1. Effective Noise Figure in Hybrid BF system
Month Year
doc.: IEEE yy/xxxxr0
July 2015
Effective Noise Figure in Hybrid BF system
Date: YYYY-MM-DD
Authors:
Ji-Ho Lee, Korea University
John Doe, Some Company

2. Month Year
doc.: IEEE yy/xxxxr0
July 2015
Abstract
This contribution presents the theoretical results of noise figure (NF) and gain in hybrid beamforming systems.
Ji-Ho Lee, Korea University
John Doe, Some Company

3. July 2015
Motivation
In hybrid beamforming systems, the received signals from multiple antennas are phase corrected by phase shifter and then combined in RF combiner, usually before down-converting at RX.
The additional RF blocks (i.e., phase shifter and combiner) are added to RF chain, which increases noise figure.
Note that the RF combiner has multiple input signals and single output signals (multi-to-one RF path).
In this case, the NF should be appropriately considered for the calculation of carrier to noise ratio (CNR).
Ji-Ho Lee, Korea University

4. Block Diagram of Hybrid Beamforming
Month Year
doc.: IEEE yy/xxxxr0
July 2015
Block Diagram of Hybrid Beamforming
Phase
shifter
LNA
Down-converting
Low-pass filter
ADC
Baseband
Space-time
processing
Down-converting
Low-pass filter
LNA
Phase
shifter
ADC
The received signals from each antenna are phase-shifted by phase shifter and combined by combiner after LNA.
At baseband, the conventional MIMO space-time processing is performed for multiplexing gain or/and diversity gain.
Ji-Ho Lee, Korea University
John Doe, Some Company

5. Noise Figure Calculation
Month Year
Noise Figure Calculation
Phase
shifter
LNA
𝐺 𝑘 , 𝐹 𝑘
𝐺 𝑘 1 , 𝐹 𝑘 1
𝐺 𝑘 2 , 𝐹 𝑘 2
𝑘 𝑡ℎ RF chain
Equivalent 𝑘 𝑡ℎ RF chain
𝐺 𝑘 𝑖 : 𝑖 𝑡ℎ RF block’s gain of 𝑘 𝑡ℎ RF path
𝐹 𝑘 𝒊 : 𝑖 𝑡ℎ RF block’s noise figure of 𝑘 𝑡ℎ RF path
𝐺 𝑘 : Overall gain of 𝑘 𝑡ℎ RF path
𝐹 𝑘 : Overall noise figure of 𝑘 𝑡ℎ RF path
𝐹 𝑘 = 𝐹 𝑘 𝐹 𝑘 2 −1 𝐺 𝑘 𝐹 𝑘 3 −1 𝐺 𝑘 1 𝐺 𝑘 2 +⋯
Overall Noise Figure
(Friis Equation)
Overall Gain
𝐺 𝑘 = 𝐺 𝑘 1 𝐺 𝑘 2 ⋯ 𝐺 𝑘 𝑁
John Doe, Some Company

6. Multi-to-One Path system
Month Year
doc.: IEEE yy/xxxxr0
July 2015
Multi-to-One Path system
Combiner
𝐺 1 , 𝐹 1 , 𝜃 1
𝑃 𝑠 in,1 , 𝑃 𝑛 in,1
𝑃 𝑛 out,1
𝛼 1
𝑃 𝑠 in,2 , 𝑃 𝑛 in,2
𝑃 𝑛 out,2
𝛼 2
𝐺 2 , 𝐹 2 , 𝜃 2
Array output 𝑃 𝑠 out , 𝑃 𝑛 out
𝛼 𝑁
𝑃 𝑠 in,𝑁 , 𝑃 𝑛 in,𝑁
𝑃 𝑛 out,𝑁
𝐺 𝑁 , 𝐹 𝑁 , 𝜃 𝑁
𝑃 𝑠 in,𝑘 : Input signal power of 𝑘 𝑡ℎ RF path
𝑃 𝑛 in,𝑘 : Input noise power of 𝑘 𝑡ℎ RF path
𝐺 𝑘 : Overall gain of 𝑘 𝑡ℎ RF path
𝐹 𝑘 : Overall noise figure of 𝑘 𝑡ℎ RF path
𝜃 𝑘 : Insertion phase shift of 𝑘 𝑡ℎ RF path
𝑃 𝑛 out,𝑘 : Output noise power of 𝑘 𝑡ℎ RF path
𝛼 𝑘 : Amplitude combining coefficient of 𝑘 𝑡ℎ RF path
𝑃 𝑠 out : Output signal power of combiner
𝑃 𝑛 out : Output noise power of combiner
Ji-Ho Lee, Korea University
John Doe, Some Company

7. Equivalent Single-Path system
Month Year
doc.: IEEE yy/xxxxr0
July 2015
Equivalent Single-Path system
𝑃 𝑠 in,1 , 𝑃 𝑛 in,1
𝐺 1 , 𝐹 1 , 𝜃 1
𝛼 1
𝑃 𝑠 in,2 , 𝑃 𝑛 in,2
𝑃 𝑠 in,eff , 𝑃 𝑛 in,eff
𝐺 eff , 𝐹 eff
Array output 𝑃 𝑠 out,eff , 𝑃 𝑛 out,eff
𝐺 2 , 𝐹 2 , 𝜃 2
𝛼 2
Array output 𝑃 𝑠 out , 𝑃 𝑛 out
𝐺 eff : Effective overall gain of single RF path
𝐹 eff : Effective overall noise figure of single RF path
𝑃 𝑠 in,eff , 𝑃 𝑠 out,eff : Effective signal power of single RF path
𝑃 𝑛 in,eff , 𝑃 𝑛 out,eff : Effective noise power of single RF path
𝑃 𝑠 in,𝑁 , 𝑃 𝑛 in,𝑁
𝛼 𝑁
𝐺 𝑁 , 𝐹 𝑁 , 𝜃 𝑁
For an analysis purpose, a multi-to-one path system is converted into an equivalent single-path system.
We assume that the total input, output power of multi-to-one-path system and equivalent single-path system are identical, such that the above two figures are equivalent.
Ji-Ho Lee, Korea University
John Doe, Some Company

8. Array output 𝑃 𝑠 out,eff , 𝑃 𝑛 out,eff
Month Year
doc.: IEEE yy/xxxxr0
July 2015
Effective Gain
𝑃 𝑠 in,eff , 𝑃 𝑛 in,eff
𝐺 eff , 𝐹 eff
Array output 𝑃 𝑠 out,eff , 𝑃 𝑛 out,eff
The effective gain of the array system is given to be [1]
If all signal paths are identical ( 𝐺 1 = 𝐺 2 =⋯ 𝐺 𝑁 =𝐺), we have
If all the 𝛼 𝑘 are 1 ( 𝛼 1 = 𝛼 2 =⋯= 𝛼 𝑁 =1), we have
𝐺 𝑒𝑓𝑓 = 𝑃 𝑠 out,eff 𝑃 𝑠 in,eff = 1 𝑁 ∙ 𝑘=1 𝑁 𝐺 𝑘 ∙ 𝑒 𝜃 𝑘 −𝑗(𝑘−1)∆𝜃 ∙ 𝛼 𝑘 2
𝐺 𝑒𝑓𝑓 = 𝐺 𝑁 ∙ 𝑘=1 𝑁 𝛼 𝑘 2
𝐺 𝑒𝑓𝑓 =𝐺
Ji-Ho Lee, Korea University
John Doe, Some Company

9. Effective Noise Figure
Month Year
doc.: IEEE yy/xxxxr0
July 2015
Effective Noise Figure
𝑃 𝑠 in,eff , 𝑃 𝑛 in,eff
𝐺 eff , 𝐹 eff
Array output 𝑃 𝑠 out,eff , 𝑃 𝑛 out,eff
The effective noise figure of the array system is given to be [1]
If all signal paths are identical ( 𝐹 1 = 𝐹 2 =⋯= 𝐹 𝑁 =𝐹), we have
If all the 𝛼 𝑘 are 1 ( 𝛼 1 = 𝛼 2 =⋯= 𝛼 𝑁 =1), we have
𝐹 𝑒𝑓𝑓 = 𝑃 𝑛 out,eff 𝐺 eff ∙ 𝑃 𝑛 in,eff = 𝑁∙ 𝑘=1 𝑁 𝐺 𝑘 ∙ 𝐹 𝑘 ∙ 𝛼 𝑘 𝑘=1 𝑁 𝐺 𝑘 ∙ 𝑒 𝜃 𝑘 −𝑗(𝑘−1)∆𝜃 ∙ 𝛼 𝑘 2
𝐹 𝑒𝑓𝑓 =𝐹∙𝑁∙ 𝑘=1 𝑁 𝛼 𝑘 𝑘=1 𝑁 𝛼 𝑘 2
𝐹 𝑒𝑓𝑓 =𝐹
Ji-Ho Lee, Korea University
John Doe, Some Company

10. Month Year
doc.: IEEE yy/xxxxr0
July 2015
Conclusion
We contribute to calculating the noise figure and gain in hybrid beamforming system.
Ji-Ho Lee, Korea University
John Doe, Some Company

11. Month Year
doc.: IEEE yy/xxxxr0
July 2015
References
Junghyun Kim, Jinho Jeong, and Sanggeun Jeon, "Improvement of Noise Performance in Phased-Array Receivers", ETRI Journal, vol. 33, no.2, pp , April (2011)
Ji-Ho Lee, Korea University
John Doe, Some Company