On the Energy Efficiency of Massive MIMO Systems With LowResolution ADCs and Lattice Reduction Aided Detectors
Abstract
:1. Introduction
 We investigate the implementation of LRSIC detectors and their improvements for massive MIMO systems with lowresolution ADCs;
 We analyze the transmission power required for achieving a target BER, the power required for signal detection, and also the power consumption due to the ADCs given the system configuration;
 We analyze and compare the EE for several different MIMO detectors under a universal systemlevel power consumption model, and discuss the influence of the number of antennas, the ADC resolution and also the signal processing algorithms on the performance.
2. System Model
2.1. MIMO With LowPrecision ADC
2.2. Additive Quantization Noise Model (AQNM)
3. MIMO Detection
3.1. MMSE Detector
3.2. LRSIC Detector
3.3. Modified MultiBranch LRSIC (MMBLRSIC)
4. Energy Efficiency
4.1. Transmission Power
4.2. Power Consumption by Signal Detection
4.3. ADC Power Consumption
4.4. Energy Efficiency
Algorithm 1 Evaluation of Energy Efficiency of MIMO Systems Employing the LRSIC Detector 
Input: Number of UEs K, number of receiver antennas N, radius of the cell ${d}_{max}$, target BER, computational efficiency ${L}_{\mathrm{BS}}$ 
Output: Energy efficiency: $\mathrm{EE}$ 

5. Simulation Results and Discussion
5.1. BER vs. SNR
5.2. EE Performance
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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K  number of UEs  N  number of receiver antennas  b  number of quantization bits 
$\Delta $  quantization step  ${\rho}_{n}$  scaling factor for the nth antenna  ${d}_{k}$  distance between UEk and the BS 
${\phi}_{k}$  largescale fading  ${\sigma}^{2}$  noise variance  $\lambda $  number of coherence blocks 
$\mathbf{H}$  channel matrix  $\mathbf{P}$  power of the UEs  $\mathbf{n}$  additive white Gaussian noise (AWGN) 
$\mathbf{x}$  transmitted signal vector  $\mathsf{\Psi}$  scaling matrix  ${\mathbf{n}}_{q}$  quantization noise 
${\mathbf{y}}_{q}$  quantized received signal  ${\mathbf{R}}_{{\mathbf{n}}_{q}}$  covariance matrix of the quantization noise  $\mathbf{W}$  weight matrix of detector 
$\Pi $  permutation matrix  $\mathbf{R}$  received signal after QR decomposition  $\xi $  noise variance after QR decomposition 
$\mathbf{y}$  received signal  $\mathbf{G}$  channel matrix after QR decomposition  ${\mathbf{y}}^{\prime}$  scaled received signal 
$\overline{\mathbf{G}}$  extended channel matrix  $\mathbf{T}$  transformation matrix  $\tilde{\mathbf{G}}$  latticereduced channel matrix 
b  1  2  3  4  5 
$\beta $  0.3634  0.1175  0.03454  0.009497  0.002499 
$\mathbf{Detection}$  ${\mathbf{C}}_{\mathbf{detection}}$  ${\mathbf{C}}_{\mathbf{QR}}$  ${\mathbf{C}}_{{\mathbf{T}}^{1}}$  ${\mathbf{C}}_{\mathbf{filter}}$ 

$\mathrm{MMB}\mathrm{LR}\mathrm{SIC}$  $8KN+40{K}^{2}L+8{K}^{2}$  $8{K}^{2}(N\frac{K}{3})$  $8({K}^{3}+{K}^{2})$  $L[8{K}^{3}+8K+{\sum}_{t=1}^{K}(4{t}^{3}+8{t}^{2}+12Kt)]$ 
$\mathrm{LR}\mathrm{SIC}$  $8KN+40{K}^{2}$  $8{K}^{2}(N\frac{K}{3})$  $8({K}^{3}+{K}^{2})$  $8{K}^{3}+8K+{\sum}_{t=1}^{K}(4{t}^{3}+8{t}^{2}+12Kt)$ 
$\mathrm{MMSE}$  $8KN$  0  0  $4{K}^{3}+8{K}^{2}+12{K}^{2}N+4KN$ 
Parameter  Value 

Minimum distance: ${d}_{\mathrm{min}}$  35 m 
Largescale fading: ${\beta}_{k}$  ${10}^{3.53}/{d}_{k}^{3.76}$ 
Transmission bandwidth: B  $20\phantom{\rule{0.166667em}{0ex}}\mathrm{MHz}$ 
Channel coherence time: ${T}_{C}$  $10\phantom{\rule{0.166667em}{0ex}}\mathrm{ms}$ 
Channel coherence bandwidth: ${B}_{C}$  180 $\mathrm{kHz}$ 
Total noise power: $B{\sigma}^{2}$  −96 $\mathrm{dBm}$ 
$\mathrm{FOM}$  $1432.1\mathrm{fJ}/\mathrm{conv}\mathrm{step}$ 
Uplink PA efficiency at the UEs: $\eta $  0.3 
Sampling rate: ${f}_{s}$  $20\phantom{\rule{0.277778em}{0ex}}\mathrm{MHz}$ 
Carrier frequency: ${f}_{c}$  $2\phantom{\rule{0.277778em}{0ex}}\mathrm{GHz}$ 
Power per RF chain the BS: ${\mathrm{P}}_{\mathrm{BS}}$  $0.4$ W 
Power per RF chain the UE: ${\mathrm{P}}_{\mathrm{UE}}$  $0.1$ W 
${\mathrm{P}}_{\mathrm{FIX}}$  18 W 
${\mathrm{P}}_{\mathrm{SYN}}$  2 W 
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Xiao, Z.; Zhao, J.; Liu, T.; Geng, L.; Zhang, F.; Tong, J. On the Energy Efficiency of Massive MIMO Systems With LowResolution ADCs and Lattice Reduction Aided Detectors. Symmetry 2020, 12, 406. https://doi.org/10.3390/sym12030406
Xiao Z, Zhao J, Liu T, Geng L, Zhang F, Tong J. On the Energy Efficiency of Massive MIMO Systems With LowResolution ADCs and Lattice Reduction Aided Detectors. Symmetry. 2020; 12(3):406. https://doi.org/10.3390/sym12030406
Chicago/Turabian StyleXiao, Zhitao, Jincan Zhao, Tianle Liu, Lei Geng, Fang Zhang, and Jun Tong. 2020. "On the Energy Efficiency of Massive MIMO Systems With LowResolution ADCs and Lattice Reduction Aided Detectors" Symmetry 12, no. 3: 406. https://doi.org/10.3390/sym12030406