Advances in Electrical Engineering Systems (AEES) Vol. 1, No. 3, 2012, ISSN 2167-633X Copyright © World Science Publisher, United States www.worldsciencepublisher.org
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Channel Estimation for OFDM System using Training Sequence Algorithms 1
E. Ahmed, W. Aziz, G. Abbas, S. Saleem, Q. Islam Department of Electrical Engineering Institute of Space Technology, Islamabad Pakistan Email:
[email protected]
Abstract -- Orthogonal Frequency Division Multiplexing (OFDM) is a multicarrier modulation and multiplexing technique proposed for 3G, 4G LTE-A systems to achieve higher data rates with better spectral efficiency at low latency. Time varying nature of the wireless channel can cause frequency selectivity and multipath fading which affects performance of the system badly. Channel estimation techniques are proposed to tackle the issue and results in improved performance. In this paper, training based channel estimation techniques like Least Square and Minimum Mean Square Error are discussed. Both techniques are compared for Bit Error Rate (BER) performance and computational complexity in MATLAB. Keywords – OFDM; LTE-A; Frequency Selectivity; LS; MMSE
1. Introduction Orthogonal Frequency Division Multiplexing (OFDM) is a blistering area of research in the field of wireless communication for the last few decades. It is a multicarrier modulation scheme in which a wideband frequency selective channel is broken down into narrowband flat channels hence increases data rate and reduces the problem of multipath fading. It performs well as compared to single carrier transmission technique in the case of frequency selective and time varying channels; moreover low latency and better spectral efficiency makes it ideal for the transmission purposes. The main feature of OFDM has is to maintain the orthogonality among the subcarriers which minimizes the Inter Symbol Interference (ISI) and Inter Carrier Interference (ICI) accordingly. Due to this property each single carrier presents a separate channel for the transfer of the information and can be recovered at the receiver side without using complex equalization and channel estimation techniques. OFDM has been adopted in many wireless standards like ADSL, IEEE 802.11a, g, n and DVB-T and DVB-H etc [1]. In case of moving receiver occurrence of Doppler spread can demolish orthogonality among the carriers; giving birth to ISI. Wireless channel is varying all the time and results
in multipath fading and frequency selectivity which degrades performance of the system severely. Channel estimation techniques proves effective to overcome the problem of multipath fading in time varying channels by estimating response of the channel. When channel response is known at the receiver end then the recovery of transmitted symbols is not a big problem [2]. There are different methods which can be used to estimate the response of the channel like by inserting pilot or preamble information among the OFDM symbol where the pilot information is known at both transmitter and receiver ends. Pilot symbols make sure the use of different interpolation techniques to estimate the channel response for data symbols. Many factors contribute in the selection of an estimation technique for a time varying channel such as computational complexity of that technique, achieving required performance and the ability to combat the time varying of the channel. For a pilot assisted channel there exist different types of pilot arrangements like Comb, Block and Lattice type structures. In comb-type structure, pilot information is inserted among the periodic OFDM symbols along the frequency axis to estimate the channel response in frequency domain and has ability to tackle the problem of fast fading channel. The occurrence of pilot symbols among
E. Ahmed, et al., AEES, Vol. 1, No. 3, pp. 140-145, 2012
the carriers is a function of coherence bandwidth, which is related to maximum delay spread a channel can have. For a block-type structure, pilot information is inserted among all the OFDM carriers along the time axis to estimate the channel response in the time domain and having the ability to overcome the problem of frequency-selective channel [5]. The occurrence of pilot symbols among the carriers is a function of coherence time, which is accordingly related to Doppler shift in the channel. There is a third scheme commonly known as the lattice-type structure which incorporates both block and comb type techniques and insert pilot information in both frequency and time axis. It exploits both frequency and time domain interpolation techniques for the estimation of varying channel.
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we use training symbols to estimate the channel response. The use of training sequence provides required performance but at the cost of additional overhead of pilot information which degrades performance required for transfer of information data. There is a tradeoff between the required performance and the efficiency of the system, like if we can compromise on the performance then we can increase the efficiency but in some cases we can’t ignore this fact and use some estimation techniques for a required performance at the cost of less efficiency [3]. This paper is distributed as, first description of OFDM system followed by the LS and MMSE algorithms and then simulation results of the channel estimation techniques for different parameters.
Minimum Mean Square Error (MMSE) and Least Square (LS) are two available channel estimation techniques when
Figure1. OFDM System Model
2. System Description The complete block diagram of OFDM system is shown in figure 1. Data source is the digital stream of information which we intend to transmit. Channel coding is employed on the information bits for error detection and correction. In this operation, redundant bits are added along with the data bits to tackle errors. Channel coding can be done by the use of blocks, convolutional and Viterbi codes as per the requirement. To reduce the amount of burst errors, bit interleaving is employed in which we give input row wise and at the output read by column wise. By doing this number of errors
distributed among all the information bits and can be corrected easily. After interleaving, the process of modulation is performed which supports the transfer of information along the medium. In the modulation scheme different parameters of message signal are varied like amplitude, phase, and frequency or it can be the combination of these parameters. bits at the If we have , , … , total number of output of interleaver, then the modulator with the use of Marray modulation scheme maps the input bits where , where M denotes the modulation order. Then Serial to Parallel conversion is performed as it will be input to the Inverse Fast Fourier Transform (IFFT), which
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converts the time domain signal to the frequency domain. In this way data is carried by the multiple carriers rather than by the single carrier thus increases the data rate .Before the operation of IFFT, there is addition of guard interval between the data symbols. Guard Interval is of significant importance as it accounts for the multipath fading which causes Inter Symbol Interference (ISI) among the symbols. ISI occurs when the delay spread is large than the symbol duration, in this way information symbols overlap with each other and it is difficult to extract required information at the receiver end. In addition to this, guard interval also caters for the frequency offset and the instabilities in the carriers.
Let’s suppose we have an OFDM symbol with duration of and contains subcarriers. Now, if we have an information data , on the subcarrier in the OFDM symbol then we can write our transmitted symbol as:
Cyclic Prefix (CP), Cyclic Suffix (CS) and Zero Padding (ZP) are different techniques used as the guard interval between the message symbols. There are different pros and cons of these techniques but in general the addition of guard interval reduces the data rate but on the other hand provides the required performance.
Where ( denotes the guard interval which is inserted between the symbols to avoid collisions and ) denotes the total duration of the symbol including the guard interval [3].
Windowing is done after the IFFT block which specifies start and end of the OFDM symbol and extracts the required block of data. Incoming digital stream is then converted to analog data because in a real time environment channel behavior is analog. This analog data is transmitted through wireless channel which is random and time varying. Channel effect can be explained by Rayleigh fading and Rician fading channels. Rayleigh fading channel estimation technique scheme is used when there is no Line of Sight (LOS) path between the transmitter and the receiver and in the same way if there exist LOS path then Rician distribution function can be used. At the receiver side, first analog data is converted back to the digital data for processing. Multipath fading can cause frequency selectivity and ISI due to the time varying nature of channel. Channel estimation and equalization techniques prove to be fruitful to mitigate the problem of ISI and frequency selectivity. After the channel estimation the guard interval is removed and data is converted to a parallel stream for the input to Fast Fourier Transform (FFT) block which converts back time domain signal to frequency domain signal. Demodulator performs the demodulation function and feeds it to the deinterleaver block. After the deinterleaver channel decoding is performed on the incoming stream to remove the redundant bits, which gives the desired output at the end [6].
3. OFDM Model
,
Where
,
can be written as:
,
!"#$ %
,
& '
(
'
)*
Then transmitted symbol is passed through the channel which is characterized by Rayleigh Fading channel in case of wireless transmission. The impulse response of Rayleigh Fading channel can be approximated as: + ,,
∑
. /
', )
Where . denotes the time varying gain and total number of multipath.
shows the
Now after passing through the channel we have received our message signal which can be written as: ∑
0
. /
',
1
)
Where denotes the Additive White Gaussian Noise (AWGN) which is an inherited property of the channel. We can write our received symbol in frequency domain as: 0
,
2
,
∗ 4
,
15
.
Where 4 , denotes the frequency response of the channel,2 , shows the frequency response of the transmitted symbol and 5 . shows the AWGN noise added to the symbols.
4. Channel Estimation Algorithms 4.1. Least Square Channel Estimation In LS channel estimation technique we make use of the training sequences which are exact replicas of the transmitted symbols. In this technique we design our
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channel filter such as to be compatible with the transmitted symbols. LS algorithm is less complex and easy to implement as it does not require any probability function to determine the channel response [4]. Let’s suppose we denote our channel vector response as , then we can approximate the LS estimation of the channel as: 789
789
=
ɼCC F <
2 < = < = 2
4.2. Minimum Mean Square Channel Estimation MMSE performs well as compared to LS, as it uses the channel characteristics and Signal to Noise Ratio (SNR) information to estimate the channel. Its complexity is more as compared to LS but it can be reduced by assuming the finite length sequence and flat response of Power Delay Profile (PDP) which improves the performance [4]. Let’s suppose we denote our channel vector as , then we can approximate the MMSE of the channel as:
F H
789
is
Where ;?89 is approximated as: ;?89
E
Where ;89 can be approximated as: ;89
7
F;
