International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 3, Issue 6, June 2014
ISSN 2319 - 4847
Flat Rayleigh Fading Channel Estimation for
Adaptive OFDM Downlink By Using GCG
Class of Adaption Laws
M.Raju1 , O.Ravinder2 , K. Ashoka Reddy3
1
Ph.D Research Scholar, Kakatiya University, Warangal, A.P., INDIA
Associate Professor, ECE Department, SCCE, Karimnagar, A.P., INDIA
3
Professor, E & I Department, KITS, Warangal, A.P., INDIA
2
Abstract
A low-complexity channel estimation and general constant gain algorithm are developed in adaptive OFDM downlinks over
fading channels for vehicular user. A slotted OFDM interface is used in which time frequency bins are allocated adaptively to
different users within a downlink beam based on channel quality. Adaptation algorithms with constant gains are designed for
tracking smoothly time-varying parameters of linear regression models, the proposed algorithms are based on two key concepts.
First, the design is transformed into a Wiener filtering problem. Second, the parameters are modeled as correlated ARIMA
processes with known dynamics. This leads to design of simple adaption law. The algorithm can be named as Wiener LMS, is
presented here. All parameters are here assumed governed by the same dynamics and the covariance matrix of the regressors is
assumed known. Under certain model assumptions, the Wiener designed adaptation laws reduce to LMS adaptation. The
computational complexity is of the same order of magnitude as that of LMS for regressors which are either white or have
autoregressive statistics. The tracking performance is, however, substantially improved.
Index Terms—Adaptive estimation, Channel modeling, Least Mean Squares method, Wiener filtering.
1. OUTLINE
The successful deployment of OFDM in several standards and demonstrators has increased the interest in applying it also
in new broadband air interfaces beyond 3G [1]. OFDM is inherently scalable to higher bandwidths, it is spectrally
efficient and it avoids the intra-cell interference problems of CDMA systems [2]. Adaptive transmission can radically
improve the spectral efficiency when multiple users have independently fading links. The users may then share the
available bandwidth, and resources are allocated to terminals who them best and/or can need utilize them best via link
adaptation [3].
The present paper outlines the downlink of an adaptive OFDM system that employs FDD. A base station infrastructure is
assumed and the aim is a design that is feasible also for vehicular users, around 100 km/hr [2].
Channel estimators located in terminals of such systems would have to meet three challenges [2]:
1) To attain high spectral efficiency, OFDM channel must be estimated with sufficient accuracy, when using high
modulation formats payload information can also be detected [10].
2) The fading channel must be predicted with sufficient accuracy over time horizons that correspond to the feedback delay
of the adaptive transmission system.
3) To reduce computational delay and to attain low power consumption at terminals, the computational complexity of the
estimator must be limited.
In this paper we propose a novel way of extending and optimizing the structure of LMS-like adaptation laws [4].
We will here investigate the application of WLMS algorithms to the estimation of such fading channels. With large
variations in the fading rate, a key issue is the selection of appropriate statistical fading models. Several design
approaches can be conceived, some of which are listed below in decreasing order of complexity [5].
1) An autoregressive model for fading channel taps may be adjusted on line. This estimator can be implemented jointly
with a WLMS algorithm or a Kalman tracker.
2) Some fading models, specified by a few parameters, such as the speed of the mobile, which may be estimated
separately. A set of WLMS algorithms can be pre-designed within these parameters. The parameters are estimated on line
and the appropriately tuned algorithm is selected [6].
3) A single robustly designed algorithm might provide adequate performance over a wide range of Doppler shifts and
disturbance levels.
The present paper will explore properties of the WLMS algorithm for flat Rayleigh fading channels [9].
Volume 3, Issue 6, June 2014
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 3, Issue 6, June 2014
ISSN 2319 - 4847
The channel model i.e., the adaptive OFDM downlink will be outlined in Section II and Section III is about Channel
estimation process. Section IV the WLMS algorithm is summarizes. Section V is about Evaluation of Flat Rayleigh
Fading channel, Simulation Results will be discussed in Section VI, in Section VII Conclusion.
2. THE PROPOSED ADAPTIVE OFDM DOWNLINK
A. The Physical Layer
The available downlink bandwidth, S, within a sector is assumed to be slotted in time. Each slot of duration T is
partitioned into time-frequency bins of bandwidth Δfb. The channel is assumed to be described by a complex scalar, which
varies only slightly within a bin. This assumption restricts the bin size. In [7], we discuss the choice T=0.667 ms and Δfb
= 200 kHz as appropriate for stationary and vehicular users in urban or suburban environments. This size represents a
reasonable balance between the spectral efficiency of the downlink and the required uplink control bandwidth.
We also assume a subcarrier spacing of 10 kHz, a cyclic prefix of length 11µs and an OFDM symbol period (including
cyclic prefix) of Ts= 111 µs Thus, each bin of 0.667 ms x 200 kHz carries 120 symbols, with 6 symbols of length 111µs
on each of the 20 10 kHz subcarriers. Of these 120 symbols, 12 are allocated for training and downlink control, leaving
108 payload symbols that constitute the link-level packets. The 12 pilots and control symbols are located within each bin
as indicated by Fig. 1. They are assumed to use 4-QAM and can be detected by all users within the sector. They are
transmitted in all bins, also bins without payload data.
Fig. 1. One of the time-frequency bins of the proposed system, containing 20 subcarriers with 6 symbols each. Known 4QAM pilot symbols (black) and 4-QAM downlink control symbols (rings) are placed on four pilot subcarriers. The
modulation format for the other (payload) symbols is adjusted adaptively. All payload symbols within a bin use the same
modulation format
B. Resource Allocation
During slot j, each terminal predicts the signal to interference and noise ratio (SINR) for all bins, with a prediction
horizon mT that is larger than the time delay of the transmission control loop. All terminals then signal their predicted
quality estimates on an uplink control channel. They transmit the suggested appropriate modulation formats to be used
within all bins of the predicted time slot j+m. A scheduler that is located at the base station then allocates these timefrequency bins exclusively to different users and broadcasts its allocation decisions by using some of the downlink control
symbols. In the subsequent downlink transmission of slot j+m, the different modulation formats used in different bins are
those which were suggested by the appointed users.
For the payload symbols, we utilize an adaptive modulation system that uses 4 uncoded modulation formats: 4-QAM, 8QAM, 16-QAM, 32-QAM with constant transmit power.
The spacing between pilots in time, 0.666 ms, corresponds to 0.115 wavelengths at 1.9 GHz carrier frequency and 100
km/h vehicle speed. Pilot symbols are transmitted over every fifth subcarrier, in the following denoted pilot subcarriers.
Their spacing in frequency, 50 kHz, is designed to be adequate to handle the frequency selectivity encountered in
suburban propagation environments [2], [3].
Thus, all active users must estimate the channel within the whole bandwidth. The channel estimates are used for two
purposes: In bins addressed to a user, the payload symbols are de-rotated for coherent detection. Channel estimates for all
bins are furthermore used by the predictor
3. CHANNEL ESTIMATION
A. Linear regressions
The received scalar complex-valued baseband signal vectors {yt} of dimensions ny |1 is assumed available at the discrete
time instants t=0, 1, 2….and to be generated by a linear regression [4]
(1)
yt   t* ht  vt
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
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Volume 3, Issue 6, June 2014
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Where vt represents noise and all terms may be complex-valued. The known regression matrix sequence
{  t* }, of
dimension ny | nh, is defined as the Hermitian conjugate of a corresponding nh |ny matrix φt. It is known up to time t and is
assumed stationary with zero mean and nonsingular covariance matrix [4], [8]
*
R  E t t
(2)
Here we have to estimate the channel coefficients of column vector [3]
(3)
ht  (h0, t .....hn 1,t )T
h
The fading properties of the channel coefficients will depend on the maximum Doppler frequency [5]
wD  2f D 
2v0
rad/s

v0 denotes the speed of the vehicle and λ is the carrier wavelength
To describe ht, we shall use simplified fading models [4] in the form of marginally stable autoregressive models of order
nD, with equal dynamics for all channel taps [5]
_
1
ht 
D( q
1
)
Iet 
1
1  d1 q
1
        d nD q
 nD
Iet
(4)
_
The notation h t is introduced to indicate that (4) will not be a perfect description of ht. Here q-1, denotes the backward
shift operator (q-1yt =yt-1) and et is a white zero mean random vector sequence with covariance matrix Re. For symmetric
fading spectra, the scalar coefficients {di} can be assumed real-valued.
For autoregressive and integrating model [5]
 0 D 1
D( q 1 )  (1  2 cos
q   2 q  2 )(1  q 1 ) (5)
2
0
We need to select the parameters  and  D
B. The WLMS Adaption Structure
Assuming the system to be described by (1)–(4), parameter tracking becomes a signal estimation problem, with ht in (4)
being sought. Define the tracking error vector [3]
_

h t  k ht  k  h t  k |t
(6)

Where h t  k | t is an estimate of ht  k at time t representing filtering (k = 0), prediction (k > 0), or fixed lag smoothing (k
< 0). We will measure tracking performance by
~
~*
trPk  lim trE h t  k h t  k
t 
n h 1
~
(7)
E | hi, t  k  h i , t  k |t | 2
t  i  0
Where the expectation is taken with respect to in (4) and in (1) after the initial transients. The class of adaptation
algorithms, within which we here chose to minimize (7), corresponds to introducing two modifications in the LMS
algorithm

(8)
t  yt   *t h t |t 1


(9)
h t  h t |t 1   t t


(10)
h t 1|t  h t
Where
^
ht
 lim

^
^
denotes the filtering estimate
h t |t , h t  1 |t
is the one-step prediction estimate, µ is the scalar adaptation gain,
and t is the prediction error.
Volume 3, Issue 6, June 2014
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 3, Issue 6, June 2014
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4. WIENER LMS DESIGN
To provides a systematic design technique, a numerically safe implementation, the filter, operating on a fictitious
measurement signal, will be shown [3]
The Fictitious Measurements
Consider the signal prediction error (8) and insert (1) describing yt to obtain
^
t   * (ht  h t |t 1 )  vt
~
 t t   t *t h t |t 1   t vt
~
By adding and subtracting R h t | t 1 and defining
(12)
Z t   t  *t  R
~
(13)
 t  Z t h t |t 1   t vt
f t  Rht   t
(14)
(11)
The vector (11) is now reformulated as
^
~
 t t  Rht  R h t |t 1  Z t h t |t 1   t vt
(15)
~
 f t  R h t|t 1
Here, ft can be regarded as a fictitious measurement, with R ht and
 t are the signal and the noise resp.,
5. SIMULATION ON FLAT RAYLEIGH FADING CHANNEL
The methods discussed in Section III-IV are evaluated here. By applying Constant Gain estimator on Flat Rayleigh
Fading 5 MHz channel at 1900 MHz. The vehicular velocity 100 km/hr, so the maximum Doppler frequency  D is
1093 rad/s and
 D Ts  0.1212 rad. The noise vt is uncorrelated in time .The channel Signal-to-Error Ratio (SER) of
the estimator output is
SER 
E | ht | 2
~
E | h t |t 1 | 2
~
(16)
^
Where h t | t 1  ht  h t | t 1 . Here Constant Gain algorithms are based on autoregressive integrated models.
SNR V/S SER plot for GCG estimator
3
SNR V/S SER FOR AN OFDM GCG ESTIMATOR BASED RECEIVERS
10
S ER [dB]
4QAM
8QAM
16QAM
32QAM
2
10
1
10
5
10
15
20
25
30
SNR [dB]
Fig. 2. Channel signal to estimation error ratio(SER) for Flat Rayleigh fading channel at 100 km/h. This GCG filter
estimate h^ t |t when using ARIMA for downlinks of 4-different QAM modulations
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
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Volume 3, Issue 6, June 2014
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SNR V/S SER PLOT for NMSE Estimator
SNR V/S SER FOR NMSE ESTIMATOR
4
10
4QAM
8QAM
16QAM
32QAM
3
10
2
SER[dB]
10
1
10
0
10
-1
10
-2
10
5
10
15
20
25
30
SNR [dB]
Fig. 3. Channel estimated for same type of channel for each bin width of 20 subcarriers this figure represent SER Vs
SNR plot for NMSE estimator for QAM modulation. Here Channel statistics are deviated significantly.
Eb/No Vs SER plot for GCG estimator
0
10
4 QAM
8 QAM
16 QAM
32 QAM
-20
10
-40
SER (dB)
10
-60
10
-80
10
-100
10
-120
10
-140
10
0
5
10
15
20
25
Eb/N0 (dB)
Fig. 4. Energy bit per Noise ratio Vs SER plot represent results for AWGN noise for different schemes.
SNR Vs BER plot for GCG estimator
BER vs SNR
-0. 02
10
4 QAM
8 QAM
16 QAM
32 QAM
-0. 03
Bit Error Rate
10
-0. 04
10
-0. 05
10
0
5
10
15
SNR in dB
20
25
30
Fig. 5. In the Flat fading case , with h1,t=0, not much can be gained by improving the tracking. An exception is at high
SNR , where for true regressors a significantly lower BER is attained for ARIMA based designs
6. CONCLUSION
Within the class of constant gain algorithms presented here, we can control the level of design complexity and
computational complexity by selecting models for the parameters ht and the gradient noise  t .
The general constant-gain algorithm is based on linear time invariant models of the parameters and of the gradient noise.
If the gradient noise is assumed white, we obtain both a simpler design and a simpler implementation. Finally, the
generalized WLMS and WLMS algorithms of Section IV are the simplest alternatives.
Volume 3, Issue 6, June 2014
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 3, Issue 6, June 2014
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Compared with Kalman adaptation laws, a main advantage with the proposed class of algorithms is their lower
computational complexity. Another advantage is that it becomes more straightforward to design fixed-lag smoothing
estimators. A disadvantage is that our Wiener design is a steady-state solution, which could lead to worse transient
properties as compared to a Kalman estimator.
REFERENCES
[1] J. Chuang and N. Sollenberger, “Beyond 3G: Wideband wireless data access based on OFDM and dynamic packet
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adaptive OFDMA downlinks,”VTC 2003-Fall, Orlando, Fla, Oct. 2003.
[3] Mikael Sternad and Daniel Aronsson, “Channel Estimation and Prediction for Adaptive OFDM Downlinks,” IEEE
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[4] L. Lindbom, M. Sternad and A. Ahl´en, “Tracking of time-varying mobile radio channels. Part I: The Wiener LMS
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BIOGRAPHY
M.Raju received the Bachelor’s Degree in the Department of Electronics and Communication Engineering
from Gulbarga University, Gulbarga, Master’s Degree in Instrumentation and Control Systems from JNTU,
Kakinada and Pursuing Ph.D in Kakatiya University, Warangal, India. He is currently Associate Professor
in the Department of ECE, Sree Chaitanya College of Engineering, Karimnagar, India, He is pursuing
research in the area of Signal processing in wireless communication. He has published two papers in International
Conference Proceedings and one paper in International journal in the Embedded area. His areas of interest are Signal
Processing for Wireless Communication.
O.Ravinder received the Bachelor’s Degree in the Department of Electronics and Communication
Engineering from Jawaharlal Nehru Technological University, Hyderabad, A.P. India and Master’s Degree in
Digital Systems and Computer Electronics from JNTU, Hyderabad, A.P. India. He is currently Associate
Professor in the Department of ECE, Sree Chaitanya College of Engineering, Karimnagar, A.P. India, He has
published one papers in International Conference and one paper in National Conference in the Communication area. His
areas of interest include Signal Processing for Communications, Wireless Communication and Signals.
K.Ashoka Reddy received the Bachelor’s Degree in Electronics and Instrumentation Engineering from
Kakatiya University, Warangal, India in 1992, Master’s Degree in Instrumentation and Control Systems
from JNTU, Kakinada in 1994 and Ph.D from Indian Institute of Technology, Chennai, India in 2007, He is
currently Professor in the Department of Electronics and Instrumentation Engineering, Kakatiya Institute of
Technology and Science, Warangal, India. He has 45 Published papers in International and National Journals and
Conference Proceedings. His areas of interest include Signal Processing for Bio-medical Instrumentation, Wireless
Communication and Signals.
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