proposed model.

Appendix

The Optimized Number of Antennas (M) The optimized value of a number of LS-MIMO antennas (${\text{M}}^{\text{o}}$) can be calculated by using the following theorem.

$$ {\text{M}}^{\text{o}} = \left\{ {\left( {\uprho{\text{N}} - 1} \right) + {\text{e}}^{{{\text{W}}\left( {\uprho^{2} \left( {\frac{1}{e}\left( {\left( {{\text{P}}_{\text{PA}} +\upalpha_{1} } \right)/\upalpha_{2} } \right) + \left( {{\text{N}} - 1} \right)} \right) + 1} \right)}} } \right\}{\bigg/}\rho $$

(22a)

(22a) is extracted from Lambert W function. It is defined by the equation $x = W\left( x \right) e \wedge W\left( x \right)$ for any x $\in$ C, where e is the natural number [15]. $P_{PA}$ is given power in (13) that is the power consumption of amplifier. The values of $\upalpha_{1}$ and $\upalpha_{2}$ are the summations of circuit power of UT and BS given as (22a) and (22b)

$$ \upalpha_{1} = \left\{ {\left( {4 {\text{B}}\frac{{{\text{L}}^{\text{UL}} }}{{{\text{S}}_{CB}\Psi _{\text{UD}} }}} \right){\text{N}}^{2} + \left( {\frac{\text{B}}{{3{\text{S}}_{CB}\Psi _{\text{BS}} }}} \right){\text{N}}^{3} } \right\}\left\{ {\left( {{\text{P}}_{\text{fix}} + {\text{P}}_{\text{syn}} } \right) + \left( {{\text{P}}_{\text{UD}} } \right)} \right\}{\bigg/}{\text{N}} $$

(22b)

$$ \upalpha_{2} = \left\{ {\left( {{\text{B }}\left( {2 + 1/{\text{S}}_{CB} } \right)/\Psi _{\text{BS}} } \right){\text{N}} + \left( {{\text{B}}\left( {3 - 2{\text{L}}^{\text{DL}} } \right)/{\text{S}}_{CB}\Psi _{\text{BS}} } \right){\text{N}}^{2} + \left( {{\text{P}}_{\text{BS}} } \right)} \right\}{\bigg/}N $$

(22c)

The Optimized Transmit Power The optimized value of transmit power ($\uprho^{o}$) are also calculated by using Lambert function. Given as (23a)

$$ \uprho^{\text{o}} = \left\{ {{\text{e}}^{{{\text{W}}\left( {\uprho\left( {\frac{{\left( {{\text{M}} - {\text{N}}} \right) \left( {\upalpha_{1} + M\upalpha_{2} } \right)}}{\text{e}}\left( {\frac{\text{N}}{{{\text{P}}_{\text{PA}} }}} \right) + \frac{1}{\text{e}}} \right) + 1} \right)}} - \left( 1 \right)} \right\}{\bigg/}\uprho $$

(23a)

The value of ${\text{P}}_{\text{PA}}$ is given in (13) that is power consumption of amplifier. The values of $\upalpha_{1}$ and $\upalpha_{2}$ are the summations of circuit power of UT and BS given above. The value of transmit power can be calculated by multiplying the optimized value of transmit power ($\rho^{\text{o}}$) and $P_{PA}$ that is the power of amplifier $\left[ {P_{Tx}^{ZF} = \left( {\rho^{o} } \right) \left( { P_{PA} } \right)} \right]$.

The Optimized Value of N It is calculated by finding the roots of the following polynomial equation in (23b) [15].

$$ \left\{ {1 - \left( {2{\text{S}}_{CB} /\left( {{\text{L}}^{\text{DL}} + {\text{L}}^{\text{UL}} } \right)} \right) - \varLambda_{2} - 2 \varLambda_{1} + \left( {{\text{S}}_{CB} \varLambda_{1} /\left( {{\text{L}}^{\text{DL}} + {\text{L}}^{\text{UL}} } \right)} \right)} \right\} = 0 $$

(23b)

where

$$ \Lambda _{1} = \left\{ {\left( {\left( {{\text{P}}_{\text{s}} + {\text{P}}_{\text{t}} } \right) + {\text{P}}_{\text{PA}} } \right)/ \left( {\frac{\text{B }}{{3{\text{S}}_{CB}\Psi _{\text{BS}} }} + \left( {\frac{{{\text{MB}}\left( {3 - 2\uptau^{\text{DL}} } \right) }}{{{\text{S}}_{CB} {\text{N}}\Psi _{\text{BS}} }}} \right)} \right)} \right\} $$

(23c)

$$ \Lambda _{2} = \left( {\frac{{{\text{S}}_{CB} }}{{\left( {{\text{L}}^{\text{DL}} + {\text{L}}^{\text{UL}} } \right)}}\left( {\frac{{4 {\text{B L}}^{\text{UL}} }}{{{\text{S}}_{CB}\Psi _{\text{BS}} }} + \frac{{{\text{B }}\left( {\frac{2}{\text{N}} + \frac{\text{M}}{{{\text{NS}}_{CB} }}} \right)}}{{\Psi _{\text{BS}} }}} \right)} \right){\bigg/} \left( {\frac{\text{B }}{{3{\text{S}}_{CB}\Psi _{\text{BS}} }} \left( {\frac{{{\text{MB}}\left( {3 - 2\uptau^{\text{DL}} } \right) }}{{{\text{S}}_{CB} {\text{N}}\Psi _{\text{BS}} }}} \right)} \right) $$

(23d)