ANN based Rayleigh Multipath fading channel estimation of a MIMO-OFDM system Kandarpa Kumar Sarma Abhijit Mitra Dept. of Electronics and CT Dept. of Electronics and Comm. Engg. Gauhati University IIT Guwahati Guwahati-781014, Assam, India Guwahati-781039, Assam, India
[email protected] [email protected]
Abstract Multiple-Input Multiple-Output (MIMO) technology using Orthogonal Frequency Division Multiplexing (OFDM) together called MIMO-OFDM has emerged as the viable alterative to meet the demands of greater bandwidth and quality of service of the ever expanding mobile communication networks. For MIMO-OFDM systems channel estimation is one of the challenging issues. Statistical characteristics of wireless channels is partially covered by the Rayleigh distribution. It best represents the condition where there are secondary reflections due to high rise structures are always threatening to degrade communication quality. An ANN can be used to provide an estimate of the channel to minimize some of the deficiencies of multi-user transmission under Rayleigh multipath fading. The ANN can be trained to tackle such fading and associated disturbance and improve reception of MIMO-OFDM systems by providing superior Bit Error Rate (BER)s.
can be used to provide an estimate of the channel which may help to mitigate some of the deficiencies of multi-user transmission. The ANN can be trained to make it robust enough to deal with multiple channel types and improve Bit Error Rate (BER) values. The work is related to channel estimation of a MIMO-OFDM system under rayleigh multipath fading environment using ANN. Rayleigh multipath fading is a common occurrence where the signal suffers multiple reflections due to high rise structures. The work considers the use of an ANN to tackle a Rayleigh multipath faded channel to estimate the channel coefficients to determine the BERs. Some of the related works if the MIMO-OFDM and related areas are [1] to [6]. This paper is organized into the following sections. Section 2 presents an insight into MIMO-OFDM System. Study of channel characteristics of Rayleigh multipath fading channel is included in Section 3. Application of Artificial Neural Network (ANN)s for channel estimation, training considerations and related results are included in Section 4. Section 5 concludes the description.
1. Introduction: Multiple-Input Multiple-Output (MIMO) wireless technology through the use of Orthogonal Frequency Division Multiplexing (OFDM) has emerged as a viable option to tackle increased bandwidth congestion and demand of better service observed in present day mobile communication networks [1]. Yet channel estimation is one of the challenging areas which offers considerable scope to improve quality of service of the mobile networks and provide greater bandwidth. Innovative means are being formulated to tackle channel estimation and improve performance of mobile systems. Challenges are plenty with multipath faded channels which is a common occurrence in all wireless based communication. One of the viable means to better channel estimation techniques is the use of soft-computing tools like the artificial neural network (ANN)s for channel estimation under multipath fading conditions [2]. Application of ANNs for channel estimation is a challenging problem. An ANN
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2 Basic Considerations of MIMOOFDM System: Orthogonal frequency division multiplex(ing (OFDM) is becoming the chosen modulation technique for wireless communications. OFDM can provide large data rates with sufficient robustness to radio channel impairments [1], [2]. A simplified approach to the entire work of simulating an OFDM transmit-receive system with associated channel maybe depicted as in Figure 1 In an OFDM scheme, a large number of orthogonal, overlapping, narrow band sub-channels or subcarriers, transmitted in parallel, divide the available transmission bandwidth. The separation of the subcarriers is theoretically minimal such that there is a very compact spectral utilization. The attraction of OFDM is mainly due to how the system handles the multipath inter-
Figure 1: OFDM transmit-receive system with associated channel ference at the receiver. Multipath generates two effects: frequency selective fading and intersymbol interference (ISI). The ”flatness” perceived by a narrow-band channel overcomes the former, and modulating at a very low symbol rate, which makes the symbols much longer than the channel impulse response, diminishes the latter. Using powerful error correcting codes together with time and frequency interleaving yields even more robustness against frequency selective fading, and the insertion of an extra guard interval between consecutive OFDM symbols can reduce the effects of ISI even more. Thus, an equalizer in the receiver is not necessary. There are two main drawbacks with OFDM, the large dynamic range of the signal (also referred as peak-to average [PAR] ratio) and its sensitivity to frequency errors [1], [2]. The receiver performs the inverse of the transmitter. First, the OFDM data are split from a serial stream into parallel sets. The Fast Fourier Transform (FFT) converts the time domain samples back into a frequency domain representation. The magnitudes of the frequency components correspond to the original data. Finally, the parallel to serial block converts this parallel data into a serial stream to recover the original input data. MIMO architectures are useful for combined transmit receive diversity. When used in parallel mode of transmission, MIMO systems offer high data rates in a narrow bandwidth. MIMO systems, characterized by multiple antenna elements at the transmitter and receiver, have demonstrated the potential for increased capacity in rich multipath environments [6]. A generic MIMO system maybe shown as if Figure 2 [7]. MIMOs approach is to transmit and receive two or more data streams through a single radio channel. This means the system can deliver two or more times the data rate per channel. By allowing for simultaneous transmission of multiple data streams (Figure 2), MIMO multiplies wireless data capacity without using additional frequency spectrum.MIMO-OFDM combines OFDM and MIMO techniques thereby achieving spectral efficiency and increased throughput. A MIMO-OFDM system transmits
Figure 2: MIMO scheme independent OFDM modulated data from multiple antennas simultaneously. At the receiver, after OFDM demodulation, MIMO decoding on each of the subchannels extracts the data from all the transmit antennas on all the subchannels [7].
3 Study of channel characteristics of multipath channel Wireless communication utilizes modulation of electromagnetic (radio) waves with a carrier frequency varying from a few hundred megahertz to several gigahertz depending on the system. Therefore, the behavior of the wireless channel is a function of the radio propagation effects of the environment. In such an environment the following may happen [8] [9]: 1. Multiple delayed receptions of the transmitted signals due to the reflections of buildings, hills, cars and other obstacles, etc. . 2. Sometimes even a line-of-sight path is not possible. 3. Each path has a different attenuation, time delay, phase shift. 4. Due to the relative phase shifts, the signals from different paths add constructively sometimes or cancel each other resulting in a weak signal other times. This phenomenon is known as fading.
3.1 Rayleigh Multipath Fading Channels: The received signal is modelled as bandwidth at which frequency selectivity becomes relevant. r(t) = α(t)s(t) + η(t);
(1)
where
α(t) = x(t) + jy(t) = a(t)ejφ(t) ;
(2)
is a zero-mean complex Gaussian. Denoting x and y as samples taken from x(t) and y(t) where x ∼ ℵ(o, σ 2 ) and y ∼ ℵ(o, σ 2 ). Then α is described by a zero mean complex Gaussian random variable 1 x2 + y 2 exp (− ); (3) 2 2πσ 2σ 2 Fading envelop (amplitude), a = x2 + y 2 Fading phase, φ = arctan( yx ). Let x = a cosφ and y = a sinφ. Using transformation formula between random variable pairs (x, y) and (a, φ) (x, y) =
fx,y
Figure 3: Rayleigh fading using tapped delay line filter
fa,φ (a, φ) = |J(a, φ)| × fx,y (x, y) |x=acosφ |y=asinφ ; (4) where J(.) : Jacobian of the transformation. δx δx cos φ −a cos φ δa δφ = = a; J (a, φ) = δy δy sin φ a cos φ δa δφ (5) From the above Rayleigh distribution maybe given as f a (a) =
0
2π
fa,φ (a, φ)dφ =
a a2 exp(− 2 ); 2 σ 2σ
(6)
This is known as Rayleigh fading and is typically encountered in land mobile channels in urban areas where are many obstacles which make line-of-sight paths rare. For a Rayleigh distributed random variable, the average power is (7) Ω = E[a2 ] = 2 σ 2 ; 2a a2 exp(− ); Ω Ω For normalized average power ie. Ω = 1 fa (a) =
fa (a) =
2a exp(−a2 ); Ω
(8)
(9)
Multipath channel modelling represented by Rayleigh fading represents the condition in an environment full of high-rise structures and other similar obstructions. The Rayleigh multipath fading in channels has been simulated using the Clarke-Gans model assuming mobility of a receiver handset. The fading thus created is similar to a Rayleigh distribution. The Rayleigh multipath fading can also be simulated for a discrete case using a tapped delayline filter as shown in Figure 3. For this work, this model has also been adopted to simulate Rayleigh-fading, meaning that the channel taps h(t) are assumed to be circular, complex-valued, zero mean Gaussian processes. Further more, the taps are assumed to be stationary and mutually independent.
Figure 4: Training ANN for estimation of channel
4 Application of Artificial Neural Network (ANN)s for channel estimation The application of the artificial neural network (ANN) considers two aspects. The first is the training of the radial basis function- a class of feed-forward ANNs. The second stage is to test the trained ANN under varied condition to check its robustness under a range of channel conditions. To train the ANN the setup shown in Figure 4 is utilized. Here the received signal is given as S =X ∗H +N
(10)
where X is the MIMO-OFDM signal, H is the channel matrix and N is the additive Gaussian white noise. The channel matrix is determined as per the considerations described under Section 3.1. It offers the ANN to be familiar with separate approaches of channel estimation. The channel matrices thus generated serve as the reference for the ANN to train. Training a neural network by back-propagation involves three stages: the feed-forward of the input training
pattern, the backpropagation of the associated error and adjustment of the weights. Here the output of the ANN is the signal SN which is compared with the received signal S and an error matrix e generated such that e = S − SN
(11)
channel and thereby increase the reception quality of the receiver. In such a case a block diagram as shown in Figure 5 is used. The ANNs are tested with four separate data sets of channel matrices generated with varying AWGN values for both the channel models and for four different training conditions. For testing the effectiveness of the trained ANN, the setup shown in Figure 5 is utilized.
where SN is the signal generated by the ANN such that S N = X ∗ HN + N
(12)
At the trained state e −→ 0 such that SN −→ S. By noting that SN = X ∗ H N + N (13) as SN −→ S the channel matrix generated by the trained ANN HN −→ H. The simplest way of estimating a channel is to perform the following using Equation 13. Here the estimation can be evaluated using SN X
(14)
assuming that AWGN N is known or can be ignored. But if AWGN plays a significant role which is usually the case, other methods are required. In this case, channel estimation is performed by a trained ANN.
Figure 5: Configuration of ANN to determine performance of training under test condition
4.1 ANN training considerations:
4.2 ANN testing and results:
The training is carried out by using signal inputs from the transmitter section. The greatest strength of an ANN is that it can tackle any estimation problem despite the presence of irregularities. Thus, the trained ANN though receives stimulations from the transmitter side (Figure 4), in practice it is designed to handle received signals and thereby perform channel estimation (Figure 5). The received signal given by Eq. 10 contains irregularities in the channel due to multipath fading and a large component of AWGN. Training continues till e approaches the desired goal. The ANN is a three layered network with one input, one hidden and one output layer. In this case a 4 x 4 Tx -Rx configuration is considered for which the input and output layers of the ANN will have four neurons each. The back-propagation algorithm used for training often suffers from more than one problems leading to difficulties in mean square error (MSE) convergence. Hence, varied AWGN considerations are used in the OFDM signal to make the correlation between adjacent samples of the training data as low as possible. The training continues till the MSE convergence attains the desired goal and the accuracy of generating the channel matrix by the ANN reaches the required precision level. After the training is over, inputs from the receiver end are fed to the ANN so as to provide a correct estimate of the
The training of the ANN for the channel estimation considers four ANN training methods to ascertain the best configuration for testing. The size of the data involved in the training is not very large, hence a careful selection of training sessions is an important criteria to prevent over training the ANN and thereby ensure optimum performance. It the ANN is overtrained it will fail to generalize instead will start to memorize. The number of training epochs required therefore are limited to a few hundreds only. The performance achieved during these epochs are noted. The ANN training considers the mean-square error (MSE) convergence and precision generated in channel estimation and the BER calculation. If the MSE has converged to the fixed target value, the precision levels and the associated BER values are calculated. If the values fall within the desired levels, the training is extended to include more number of samples which represent varying channel conditions. The iterations are confined to only to a few hundreds during which a minimum MSE convergence of 0.006 x 10−2 has been attained using the Gradient Descent with Adaptive Learning Rate and Momentum BP(GDALRMBP)training method. The MSE values by other training methods too are comparable. The GDMALRBP based training to the ANN generates the best performance. The highest precision performance attained is around 92.5 %. The ANN trained by following
Table 1: BER values generated by a trained ANN for a Rayleigh multipath fading channel Sl Num SNR in dB BER Value 1 1 dB 1.08 × 10−5 2 3 dB 1.02 × 10−5 3 5 dB 0.8 × 10−5 4 10 dB 0.72 × 10−5 5 15 dB 0.55 × 10−5 6 20 dB 0.41 × 10−5 7 25 dB 0.11 × 10−5 these considerations is taken for performing the channel estimation. The greatest strength of the ANN in such application is related to the opportunity that the ANN provides in extending the performance domain by adopting better configuration and allowing increased number of sessions to continue the learning till the desired performance levels are attained. The learning patterns and thereby performance of ANN varies with training method. The sample size considered for training includes two different forms of Rayleigh multipath fading channel model each generated using three different AWGN values viz.- 3dB, 5dB and 10dB. This way six sample sets are obtained for a 4x4 MIMO-OFDM set-up. The testing includes a range of signal conditions with SNR values ranging from 1 to 25 dB. The testing carried out with inputs from the receiver side calculates channel coefficients and compares them to the theoretically generated values for a frequency range of 0.2Ghz to 8GHz. Under 3dB AWGN the channel estimation attained is around 95 % which is the best performance attained by the ANN. Table 1 shows the BER values generated by the coefficients estimated by a trained ANN for a Rayleigh multipath fading channel model simulated using the tapped delay line filter model depicted in Figure 3. The values for SNR ranges between 1 to 25 dB is around 1.1 to 0.12 × 10−5 .
5. Conclusion Application of ANN for Rayleigh multipath fading channel estimation is an effective means to improve performance of a MIMO-OFDM system. The results obtained show that ANN is an effective aid to strengthen traditional methods of channel estimation and make reception quality better in wireless based communication. The ANN with its ability to learn though helps in identifying channel properties and responses, suffers from the fact that when the nearby samples have greater correlation the learning stops. ANNs specially feed-forward networks- the type used in this work are the worst sufferers if proper care is not taken. With better configuration of the ANNs and optimized conditions of training and testing, the ANN can be used as part of hybrid blocks to
improve performance even further while estimating parameters of Rayleigh multipath fading channel .
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