2D Beamforming algorithms (LMS, NLMS RLS and CM)

1. KOCAELI UNIVERSITY
Graduate School of
Natural and Applied Sciences
Prepared By: Mohammed ABUIBAID
Email: m.a.abuibaid@gmail.com
Electronic and Communication Engineering
Adaptive Beam-Forming
AcademicYear
2015/2016

2. The radiated energy in direction to UEs
are much stronger than the other
parts which is not directed to UEs.
Motivation (Why we need Beam-Forming ?)
The radiated energy in almost same
amount in all direction but a large
portions of energy not directed to
those UEs is wasted

3. Technologies for BeamForming
Switched Array Antenna
 This technique changes the beam
pattern by switching on/off
antenna selectively from the array
of a antenna system.
 Used in WPAN applications
DSP Based Phase Manipulation
 This technique changes the beam
pattern by changing the phase of
the signal going through each
antenna.
 Used in military applications of
SONAR and RADAR.
Beamforming by Precoding
 This technique changes the beam
pattern by applying a specific
precoding matrix.
 Used in 3GPP LTE, WiMax.

4. Basic Concept:
Phased Array Beam-Forming
 Phased Array is a directive antenna made with
individual radiating sources (several units to
thousands of elements).
 Radiating Elements might be: dipoles, open-
ended waveguides, slotted waveguides, micro-
strip antennas, helices, spirals etc.
 The Shape and Direction of pattern is
determined by:
1. Number of Radiating Elements
2. Relative Phases and Amplitudes applied to
each radiating element
3. Spacing between radiating elements
4. Operating Frequency

5. Generic Adaptive
Antenna Array System
For optimal transmission/reception of the
desired signal d, an adaptive update of the
Weight Vector W is needed to steer spatial
filtering beam to the target’s time-varying
DOA and thus get rid of interferers.
Adaptive Beamforming Schemes:
1. Least Mean Squares (LMS) Algorithm
2. Normalized LMS Algorithm
3. Recursive Least Square (RLS) Algorithm
4. Constant Modulus (CM) Algorithm

6. General Classifications Of Adaptive Array Algorithms
Non-blind Adaptive Algorithms
rely on statistical knowledge
about the transmitted signal in
order to converge to a solution.
Blind Adaptive Algorithms
do not require prior training, and
hence they are referred to as
“blind” algorithms.

7. Least Mean Squares (LMS) Algorithm
LMS Algorithm Summary
The LMS algorithm for a 𝑝 𝑡ℎorder algorithm can be
summarized as:
Parameters: 𝑝 = filter order
𝜇 = step size
Initialization: ℎ 0 = 𝑧𝑒𝑟𝑜𝑠(𝑝)
Computation: For 𝑛 = 0,1,2, . . .
𝑥 𝑛 = [𝑥 𝑛 , 𝑥 𝑛 − 1 , . . . , 𝑥 𝑛 − 𝑝 + 1 ] 𝑇
𝑒 𝑛 = 𝑑 𝑛 − ℎ 𝐻(𝑛) 𝑥 𝑛
ℎ 𝑛 + 1 = ℎ 𝑛 − 𝜇𝑒∗ 𝑛 𝑥 𝑛
Advantages & DisAdvantages of LMS algorithm:
1. Simplicity in implementation
2. Stable and robust performance against different
signal conditions
3. Slow convergence (due to eigenvalue spread)

8. Adaptive Beam-Forming by LMS Algorithm
Polar Beam Pattern X-Y Beam Pattern

9. Error and Weight Vector Convergence by LMS Algorithm

10. Error Performance
Adaptive Beam-Forming by LMS
Algorithm

11. Normalized LMS Algorithm
NLMS Algorithm Summary
The NLMS algorithm for a 𝒑 𝒕𝒉
order algorithm can be summarized as:
Parameters: 𝑝 = filter order
𝜇 = step size
Initialization: ℎ 0 = 𝑧𝑒𝑟𝑜𝑠(𝑝)
Computation: For 𝑛 = 0,1,2, . . .
𝑥 𝑛 = [𝑥 𝑛 , 𝑥 𝑛 − 1 , . . . , 𝑥 𝑛 − 𝑝 + 1 ] 𝑇
𝑒 𝑛 = 𝑑 𝑛 − ℎ 𝐻
(𝑛) 𝑥 𝑛
ℎ 𝑛 + 1 = ℎ 𝑛 −
𝜇𝑒∗
𝑛 𝑥 𝑛
𝑥 𝐻 𝑛 𝑥 𝑛
Improvements on ‘Pure’ LMS algorithm:
 LMS algorithm is sensitive to the scaling of its input 𝑥 𝑛
 Choosing a learning rate 𝜇 that guarantees stability of
LMS algorithm is impossible.
 NLMS Algorithm solves this problem by normalizing with
the power of the input, thereby converging faster than
LMS

12. Polar Beam Pattern X-Y Beam Pattern
Adaptive Beam-Forming by NLMS Algorithm

13. Error and Weight Vector Convergence by NLMS Algorithm

14. Error Performance
Adaptive Beam-Forming by NLMS
Algorithm

15. Recursive Least Square (RLS) Algorithm
RLS Algorithm Summary
The RLS algorithm for a 𝒑 𝒕𝒉
order RLS filter can be
summarized as:
Parameters: 𝑝 = filter order
𝜆 = forgetting factor
𝛿 = value to initialize 𝑷 0
Initialization : 𝑤 𝑛 = 0
𝑥 𝑘 = 0, 𝑘 = −𝑝, . . . , −1
𝑑 𝑘 = 0, 𝑘 = −𝑝, . . . , −1
𝑷 0 = 𝛿−1
𝐼 𝑝×𝑝
Advantages & DisAdvantages of RLS algorithm:
 No need to invert matrices, thereby saving computational
power.
 It provides intuition behind its results.
 Faster than LMS and NLMS but more complex
Computation: For 𝑛 = 0,1,2, . . .
𝑥 𝑛 = [𝑥 𝑛 , 𝑥 𝑛 − 1 , . . . , 𝑥 𝑛 − 𝑝 ] 𝑇
𝛼 𝑛 = 𝑑 𝑛 − 𝑥 𝑇(𝑛) 𝑤 𝑛 − 1
𝒈 𝑛 =
𝑷 𝑛 − 1 𝑥∗ 𝑛
𝜆 + 𝑥 𝑇 𝑛 𝑷 𝑛 − 1 𝑥∗ 𝑛
𝑷 𝑛 = 𝜆−1 𝑷 𝑛 − 1 − 𝑔 𝑛 𝑥 𝑇(𝑛)𝜆−1 𝑷 𝑛 − 1
w 𝑛 = 𝑤 𝑛 − 1 − 𝛼(𝑛) 𝑔 𝑛

16. Polar Beam Pattern X-Y Beam Pattern
Adaptive Beam-Forming by RLS Algorithm

17. Error and Weight Vector Convergence by RLS Algorithm

18. Error Performance
Adaptive Beam-Forming by RLS
Algorithm

19. Constant Modulus (CM) Algorithm
CM Algorithm Summary
 Used for blind equalization of signals that have a constant
modulus such as MSK signal.
 It updates the weight coefficients exactly as LMS algorithm
 The error is defined by
𝑒 𝑛 = 1 − 𝑦 𝑛 2
− 𝑦∗
𝑛
Advantages:
 It only needs the instantaneous amplitude of the array output
𝑦 𝑛 , thereby, No synchronization is required.
 Simple to implement.
Dis-Advantages:
 Limited Applications since it valid only for constant modulus
Signals
Non-Constant Modulus
source constellation
(16-QAM)
CM source
Constellation
(4-PSK)

20. Polar Beam Pattern X-Y Beam Pattern
Adaptive Beam-Forming by CM Algorithm

21. Error and Weight Vector Convergence by CM Algorithm

22. Eye-Diagram Performance
Adaptive Beam-Forming by CM Algorithm
Transmitted Signal Received Signal before BF Received Signal After BF

23. Motivation to 3D Beam-Forming with
Full Dimension MIMO

24. Agenda
1. Introduction Videos about LTE AP Pro
2. Overview on LTE and 4.5 G Evolution Around the World
3. LTE Advance Pro: Enhancements
4. LTE Advance Pro: New Use Cases
5. Case Study: Turkey’s Mobile Operators Evolution towards 4.5 G
6. Summary of LTE Advance Pro
7. MATLAB Simulation: 2D Beamforming algorithms (LMS, NLMS RLS and CM)
8. References

25. References
[1] http://www.dailysabah.com/technology/2015/08/26/turkeys-45g-mobile-technology-tender-concludes-with-a-record-bid-
of-396-billion
[2] http://www.huawei.com/en/news/2016/2/Huawei-Opened-Massive-Commercial-Use-Era-of-45G
[3] http://www.huawei.com/en/news/2016/5/Huawei-Helps-Turkey-with-45G
[4] White paper: LTE-Advanced Pro Pushing LTE capabilities towards 5G, Nokia Solutions and Networks
[5] White paper: Nokia Active Antenna Systems: A step-change in base station site performance, Nokia Solutions and Networks
[6] Ericsson White paper: LTE release 13, Uen 284 23-8267 | April 2015 ,
[7] Leading the path towards 5G with LTE Advanced Pro January 2016 Qualcomm Technologies, Inc.
[8] Progress on LAA and its relationship to LTE-U and MulteFire™ Qualcomm Technologies, Inc. February 22, 2016
[9] Mobile technology shares: 2020 forecast, Global mobile Suppliers Association (GSA), March 3, 2016.
[10] Global 4.5G Development presented in Turkey 4.5G Industry Summit on May 10, 2016 – Istanbul, Turkey
[11] LTE MTC: Optimizing LTE Advanced for Machine-Type Communications, Qualcomm Technologies, Inc. November 2014

26. Mohammed Abuibaid
Live & Breathe Wireless