COMBINED BLIND EQUALIZATION AND AUTOMATIC MODULATION CLASSIFICATION FOR COGNITIVE RADIOS UNDER MIMO ENVIRONMENT

Transcription

1 COBINED BLIND EQUALIZATION AND AUTOATIC ODULATION CLASSIFICATION FOR COGNITIVE RADIOS UNDER IO ENVIRONENT Barathram Ramkumar Bradley Department of Electrical Computer Engineering, Virginia Tech, Blacksburg, VA-46, ); Tamal Bose Bradley Department of Electrical Computer Engineering, Virginia Tech, Blacksburg, VA-46, Jeffrey H. Reed Bradley Department of Electrical Computer Engineering, Virginia Tech, Blacksburg, VA-46, iloje S. Radenkovic (Electrical Engineering Department, University of Colorado, Denver, CO-87, ABSTRACT Blind equalization Automatic odulation Classification (AC) have been of significant importance for cognitive radios when the receiver has no information about the channel or modulation type. Choosing an appropriate equalizer is difficult when the channel is ulti Input ulti Output (IO), when there is no information about the channel. In this paper, an AC based on cyclostationary feature detection IO based Constant odulus Algorithm (CA) blind equalizers are used in conjunction. The probability of classification of the AC is used as a metric fed back to update the blind equalizer order. The equalizer the AC enhance the performance of each other. Computer simulations are given to illustrate the concept yield promising results.. INTRODUCTION One of the important aspects of cognitive radios is the ability to sense characterize its RF environment adapt accordingly []. Blind equalizers are used for recovering the transmitted input sequence using only the output signal with no knowledge of the channel. CA is one of the popular blind equalization algorithms used for Single Input Single Output (SISO). The etension of CA to IO systems is shown in []. It is also shown in [] that the CA equalizer can perfectly recover one of the input sequences from the output of the OO FIR channel thus reducing Co-Channel Interference (CCI) Inter Symbol Interference (ISI). Another important component of cognitive radio is AC. AC improves the spectral efficiency of cognitive radio by adapting transmission according to the spectral environment []. In this paper, cyclostationary based signal detection pattern matching proposed in [6] [7] are used. Neural Networks trained using the Cyclic Domain Profiles (CDP) are used for signal classification due to their good pattern matching capabilities. It is shown in [6] that this AC gives good performance under low SNR. The performance degradation of this AC in the presence of the IO-FIR channel is shown. When the channel information is not known, choosing the length of the equalizer becomes a difficult task. In this paper, a unified framework for IO cognitive radios is proposed, i.e. IO based CA is used in conjunction with the AC. The order of the blind equalizer is adjusted based on the probability of classification of the AC. This paper is organized as follows. In Section II, a brief background on blind IO equalization IO based CA is presented. In Section III, the spectral correlation based AC is discussed. The proposed unified framework the algorithm for adjusting the number of taps in the equalizer are discussed in Section IV. Simulation results are shown in Section V, followed by the conclusion in Section VI.. BLIND IO EQUALIZATION The basic block diagram of the IO system is shown in Fig.. The d comple signals are passed through channels h ij [ for i..., j,..., d to generate outputs ( d < ). Let [ a[ [, a[ [ ad [ () Proceedings of the SDR 8 Technical Conference Product Eposition, Copyright 8 SDR Forum, Inc. All Rights Reserved

2 h[ L hd [ H[. () h[ L hd [ d] The channel output [ is [ H[ a[. (3) Equation (3) can be written in the Z-domain as ( z) H ( z) a( z), (4) where (z), a (z) H (z) are Z-transforms of [, a[ H[ respectively. permutation ambiguity. Therefore the best possible equalizer is G ( z) H ( z) PD( z), (7) where P is the permutation matri D(z) is the diagonal matri defined as jθ n jθd n D( z) diag{ e z,..., e z }, where θ i { π, π}. The equalizer which satisfies (7) is known as the distortion-less recovery equalizer. g [ ] n y [ h [ ] n [ n ] g [ [ a [ ] n h d [ [ g d [ n ] y d [ a d [ h [ [ h d [ [ g d Algorithm Fig : Blind Equalization for IO channels Fig: IO-FIR Channel Blind equalizers are used to recover the input sequence a [ only from the output [. The block diagram of the IO equalizer is shown in Fig.. To recover the input sequence we need to find G[ such that G H[ I, (5) [ d where I d is a d d identity matri G[ is the equalizer matri given by g[ L G[ gd[ L g g [ [ d Only the statistics of input signals are known, hence the IO blind equalizer is subjected to phase (6).) CA for IO FIR Channel CA for SISO is etended to IO systems in []. A brief overview of IO CA from [] is presented here. The block diagram of the IO CA is shown in Fig 3. In order to recover the input sequence from the output [, after each channel output, a linear filter is added. The coefficients of the filter are adjusted to minimize the Godard cost function [], [3] [4]: C( y[ ) E{( y( n) r) }, (8) 4 m4 where r, m m E{ a [ ] }, m E{ a [ ] }. (9) i n 4 i n One of the important theorems from [] is stated here. 4 Proceedings of the SDR 8 Technical Conference Product Eposition, Copyright 8 SDR Forum, Inc. All Rights Reserved

3 Theorem: For a IO FIR channel of length L, if H (z) is irreducible with H[ L ] being of full rank, then any IO-CA FIR blind equalizer with length ( L ) d K can achieve global convergence regardless d of the initial setting. The above theorem states that the IO-CA equalizer can recover one of the input signals, remove ISI, suppress CCI, regardless of the initial setting. CA Fig 3: IO-CA Blind Equalizer 3. CYCLOSTATIONARITY BASED AC 3.. Background on cyclostationary spectral analysis. If the mean autocorrelation of a process (t) is periodic, then the process is said to be a cyclostationary process [8] i.e. ( t + T ) ( t) R ( t + T, u + T ) R u) for all t u. Since the autocorrelation function is periodic it can be epressed as a Fourier series [9]. τ τ ( +, ) ( ), j πt R t t R τ e () where R Z / τ τ jπt ( τ ) lim R ( t, t ) e dt. Z + () Z / The Weiner theorem for stationary processes can be etended to cyclostationary processes. The Spectral Correlation Function (SCF) is defined as a Fourier transform of () S [ ] n [ ] n [ g [ ] n g [ [ g jπfτ R ( τ ) e dτ. (3) y[ In practice there is only a limited number of samples available hence SCF needs to be estimated from these samples. Let us define the cyclic periodogram as [], []: * S T f ) X T f + ) X T f ), T (4) where X T f ) is the time invariant Fourier transform given by X T f ) t+ T / t T / ( u) e jπfu du. (5) The estimate of SCF can be obtained by the frequency smoothing of (4) S T f ) Δf Δf f +Δf / S T f Δf / v) dv. (6) It is shown in [7] that SCF can be obtained by increasing the observation length T decreasing Δf, that is Δf T T S ( f ) lim lim S f ). (7) T 3.. Spectral Coherence (SC) profile: SCF is a correlation of frequency components shifted by f f +. It is intuitive to define Spectral Coherence (SC) as S ( f ) C. (8) [ S( f + ) S( f )] The magnitude of SC is always between. In order to reduce the computational compleity, one just uses the Cyclic Domain Profile (CDP) or -profile which is defined as I( ) ma C ( f ). (9) f 3.3. Automatic odulation Classifier ost modulated signals ehibit second order cyclostationarity [8]. From the CDP of the signal, important information about the signal like modulation type, keying rate, pulse shape, carrier frequency can be obtained, [6] [5]. Fig. 4 Fig. 5 show the Cyclic Domain Profile (CDP) function for BPSK QPSK respectively. To generate these plots the SQRC pulse with a roll off factor of.3 was used. Time domain frequency domain smoothing were performed in order to estimate the SC. For time averaging the method suggested in [7] is used, i.e. S T N N S T k ( t, f ). () k Proceedings of the SDR 8 Technical Conference Product Eposition, Copyright 8 SDR Forum, Inc. All Rights Reserved

4 N T 8 are used, which means a total of 56 samples were used. N T SCF creation [ The block diagram of the cyclostationarity based AC is shown in Fig. 6. SCF creation CDP etraction were discussed in the previous section. The final stage of the AC is to classify the -profile using pattern matching. Pattern matching is performed using a feed forward neural network. The AXNET structure shown in Fig. 7 is used. Each feed forward network has two hidden layers with 5 neurons in each layer, the activation function used is tanh(). The network is trained using the back propagation algorithm with an initial learning rate of η.5 a momentum constant of.7. The input to the feed forward network is the point -profile the output varies between [-, ]. The function of the AXNET structure is to choose the highest value among all the feed forward networks. -profile CDP Etraction Pattern atching Fig 7: Block Diagram of the AC. BPSK QPSK Y Y A X N E T FSK Y SK Y4 CDP alpha/fs Fig 5: Cyclic Domain Profile for BPSK..4.. Fig 7: Neural Network structure. 4. PROPOSED ETHOD In general, all fading channels are modeled as time varying FIR filters hence the length of the above equalizer, i.e. K, plays an important role. When the receiver has no information about the channel, choosing the length of the equalizer (K) is difficult. In this paper we choose the value of K based on the probability of classification of the AC. The block diagram of the proposed method is shown in Fig 8. A simple algorithm to choose the value of K is shown below..8 CDP.6 [ g [ n ] alpha/fs Fig 6: Cyclic Domain Profile for QPSK. [ g [ y [ AC [ g [ CA Fig 8: Proposed system block diagram Proceedings of the SDR 8 Technical Conference Product Eposition, Copyright 8 SDR Forum, Inc. All Rights Reserved

5 Algorithm Step : Choose a small initial length for the equalizer, i.e. K. Step : find the probability of classification for the AC ( pa ). Step 3: increase the number of taps in the equalizer if p a < p th. Step 4: again find there is no need of updating if p > or else repeat step. a p th 5. SIULATION RESULTS Eperiment : To show the performance of the AC a) Performance of AC The network was trained with 5 -profiles (each -profile has points) of each BPSK, QPSK, FSK SK. No noise was added during the training process. The performance of the AC in the presence of AWGN is evaluated using onte Carlo simulations. Table shows the probability of classification of AC in the presence of the noise of SNR 5dB. It is also shown in [7] that the performance of the AC improves when the network is trained in the presence of noise of different variances. Eperiment : To show the recovered symbol sequence convergence. In this eperiment a -input/3-output IO channel is considered, the channel impulse response is given by Convergence.8 H [] ,.7.5 H [] Two QPSK sequences at SNR 5dB is considered. The length of the equalizer considered was K6 the learning rate considered was μ..the received constellation of the signal before after equalization is shown in Fig 9. It can be seen from the simulation that only one the sequence can be recovered, but we don t know which of the input signals. In order to show convergence, the cost function is plotted number of iterations is shown in Fig. Image Received samples - - Real Image Equalized symbols - - Real C[y(n)] n 4 Fig : Convergence of CA to one input sequence. BPSK QPSK FSK SK BPSK QPSK FSK SK Table : Probability of classification of AC in the presence of AWGN (SNR 5dB). b) Performance of AC in the presence of a FIR channel. In this section, degradation in the performance of AC due to the presence of the IO FIR channel is shown using simulations. The channel considered was a - input /3- output IO channel with each entry modeled as a rom 8-Tap FIR filter. The -inputs considered were of the same modulation type AC was added to all 3-outputs. onte Carlo simulation is performed on each output the average probability of classification for each modulation scheme is presented in Table. The simulation results indicate that AC provides inconsistent results in the presence of a multipath fading channel for a particular modulation scheme hence the probability of correct classification decreases. Fig 9: Received Samples ( ) equalized symbols y(n). n Proceedings of the SDR 8 Technical Conference Product Eposition, Copyright 8 SDR Forum, Inc. All Rights Reserved

6 BPSK QPSK FSK SK BPSK QPSK FSK SK Table : Probability of classification for AC in presence of a IO FIR channel (SNR5dB). C) Performance of AC in the presence of an equalizer of different lengths. In this section the effect of using an equalizer of different order for a particular channel is shown using simulations. For the -input/3-output IO FIR channel considered in the previous section, IO CA is added one of the input sequences is recovered. The length of the IO CA equalizer is varied. onte Carlo simulations are performed results are shown in Fig. The results show that the performance of AC improves by increasing the order of the equalizer. These results illustrate the promise of the algorithm proposed. 5. CONCLUSION In this paper, performance degradation of the cyclostationarity based AC in the presence of a IO FIR channel was shown by simulation. IO CA was implemented it was shown that one of the input sequences can be recovered, suppressing the others. Hence by proper initialization, the desired signal can be obtained thereby reducing ISI CCI. A combined IO CA blind equalizer AC was proposed. The effect of the length of the equalizer on the performance of AC was demonstrated based on a simple algorithm to update the length of the equalizer. P robability of Classifiction BPSK QPSK FSK SK 6. REFERENCE [] S. Haykin, Cognitive radio: Brain-empowered wireless communications, IEEE J. Select. Areas Commun., vol. 3, pp. -, 5. [] J. Polson, Cognitive radio applications in software defined radio, in Proc. of the SDR Forum Conference, 4. [3] S. Haykin, Unsupervised adaptive filtering, Vol. II: Blind Deconvolution, John Wiley & Sons, Inc,. [4] A. Fehske, J. Gaeddert J. H. Reed, A new approach to signal classification using spectral correlation neural networks, in Proc. IEEE Dynamic Spectrum Access Nets, pp. 44-5, 5. [5] K. Kim, I. A. Akbar, K. K. Bae, J. Um, C.. Spooner, J. H. Reed, Cylostationary approaches to signal detection classification in cognitive radios, in Proc. IEEE Dynamic Spectrum Access Nets., pp. - 5, 7. [6] W. A. Gardner, Introduction to Rom Process with Applications to Signals Systems. acillan, 986. [7] W. A. Gardner, Statistical Spectral Analysis A Nonprobabilistic Theory. Prentice Hall, 988. [8] R. S. Roberts, Computationally efficient algorithms for cyclic spectral analysis, IEEE Signal Processing ag, Apr. 99. [9] W.. Gardner, easurement of spectral correlation, IEEE Trans on Acoust, Speech, Signal Processing, Vol. ASSP-34, no. 5, Oct.986 [] W.. Gardner C.. Spooner, Signal interception: Performance advantages of cycle-feature detectors, IEEE Trans Commun, vol. 4, no., Jan. 99. [] Y.Li, K. J. Ray Liu, On Blind Equalization of IO Channels, IEEE International Conference on Communication, vol., pp.-4, 996. [] D. N. Godard, Self-recovering equalization carrier tracking in two-dimensional data communication systems, IEEE Trans. Communn., CO-8:pp , 98. [3] J. R. Treichler.G. Larimore, New processing techniques based on the constant modulus adaptive algorithm, IEEE Trans. Acoust, Speech Signal Processing, ASSP-33, pp. 4-43,985. [4] J. R. Treichler B. G. Agee A new approach to multipath correction of constant modulus signals, IEEE Trans. Acoust, Speech Signal Processing, ASSP- 3, pp , Length of the Equalizer Fig : Effect of length of the equalizer on the performance of AC (5dB noise). Proceedings of the SDR 8 Technical Conference Product Eposition, Copyright 8 SDR Forum, Inc. All Rights Reserved

7