Bo Bernhardsson
Professor
bob@control.lth.se
Phone: +46 46 222 87 86
Fax: +46 46 13 81 18

My current main research interest is in combinations of control and communication. I also have a broad interest ranging from pure mathematics to industrial applications of control. I have a PhD in control (Lund 1992) and have been a professor in Automatic Control since 1999. During the years 2001-2010 I worked at Ericsson with mobile phone systems. From 2010 I am working full time as (ELLIIT) professor in Automatic Control at Lund University.

## Research

I am part of

• ELLIIT, a network organization for Information and Communication Technology (ICT) research at Linköping, Lund, Halmstad and Blekinge
• LCCC, the Lund center for Control of Complex Engineering Systems

The following is a list of main present and past research

### Collaboration with the European Spallation Source

Researchers: Bo Bernhardsson, Anders J Johansson (Dept. of Electrical and Information Technology), Rolf Johansson, Olof Troeng

Funding: European Spallation Source

The European Spallation Source will be a major user facility at which researchers from academia and industry will investigate scientific questions using neutron beams.

Neutron methods provide insights about the molecular building blocks of matter not available by other means. Applications include research in life science, soft condensed matter physics, chemistry of materials, fundamental particle physics and engineering materials. More info here.

#### RF Field Control

The neutrons are produced by colliding high-speed protons with a rotating tungsten target. The protons are accelerated by oscillating electro-magnetic fields in more than 150 radio-frequency cavities along the 482 meter long linear accelerator. In order to avoid defocusing of the beam (which leads to activation of the accelerator structure), it is important that the amplitude and phase of the field in every cavity are kept very close to their nominal values. In order to achieve this individual feedback loops with sampling frequencies of 10 MHz will be used to regulate the fields.

The layout of the ESS linear accelerator

The Department of Automatic Control is involved in modeling and controller design for the RF system through this group at the Department of Electrical and Information Technology.

Schematic description of the control problem for a single cavity

### Joint Positioning and Radio Channel Estimation

with Anders Mannesson (AC), Fredrik Tufvesson (EIT), Atif Yaqoob (EIT)

The idea is to combine information from gyros, accelerometers and compass sensors with radio channel estimation and to determine the fundamental properties of such schemes. The hope is to enable two technology advancements:

• a new method for significantly reduced drift in low cost navigation systems
• improved radio channel estimation for moving terminals

Initial research show promising result as presented in the licentiate thesis by Anders Mannesson and in this presentation

The work is based on angle of arrival estimation using antenna arrays which is a well studied problem with many different algorithms resolving the individual rays impinging on the array. However, less attention has been given to so called virtual array antennas where only one receiver element is used. By tracking the movement of the element, an array with properties similar to a stationary array with multiple elements is formed. By combining the IMU and the radio channel information, a map of the local radio environment can be obtained, such as in this picture illustrating the complex valued radio channel for three impinging planar radiowaves in a noise-free situation

Tightly coupled nonlinear state estimation algorithms between IMU signals and radio channel estimates are used to simultaneously estimate this map and obtain improved pose estimates.

The major challenge is to battle the drift in sensors and radio crystal oscillators. We work with both real-world measurements and simulations to evaluate performance. Initial experiments show promising results. The following figure shows performance (simulations left, real experiments right) with realistic radio and IMU imperfections. There is a dramatic improvement by including radio channel information compared to using dead reckoning, especially for movements longer than 10 seconds.

Our future research now focuses on improving radio channel estimation and prediction by adding IMU information and using motion models.

### Marine Vibrator Control

The goal is to model and control large loudspeakers, so called marine vibrators, that are used to generate acoustic underwater signals.

Performance requirements on out-of-band spectrum of the acoustic signal are achieved by careful characterisation of the dynamical behavior of the vibrators and use of frequenyc domain Iterative Learning Control (ILC). This has been found  to successfully reduce the impact of nonlinearities such as friction and backlash. A 40 dB suppression of out-of-band harmonics has been acheived in experiments (in air).

The project is funded by the Norwegian company PGS.

### Control with Communication Constraints

with Erik Johannesson, Ather Gattami, Anders Rantzer, Andrey Gulchak

Classical control theory assumes perfect communication, without limitations, between different parts of the control system and the process. The trend towards large-scale distributed systems makes it interesting to study the interplay between communication and control such as fundamental limitations of control performance arising from communication constraints.

In Erik Johanesson's PhD thesis several such situations are studied. We model the communication constraints as an signal to noise ratio (SNR) constraint for the communication channel. Such constraints give an incentive to perform coding and decoding of the transmitted signal in addition to the usual filtering and computation of control signals.

The problem of designing the controller, coder and decoder simultaneously is found to be solvable by convex optimization and spectral factorization giving efficient methods for their calculation.

The situation in the following figure with an SNR constraint on the channel is studied in

• E. Johannesson, A. Rantzer, B. Bernhardsson and A. Ghulchak, "Encoder and Decoder Design for Signal Estimation," in Proc. American Control Conference, Baltimore, USA, June 2010.
• E. Johannesson, A. Ghulchak, A. Rantzer and B. Bernhardsson, "MIMO Encoder and Decoder Design for Signal Estimation," in Proc. 19th Inter- national Symposium on Mathematical Theory of Networks and Systems, Budapest, Hungary, July 2010.
• E. Johannesson, "Signal Estimation over Channels with SNR Constraints and Feedback," in Proc. 18th IFAC World Congress, Milano, Italy, August 2011.

The main result is that if encoders and decoders are restricted to linear filters the optimal ones can be found by solving an extension of the Wiener filter equations

where R is in L_infinity and X in H_2. The first term is the same as in the classical Wiener filter design and the new last term, where sigma is the SNR constraint on the channel, describes the added cost of imperfect communciation.

Problems concerning feedback design is also studied as described in the following figure. Here the communication channel is modeled as having an SNR constraint with the added possibility of using also a perfect communication feedback channel (through the filter B). The joint design of coder C, decoder D, and feedback filter B is solved through convex optimization.

• E. Johannesson, A. Rantzer and B. Bernhardsson, "Optimal linear control for channels with signal-to-noise ratio constraints," in Proc. American Control Conference, San Francisco, CA, USA., June 2011.
• E. Johannesson, A. Rantzer and B. Bernhardsson, "A Framework for Lin- ear Control over Channels with Signal-to-Noise Ratio Constraints," 9th IEEE International Conference on Control & Automation, Santiago, Chile, December 2011.

Another line of research focuses on the impact of feedback for  communication under a delay constraint. In

I study the energy needed to transmit one bit of information over a Gaussian channel achieving a certain bit error rate. The setup in the following figure is used, with a constraint on the average expected energy of the sequence u=(u_1,...,u_N).

In the paper only the case N=2 is treated but similar techniques can be used to derive the result in the following figure for any N using dynamic programming (the needed work grows linearly with N).

The red curve for N=infinity is the well known Shannon limit.

### Real-time Control Systems with Delays

with Johan Nilsson and Björn Wittenmark

### Event-based Control

with Karl Johan Åström, Toivo Henningsson and Anton Cervin

### Iterative Learning Control

with Olof Sörnmo, Mahdi Ghezai and Bo Lincoln

### Dynamical Analysis of Harmonics in Electrical Systems

with Erik Möllerstedt and Henrik Sandberg

### Control of Liquid Slosh

with Mattias Grundelius

with Jaak Peetre

### Control of Hybrid Systems

with Jörgen Malmborg

### The Real Stability Radius and Real Perturbation Values

with Anders Rantzer and Qiu Li

### An Extension of Bohr's Inequality

with Lars Hörmander

Bohr's inequality states that if u(t) is a high-frequency signal in the sensethat u has no spectrum in [-R,R] and if du/dt is bounded then u is continuous and bounded by: R sup |u| <= pi/2 sup |du/dt|. In the paper

An Extension of Bohr's Inequality

we prove that when the spectrum of u is outside the disc |z| < R then a similar bound is valid for the Cauchy-Riemann operator

R sup |u| <= C sup |du/dx + idu/dy|

and we calculate the optimal constant C=2.903887282.. and the extremal u for this bound.

### Modeling and Analysis of Flow-Through Dialyzers

with Eduardo Martins and Gillis Johansson

## PhD Students

Currently I am supervisor or co-supervisor* for

## Teaching

I have taught the following courses

PhD courses
• Linear Systems 2014
• Game Theory 2014
• Linear Systems 2013
• Convex Optimization 2012, 2013
• Linear Systems II, 2010
• Robust Control 2007
• Control in Mobile Communication, 2004
• Game Theory 1999, 2000, 2006
• Tools in Control 1999
• Hybrid Control 1996
• Hilbert Space Theory 1995
• Non-Smooth Analysis 1995
• Stochastic Systems 1995
• Nonlinear Control Theory 1993
• Control Synthesis 1991, 1995, 2000, 2010
• H-infinity Control 1990
• Linear Systems 1989, 2009, 2007, 2009, 2010, 2013

Basic Education

• Predictive Control 2012
• Automatic Control Basic Course 2011, 2013
• Market-driven Systems (minor part of)
• Systems Engineering 2001
• Nonlinear Control and Servo Systems 1998, 1999

As a student I was also teaching assistant in different courses in Control, Mathematics and Telecommunication.

## Publications

Bibliometry (Google Scholar) is available here

My Erdös number is 3 (BoB -> Jaak Peetre -> Svante Jansson -> Erdös)

The following list is automatically generated and is unfortunately not complete

104 publications found.
Title Authors Year Type
Control of convex-monotone systems Anders Rantzer, Bo Bernhardsson 2014 Conf
On the Performance of Random Antenna Arrays for Direction of Arrival Estimation Muhammad Atif Yaqoob, Anders Mannesson, Bo Bernhardsson, Naveed Butt, Fredrik Tufvesson 2014 Conf
Optimal Virtual Array Length Under Position Imperfections Anders Mannesson, Bo Bernhardsson, Muhammad Atif Yaqoob, Fredrik Tufvesson 2014 Conf
Information and Control in Networks Giacomo Como, Bo Bernhardsson, Anders Rantzer (Eds.) 2014 book
PID Design by Convex-Concave Optimization Martin Hast, Karl Johan Åström, Bo Bernhardsson, Stephen P. Boyd 2013 Conf
Using a Gaussian Channel Twice Bo Bernhardsson 2013 Conf
Models and Methodology for Optimal Vehicle Maneuvers Applied to a Hairpin Turn Karl Berntorp, Björn Olofsson, Kristoffer Lundahl, Bo Bernhardsson, Lars Nielsen 2013 Conf
Direction of Arrival Estimation with Arbitrary Virtual Antenna Arrays using Low Cost Inertial Measurement Units Muhammad Atif Yaqoob, Fredrik Tufvesson, Anders Mannesson, Bo Bernhardsson 2013 Conf
Information and Control in Networks Giacomo Como, Bo Bernhardsson, Anders Rantzer (Eds.) 2013 book
Automatic Control 2011. Activity Report Eva Westin, Bo Bernhardsson (Eds.) 2012 Rep
Radio and IMU based indoor positioning and tracking Anders Mannesson, Muhammad Atif Yaqoob, Bo Bernhardsson, Fredrik Tufvesson 2012 Conf
A machine-learning approach to information extraction from cylinder pressure sensors Maria Henningsson, Bo Bernhardsson, Per Tunestål, Rolf Johansson 2012 Conf
Robust Team Decision Theory Ather Gattami, Anders Rantzer, Bo Bernhardsson 2012 Art
A Framework for Linear Control over Channels with Signal-to-Noise Ratio Constraints Erik Johannesson, Anders Rantzer, Bo Bernhardsson 2011 Conf
Optimal Linear Control for Channels with Signal-to-Noise Ratio Constraints Erik Johannesson, Anders Rantzer, Bo Bernhardsson 2011 Conf
Control Inside Mobile Phones Bo Bernhardsson 2010 Rep
MIMO Encoder and Decoder Design for Signal Estimation Erik Johannesson, Andrey Ghulchak, Anders Rantzer, Bo Bernhardsson 2010 Conf
Encoder and Decoder Design for Signal Estimation Erik Johannesson, Anders Rantzer, Bo Bernhardsson, Andrey Ghulchak 2010 Conf
Minimax Team Decision Problems Ather Gattami, Bo Bernhardsson 2007 Conf
Quaternary binary trilinear forms of norm unity Bo Bernhardsson, Fernando Cobos, Thomas Kuhn, Daniel Mondoc, Jaak Peetre 2006 Art
Frequency-Domain Analysis of Linear Time-Periodic Systems Henrik Sandberg, Erik Möllerstedt, Bo Bernhardsson 2005 Art
A Bode Sensitivity Integral for Linear Time-Periodic Systems Henrik Sandberg, Bo Bernhardsson 2004 Conf
A Bode sensitivity integral for linear time-periodic systems Henrik Sandberg, Bo Bernhardsson 2004 Art
Frequency-Domain Analysis of Linear Time-Periodic Systems Henrik Sandberg, Erik Möllerstedt, Bo Bernhardsson 2004 Conf
Automatic Gain Control In WCDMA Terminals Peter Alriksson, Bo Bernhardsson, Bengt Lindoff 2004 Conf
A Bode sensitivity integral for linear time-periodic systems Henrik Sandberg, Bo Bernhardsson 2004 Conf
Control Of GDI Engines using Torque Feedback Exemplified by Simulations Magnus Gäfvert, Karl-Erik Årzén, Lars Malcolm Pedersen, Bo Bernhardsson 2004 Art
Control of Gasoline Direct Injection Engines using Torque Feedback: A Simulation Study Magnus Gäfvert, Karl-Erik Årzén, Bo Bernhardsson, Lars Malcolm Pedersen 2003 Chap
LQR Optimization of Linear System Switching Bo Lincoln, Bo Bernhardsson 2002 Art
Feedback-Feedforward Scheduling of Control Tasks Anton Cervin, Johan Eker, Bo Bernhardsson, Karl-Erik Årzén 2002 Art
Comparison of Riemann and Lebesque sampling for first order stochastic systems Karl Johan Åström, Bo Bernhardsson 2002 Conf
Constrained Iterative Learning Control of Liquid Slosh in an Industrial Packaging Machine Mattias Grundelius, Bo Bernhardsson 2000 Conf
Out of Control Because of Harmonics — An Analysis of Harmonic Response of an Inverter Train Erik Möllerstedt, Bo Bernhardsson 2000 Art
Simple Feedback Control and Mode Switching Strategies for GDI Engines Magnus Gäfvert, Lars Malcolm Pedersen, Karl-Erik Årzén, Bo Bernhardsson 2000 Conf
Efficient Pruning of Search Trees in LQR Control of Switched Linear Systems Bo Lincoln, Bo Bernhardsson 2000 Conf
Singular Values of Trilinear Forms Jaak Peetre, Bo Bernhardsson 2000 Rep
A Harmonic Transfer Function Model for a Diode Converter Train Erik Möllerstedt, Bo Bernhardsson 2000 Conf
Optimal Control over Networks with Long Random Delays Bo Lincoln, Bo Bernhardsson 2000 Conf
Control of Liquid Slosh in an Industrial Packaging Machine Mattias Grundelius, Bo Bernhardsson 1999 Conf
Integrated Control and Scheduling Karl-Erik Årzén, Bo Bernhardsson, Johan Eker, Anton Cervin, Klas Nilsson, Patrik Persson, Lui Sha 1999 Rep
Comparison of Periodic and Event Based Sampling for First-Order Stochastic Systems Karl Johan Åström, Bo Bernhardsson 1999 Conf
Motion Control of Open Containers with Slosh Constraints Mattias Grundelius, Bo Bernhardsson 1999 Conf
Research Abatracts 1999—PhD Projects in Automatic Cotrol Mikael Johansson, Bo Bernhardsson 1999 Rep
Some Properties of Switched Systems Bo Bernhardsson, Karl Henrik Johansson, Jörgen Malmborg 1999 Conf
A Load Model Structure for Analysis and Control of Electric Distribution Network Erik Möllerstedt, Bo Bernhardsson, Sven Erik Mattsson 1999 Conf
Control of Realtime System With Unknown Timing Behavior Bo Bernhardsson 1999 Conf
Control and simulation of hybrid systems Jörgen Malmborg, Bo Bernhardsson 1998 Art
Comments on 'Mixed L/H Suboptimal Controllers for SISO Continuous Time Systems' Bo Bernhardsson, Hélène Panagopoulos 1998 Art
Some Topics in Real-time Control Johan Nilsson, Bo Bernhardsson, Björn Wittenmark 1998 Conf
A New Approach to Steady-State Analysis of Power Distribution Networks Erik Möllerstedt, Sven Erik Mattsson, Bo Bernhardsson 1998 Conf
Real Perturbation Values and Real Quadratic Forms in a Complex Vector Space Bo Bernhardsson, Anders Rantzer, Li Qiu 1998 Art
Some properties of switched systems Bo Bernhardsson, Karl Henrik Johansson, Jörgen Malmborg 1998 Conf
Stochastic Analysis and Control of Real-Time Systems with Random Time Delays Johan Nilsson, Bo Bernhardsson, Björn Wittenmark 1998 Art
Preprints of Reglermöte '98 Bo Bernhardsson, Björn Wittenmark (Eds.) 1998 Proc
A Simple Model for Harmonics in Electrical Distribution Networks Erik Möllerstedt, Bo Bernhardsson, Sven Erik Mattsson 1997 Conf
Modeling of Electricity Distribution Networks and Components. Status Report 1997-11-30 for Elforsk project 3153 Erik Möllerstedt, Sven Erik Mattsson, Bo Bernhardsson 1997 Rep
A New Approach to Steady-State Analysis of Power Distribution Networks Erik Möllerstedt, Sven Erik Mattsson, Bo Bernhardsson 1997 Conf
Modeling of Electricity Distribution Networks and Components. Status Report for Elforsk project 3153 Erik Möllerstedt, Sven Erik Mattsson, Bo Bernhardsson 1997 Rep
Timing Problems in Real-Time Systems Johan Nilsson, Bo Bernhardsson, Björn Wittenmark 1997 Conf
Modeling and Control of Fuzzy, Heterogeneous and Hybrid Systems Mikael Johansson, Jörgen Malmborg, Anders Rantzer, Bo Bernhardsson, Karl-Erik Årzén 1997 Conf
LQG Control Over a Markov Communication Network Johan Nilsson, Bo Bernhardsson 1997 Conf
Real Perturbation Values and Quadratic Forms in Complex Vector Space Bo Bernhardsson, Anders Rantzer, Li Qiu 1996 Conf
A Stabilizing Switching Scheme for Multi Controller Systems Jörgen Malmborg, Bo Bernhardsson, Karl Johan Åström 1996 Conf
Analysis of Real-Time Control Systems with Time Delays Johan Nilsson, Bo Bernhardsson 1996 Conf
A Summary on the Real Stability Radius and Real Perturbation Values Bo Bernhardsson, Anders Rantzer, Li Qiu 1996 Conf
Stochastic Analysis and Control of Real-Time Systems with Random Time Delays Johan Nilsson, Bo Bernhardsson, Björn Wittenmark 1996 Conf
Stochastic analysis and control of real-time systems with random time delays Johan Nilsson, Bo Bernhardsson, Björn Wittenmark 1996 Conf
Control System Synthesis—The PhD Course 1995 Bo Bernhardsson 1995 Rep
A Summary on the Real Stability Radius and Real Perturbation Values Bo Bernhardsson 1995 Conf
Linear Quadratic Control Design—The PhD Course 1994 Bo Bernhardsson 1995 Rep
A formula for Computation of the Real Stability Radius Li Qiu, Bo Bernhardsson, Anders Rantzer, E. J. Davison, P. M. Young 1995 Art
Robust Performance Optimization of Open Loop Type Problems Using Models From Standard Identification Bo Bernhardsson 1995 Art
Nonlinear Control Theory, the PhD Course 1994 Anders Rantzer, Bo Bernhardsson 1994 Rep
Simultaneous Block-Diagonalization of One Hermitian and One Symmetric Form Bo Bernhardsson 1994 Rep
Min-Mix Control in Discrete Time by Completion of Squares Per Hagander, Bo Bernhardsson 1993 Conf
A Stochastic Differential Games Approach to Mixed H2/H-Control Bo Bernhardsson, Per Hagander 1993 Conf
Sampling of State Space Systems with Several Time Delays Bo Bernhardsson 1993 Conf
On the Real Structured Stability Radius Li Qiu, Bo Bernhardsson, Anders Rantzer, E. J. Davison, P. M. Young 1993 Conf
On Simultaneous $H_2$-Optimization of Several Performance Bounds Bo Bernhardsson, Karl Henrik Johansson 1993 Conf
Robust Stochastic Performance Optimization Bo Bernhardsson 1993 Conf
A Formula for Computation of the Real Stability Radius Li Qiu, Bo Bernhardsson, Anders Rantzer, E. J. Davison, P. M. Young 1993 Unpublished
An Extension of Bohr's Inequality Lars Hörmander, Bo Bernhardsson 1993 Chap
Feedforward Control is Dual to Deconvolution Bo Bernhardsson, M. Sternad 1993 Art
Topics in Digital and Robust Control of Linear Systems Bo Bernhardsson 1992 PhD
An Extension of Bohr's Inequality Lars Hörmander, Bo Bernhardsson 1992 Rep
A Simple But Rich Test Example for H-Optimal Control Per Hagander, Bo Bernhardsson 1992 Conf
Structured Stability Margin and the Finite Argument Principle Anders Rantzer, Bo Bernhardsson 1991 Conf
Solution Using Robust Adaptive Pole Placement Karl Johan Åström, Bo Bernhardsson, Anders Ringdahl 1991 Conf
Structure of $H_\infty$ Optimal Controllers. The Golden Section Example Per Hagander, Bo Bernhardsson 1990 Rep
Control Design for Two Lab-Processes: The Flexible Servo, the Fan and the Plate Kjell Gustafsson, Bo Bernhardsson 1990 Rep
The Predictive First Order Hold Circuit Bo Bernhardsson 1990 Rep
Exercises in Linear System Theory Bo Bernhardsson, Per Hagander 1990 Rep
Geometric Theory for Multivariable Linear Systems with MATLAB Examples Bo Bernhardsson 1990 Rep
On the notion of strong stabilizability Per Hagander, Bo Bernhardsson 1990 Art
Structured Stability Margin and the Finite Argument Principle Bo Bernhardsson, Anders Rantzer 1990 Conf
The Predictive First Order Hold Circuit Bo Bernhardsson 1990 Conf
Corrections to `A discussion of adaptive stabilization and robust adaptive control' Bo Bernhardsson, Lennart Ljung, K. Wang 1990 Art
An Improved Moment Method for Transfer Function Identification Bo Bernhardsson, Per Persson 1990 Conf
Does Computer Technology Change the Education in Mathematics? Bo Bernhardsson 1990 Conf
ARNE Bo Bernhardsson 1989 Conf
Dual Control of a First-Order System with Two Possible Gains Bo Bernhardsson 1989 Art
Implementation of a Control Strategy for an Inverted Pendulum Kjell Gustafsson, Bo Bernhardsson 1988 Rep
Dual Control of a First Order Dynamical System Bo Bernhardsson 1988 Conf
Implementation of Fast Recursive Parameter Estimation Algorithms on the Signal Processor TMS 320 Bo Bernhardsson 1986 MSc

## Work in the Mobile Phone Industry

During the years 2001-2010 I worked at Ericsson as an Expert in Mobile System Design and Optimization. I worked with debugging and optimization of mobile phone performance in the 3G (WCDMA) system and later with the early design of the 4G (LTE) system.

### Patents

Each line correponds to a patent family with at least one granted patent. The total number of granted patents is probably 2-3 times higher. Most listed patents have 1-3 coinventors.

1. Sampling device and method in digital receivers, EP 1480369B1, 23-Aug 2006
2. Method and apparatus for improved cell detection US 7110376, 19-Sep-06
3. WIRELESS TRANSCEIVERS, METHODS, AND COMPUTER PROGRAM PRODUCTS FOR RESTRICTING TRANSMISSION POWER BASED ON SIGNAL- TO-INTERFERENCE RATIOS US7149538, 12-Dec-06
4. Electronic devices having automatic frequency control systems and methods US 7177602, 13-Feb-07
5. Method and apparatus for power control in a mobile radio system US 7283791, 16-Oct-07
6. Methods, receivers, and computer program products for determining transmission power control commands using biased interpretation US 7184791, 27-Feb-07
7. METHOD AND SYSTEM FOR DETERMINING UPLINK/DOWNLINK PATH-LOSS DIFFERENCE EP 2004819603, US7302276, 27-Nov-07
8. METHOD FOR DETERMINING A GAIN OFFSET BETWEEN TRANSMISSION CHANNELS US 7346126, 18-Mar-08
9. Channel Estimation by Adaptive Interpolation US 7433433, 7-Oct-08
10. Synchronization Detection Methods and Apparatus US 7437175, 14-Oct-08
11. Calculation of soft decision values using reliability information of the amplitude US 7583760, 1-Sep-09
12. Simplified Generalized Rake Receiver Method and Apparatus US 7680176, 16-Mar-10
13. Method and apparatus for communication channel estimation US 7680218, 16-Mar-10
14. METHOD AND APPARATUS FOR FAST FFT PROCESSING OF PAGING INFORMATION EP20060841155, US7684312, 23-Mar-10
15. METHOD OF AND APPARATUS FOR ADAPTIVE FREQUENCY ERROR ESTIMATION EP20070822391, 11-Aug-10
16. Method and apparatus for delay spread estimation, EP2071784
17. Determining a detection signal in a spread spectrum communications systems, US 7949036, 24-Mar-11
18. TIME-ERROR AND FREQUENCY-ERROR CORRECTION IN A MULTI-CARRIER WIRELESS COMMUNICATIONS SYSTEM, US7991378, 2-Aug-2011
19. Method and device for power control in a wireless communication system, US 8036694, 11-Oct-11
20. Alleviating Mobile Device Overload Conditions in a Mobile Communication System, US8086229, 27-Dec-2011
21. METHOD AND APPARATUS FOR FREQUENCY CONTROL IN WIRELESS COMMUNICATIONS, US8103219, 24-Jan-12
22. Method and apparatus for channel quality derivation, US8385222B2, 26-Feb-2013