Capacity Improvement for TDD-MIMO Systems via AR Modeling ...
Wireless Pers Commun DOI 10.1007/s11277-009-9823-z
Capacity Improvement for TDD-MIMO Systems via AR Modeling Based Linear Prediction Halil Yigit · Adnan Kavak · Kerem Kucuk
© Springer Science+Business Media, LLC. 2009
Abstract The quality of channel state information (CSI) affects the performance of multiple input multiple output (MIMO) systems which employ multi-elements antenna arrays at both the transmitter and the receiver. In a time division duplex (TDD) systems, the CSI for downlink can be obtained from uplink channel using reciprocity principal. However, the performance of a MIMO system can be degraded due to channel impairments especially in fast fading scenarios when the CSI obtained from uplink is used for downlink transmission. In this paper, we study performance of autoregressive (AR) modeling based MIMO channel prediction under varying channel propagation conditions (mobile speed, multipath number and angle spread) and prediction filter order. Our simulation results show that using the predicted CSI for downlink provides capacity improvement compared to conventional method. Keywords
TDD-MIMO · Channel capacity · CSI · Waterfilling
1 Introduction Recently, the multiple-input multiple-output (MIMO) technology has received significant attention of the researchers because of the capacity enhancement and other advantages provided by it [1–4]. MIMO channel matrix describes propagation characteristics of the signals present at transmit and receive antenna arrays [5,6]. For time division duplex (TDD) systems, the last known channel state information (CSI) estimated during the uplink interval can be
H. Yigit · A. Kavak (B) · K. Kucuk Wireless Communications and Information Systems Research Center, Kocaeli University, Izmit, Kocaeli 41380, Turkey e-mail: [email protected] H. Yigit e-mail: [email protected] K. Kucuk e-mail: [email protected]
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used as long as the duplexing time is shorter than the channel coherence time, which may or may not be realized depending on the mobile’s velocity [7]. When the mobile terminal is stationary or moving at a relatively small speed, MIMO channel variations are not significant [8]. However, if the mobile user moves at a relatively high speed, the CSI changes rapidly due to fast fading induced by Doppler shift and other effects in the channel. Under such circumstances, using the CSI of the previous uplink time slot may result in performance (capacity) degradation of the system. This can be avoided by accurately updating the CSI [9,10]. One way of overcoming the fast fading effects and improving the performance of a MIMO system is to predict CSI based on its autoregressive (AR) modeling. In this paper, we investigate the capacity improvement for MIMO systems using AR based channel prediction under varying conditions such as mobile speed (VRx ),transmit and receive multipath angle spreads (θTx , θRx ), number of multipaths (L), and prediction filter order (p). The remainder of this paper is organized as follows. Section 2 introduces MIMO system model and describes TDD-MIMO channel modeling to be used in the prediction. In Section 3, AR modeling based prediction method is explained. Section 4 presents simulation setups and results. Finally, the concluding remarks are given in Section 5.
2 TDD-MIMO Channel Modeling Consider a MIMO system with MT transmit antennas at the base station (BS) and MR receive antennas at the mobile station (MS). Denoting the MR × MT channel transfer matrix by H, its input–output relation is given by Es y= Hs + n (1) MT where y is the MR × 1 received signal vector, s is the MT × 1 transmitted signal vector, n is the zero mean complex Gaussian noise vector with covariance matrix E{nnH } = N0 IMR and Es is the total average energy available at the transmitter. In case of negligible path delay in the channel, MIMO channel model can be written as, H(t) =
L
T jωl t αl aR,l aT,l e
(2)
l=1
where L is the number of multipaths, αl is the complex attenuation caused by reflections from local scatterers, which can be modeled as a Rayleigh fading parameter, aR,l is the MR × 1 dimensional array response vector for the l-th multipath component for the receive antenna array, aT,l is the MT × 1 dimensional array response vector for the l-th multipath component for the transmit antenna array, and ωl is the phase shift induced by varying path lengths due to mobile movement (Doppler effect). If a uniform linear array (ULA) antenna configuration is used, array response vector at the BS is defined as follows T aT,l = 1 e−jT,l · · · e−j(MT −1)T,l (3) where T,l = kdT sin ϕT,l the angular frequency, k is the wave number 2π/λ, λ is the carrier wavelength in meters, dT is the element-spacing of the transmit antenna array, ϕT,l is the direction of departure (DoD) for l-th multipath with respect to BS broadside. aR,l is defined similarly for the receiver (MS).
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Capacity Improvement for TDD-MIMO Systems via Ar Modeling Based Linear Prediction
We consider a TDD-MIMO system where uplink and downlink channels share the same carrier frequency. The uplink CSI can be directly reused for downlink transmission as long as channel variations remain within an acceptable level. This is not valid for fast fading propagation environments wherein a relative motion exists. In the fast fading mobile environments, using the uplink CSI for the downlink transmission causes degradation in the channel capacity. This degradation can be reduced by updating the downlink CSI using some kind of prediction model as we proposed below. The channel capacity is given by C=
r
log2
i=1
E s γi λi 1+ MT N0
(4)
where r is the rank of channel and λi (i = 1,2,…,r) are the positive eigenvalues of channel covariance matrix HHH , representing the power gain, Es /MT denotes transmit power of r sub-channels. γ i reflects the transmit energy in the i-th sub-channel, which is determined iteratively through the waterfilling algorithm [4,5].
3 Autoregressive (AR) Based Prediction It is known that dynamic propagation environments can be well modeled by time varying autoregressive process [11]. The p-th order AR model of the k-th MIMO channel coefficient is
hk (t) =
p
ak,m (t) hk (t − m) + v(t), k = 1,2,…,MR MT
(5)
m=1
where p is the model or prediction filter order and ak,m is the filter coefficients for the k-th channel coefficient, v(t) is the white noise with zero mean and variance σv2 . These parameters are obtained by solving the Yule-Walker equation [11,12]. For prediction analysis, it is convenient to vectorize the above MIMO channel model in (2) as follows, h = vec {H}
(6)
where vectorization operator vec{H} stacks the columns of H into a vector of length MR MT . In AR modeling, for each complex element of the vectorized MIMO channel matrix, h, the model coefficients with order p is constructed from the first N/2 samples in the uplink interval. Then, in the downlink interval, next N/2 samples are predicted using these AR model coefficients.
4 Simulation and Results 4.1 Performance Measure To test the accuracy of the above AR prediction model, we define a relative capacity improvement (C ) metric given by,
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C (dB) = 20 log10
˜ C(H) − C(H) ˆ C(H) − C(H)
(7)
ˆ are the actual and the predicted channel capacities, respectively, for where C(H) and C(H) ˜ is the channel capacity of the prethe current time slot in the downlink interval, and C(H) vious uplink time slot. C indicates how close the capacity of predicted channel to that of actual MIMO channel, and how much error in capacity can be reduced when using predicted channel rather than outdated (previous time interval) channel. 4.2 Simulation Setup Computer simulations are carried out to evaluate the performance of AR modeling based predictions for TDD-MIMO system under different propagation scenarios. We consider that the BS is stationary and the MS is moving at a speed of VRx . We generate N MIMO channel samples using the model in (2) for the given mobile speed (VRx ), the number (L) and mean DoD (θTx ) and DoA (θRx ) of multipaths, and angle spreads (θTx , θRx ). Since we consider TDD mode of operation, we take duplexing time (time between consecutive samples) as 10/15 ms and to be compatible with UTRA-TDD standard [13] we set N = 30. The carrier frequency is set to 1.8 GHz. Within each 20 ms TDD frame, we assume that L, θTx and θRx are constant, and other parameters such as complex fading attenuation αl and Doppler frequency ωl for each multipath are time dependent variables. Complex attenuation is selected from Rayleigh distribution. The Doppler frequency ωl is given by ωl = 2πk VRx cos (ψl )
(8)
where ψl is the angle between the direction of incoming wave in the l-th multipath and the direction vector of the mobile movement. To obtain statistically conclusive results, multiple simulation runs are performed (1000 times). Each simulation run starts with a random position of the MS and scatterers (i.e., DoDs and DoAs of multipaths randomly change with an uniform distribution) and throughout a simulation run V, L, and θ parameters are assumed unchanged but DoDs and DoAs of multipaths change randomly with a uniform distribution in [θ − θ/2, θ + θ/2] where θ is the mean DoA or DoD of multipaths. We calculate capacity values of TDD-MIMO channel for each TDD slot. We take the signal to noise ratio (SNR) value is 10 dB.Then, these values are averaged over the same interval to obtain their cumulative distributions for 1000 simulation runs. 4.3 Results The effects of varying mobile speeds and prediction filter order on the predictor performance are given in Fig. 1. The predictor provides better relative capacity improvement with increasing VRx and p. As clearly seen that for p = 8 and VRx = 90 km/h parameters, AR modeling has approximately 2.3 dB relative capacity improvement. Figure 2 shows the performance of prediction method with varying p and L parameters. As the number of multipaths is increased, the relative capacity improvement increases. For instance, AR method results in approximately 2.2 dB and 1.3 dB improvement at p = 8 and p = 3, respectively, for L = 10.
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Capacity Improvement for TDD-MIMO Systems via Ar Modeling Based Linear Prediction
5x5 MIMO, ∆θ =30°, ∆θ =60°, L=10, SNR=10dB Tx
Rx
3
2
∆C (dB)
1
0
−1
p=3 p=8
−2
−3 50
55
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65
70
75
80
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100
mobile speed, VRx (km/h) Fig. 1 Mean values of cumulative distributions of C for AR modeling based prediction of a MIMO channel for varying mobile speed (VRx ) and filter order (p)
5x5 MIMO, VRx=90km/h, ∆θTx=30°, ∆θRx=60°, SNR=10dB 3
2
∆C (dB)
1
0
−1
−2
p=3 p=8 −3
4
5
6
7
8
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multipath number, L Fig. 2 Mean values of cumulative distribution of C for AR modeling based prediction of a MIMO channel for varying filter order (p) and multipath (L)
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5x5 MIMO, VRx=90km/h, ∆θTx=30°, p=8, SNR=10dB 4
3
2
∆C (dB)
1
0
−1
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∆θ =0° Rx ∆θRx=30° ∆θ =60° Rx ∆θ =90°
−3
Rx
−4
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multipath number, L Fig. 3 Mean values of cumulative distribution of C for AR modeling based prediction of a MIMO channel for varying multipath number (L) and angle spread at the receiver (θRx )
5x5 MIMO, VRx=90km/h, ∆θRx=60°, p=8, SNR=10dB 6
4
∆C (dB)
2
0
−2
∆θ =0° Tx ∆θ =30° Tx ∆θTx=60° ∆θ =90°
−4
Tx
−6
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multipath number, L Fig. 4 Mean values of cumulative distribution of C for AR modeling based prediction for varying multipath number (L) and angle spread at the transmitter (θTx )
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The effects of angle spread at the transmitter and the receiver on the relative capacity improvement of a MIMO channel are given in Figs. 3 and 4. As clearly seen, when the angle spread is large, the capacity improvement is much degraded because in larger angle spread environment, consecutive channel matrix samples might become less correlated.
5 Conclusions For MIMO systems that operate in a time division duplex (TDD) mode, AR modeling based prediction of the uplink MIMO channel for the capacity improvement in fast fading wireless scenarios is studied. The performance of prediction model is investigated for various channel propagation (mobile speed, angle spread, and multipath number) and filter order conditions. The performance measure is relative capacity improvement (C ) that indicates the proximity of the predicted MIMO channel’s capacity to the actual channel’s capacity. We found that for low mobile speeds (i.e., VRx = 65 km/h or below), using AR modeling for MIMO channel prediction has no advantage in terms C . The predictors effect is more prominent under high mobile speeds (i.e., VRx = 90 km/h) and large filter order (i.e., p=8) conditions. The larger the number of multipaths, the more capacity improvement is obtained. When the multipath angle spread at the transmitter and the receiver is small, better relative capacity improvement can be obtained via AR based MIMO channel prediction.
References 1. Bialkowski, M. (2006). Research into multiple element antennas to enhance performance of wireless communication systems. In Proceedings XVI international conference on microwaves, radar, wireless communications (Vol. 3, pp. 1071–1082). 2. Winters, J. (1987). On the capacity of radio communication systems with diversity in a Rayleigh fading environment. IEEE Journal on Selected Areas in Communications, SAC-5, 871–878. 3. Foschini, G. J., & Gans, M. J. (1998). On limits of wireless communications in an fading environment when using multiple antennas. Wireless Personal Communications, 6(3), 311–335. 4. Telatar, E. (1999). Capacity of multi-antenna Gaussian channels. European Transactions on Telecommunications, 10(6), 585–595. 5. Gesbert, D., Shafi, M., Shiu, D. S., Smith, P. J., & Naguib, A. (2003). From theory to practice: An overview of MIMO space-time coded wireless systems. IEEE Journal on Selected Areas in Communications, 21(3), 281–302. 6. Molisch, F., Steinbauer, M., Toeltsch, M., Bonek, E., & Thoma, R. (2002). Capacity of MIMO systems based on measured wireless channels. IEEE Journal on Selected Areas in Communications, 20(3), 561–569. 7. Krim, H., & Viberg, M. (1996). Two decades of array signal processing research. IEEE Signal Processing Magazine, 13(4), 67–94. 8. Kavak, A., Yang, W., Xu, G., & Vogel, W. J. (2001). Characteristics of vector propagation channels in dynamic mobile scenarios. IEEE Transactions on Antennas and Propagation, 39(12), 1695–1702. 9. Kavak, A., Yigit, H., & Ertunc, H. M. (2005). Using adaline neural network for performance improvement of smart antennas in TDD wireless communications. IEEE Transactions Neural Networks, 16(6), 1616–1625. 10. Svantesson, T., & Swindlehurst, L. (2006). A performance bound for prediction of MIMO channels. IEEE Transactions Signal Process, 54(2), 520–529. 11. Dong, L., Xu, G., & Ling, H. (2001). Prediction of fast fading mobile radio channels in wideband communication systems. In Proceedings IEEE Globecom’01, San Antonio, TX (Vol. 6, pp. 3287–3291). 12. Haykin, S. (1996). Adaptive filter theory. Englewood Cliffs, NJ: Prentice Hall. 13. Haardt, M., Klein, A., Koehn, R., Oestreich, S., Purat, M., & Sommer, V., et al. (2000). The TD-CDMA based UTRA TDD mode. IEEE Journal on Selected Areas in Communications, 18(8), 1375–1385.
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Author Biographies Halil Yigit received the B.S. and M.S. degrees in Electronics and Computer Education from Kocaeli University, Kocaeli, Turkey, in 2002 and 2005, respectively. He is currently a Ph.D. candidate and a research assistant in Electronics and Computer Education at Kocaeli University. Currently, he is a member of Wireless Communications and Information Systems (WINS) Research Center. His current area of work includes MIMO communications, MIMO channel modeling and prediction, array signal processing, neural networks, and applications to communications, wireless sensor networks.
Adnan Kavak was born in Usak, Turkey, in 1970. He received the B.S. degree from the Electrical and Electronics Engineering Department, Middle East Technical University, Ankara, Turkey, in 1992. He received the M.S. and Ph.D. degrees from the Electrical and Computer Engineering Department, The University of Texas at Austin, TX, USA, in 1996 and 2000, respectively. He was a satellite control engineer with Turksat Satellite Control Center, Ankara, Turkey, from December 1992 to May 1994. He worked as a Senior Research Engineer at Wireless Systems Laboratory, Samsung Telecommunications America in Richardson, TX, USA, from January 2000 to July 2001. He then joined Kocaeli University, Turkey, in August 2001 and worked as an Assistant Professor there until May 2005. Currently, he is the director of Wireless Communications and Information Systems (WINS) Research Center, and an Associate Professor with the Computer Engineering Department, Kocaeli University, Turkey. His current research interests include 3G and beyond wireless networks, software and cognitive radios, smart antenna systems, MIMO communications, resource allocation in wireless networks, and wireless sensor networks.
Kerem Kucuk was born in Izmit, Turkey, in 1979. He received the B.Sc. and M.Sc. degrees from the Electronics and Computer Education Department, Kocaeli University, Kocaeli, Turkey, in 2002 and 2005, respectively. He is currently pursuing his Ph.D. degree at Kocaeli University. Currently, he is a research assistant with the Department of Electronics and Computer Education, and a member of Wireless Communications and Information Systems (WINS) Research Center, University of Kocaeli, Turkey. Kucuk was awarded “Excellence in Signal Processing Award” by Texas Instruments, in May 2006. His current research interests include wireless communication, wireless sensor networks, MIMO systems, software radio, smart antenna implementation, digital signal processor. His URL is http://wins.kocaeli.edu.tr/kkucuk/.
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Capacity Improvement for TDD-MIMO Systems via AR Modeling Based Linear Prediction Halil Yigit · Adnan Kavak · Kerem Kucuk
© Springer Science+Business Media, LLC. 2009
Abstract The quality of channel state information (CSI) affects the performance of multiple input multiple output (MIMO) systems which employ multi-elements antenna arrays at both the transmitter and the receiver. In a time division duplex (TDD) systems, the CSI for downlink can be obtained from uplink channel using reciprocity principal. However, the performance of a MIMO system can be degraded due to channel impairments especially in fast fading scenarios when the CSI obtained from uplink is used for downlink transmission. In this paper, we study performance of autoregressive (AR) modeling based MIMO channel prediction under varying channel propagation conditions (mobile speed, multipath number and angle spread) and prediction filter order. Our simulation results show that using the predicted CSI for downlink provides capacity improvement compared to conventional method. Keywords
TDD-MIMO · Channel capacity · CSI · Waterfilling
1 Introduction Recently, the multiple-input multiple-output (MIMO) technology has received significant attention of the researchers because of the capacity enhancement and other advantages provided by it [1–4]. MIMO channel matrix describes propagation characteristics of the signals present at transmit and receive antenna arrays [5,6]. For time division duplex (TDD) systems, the last known channel state information (CSI) estimated during the uplink interval can be
H. Yigit · A. Kavak (B) · K. Kucuk Wireless Communications and Information Systems Research Center, Kocaeli University, Izmit, Kocaeli 41380, Turkey e-mail: [email protected] H. Yigit e-mail: [email protected] K. Kucuk e-mail: [email protected]
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used as long as the duplexing time is shorter than the channel coherence time, which may or may not be realized depending on the mobile’s velocity [7]. When the mobile terminal is stationary or moving at a relatively small speed, MIMO channel variations are not significant [8]. However, if the mobile user moves at a relatively high speed, the CSI changes rapidly due to fast fading induced by Doppler shift and other effects in the channel. Under such circumstances, using the CSI of the previous uplink time slot may result in performance (capacity) degradation of the system. This can be avoided by accurately updating the CSI [9,10]. One way of overcoming the fast fading effects and improving the performance of a MIMO system is to predict CSI based on its autoregressive (AR) modeling. In this paper, we investigate the capacity improvement for MIMO systems using AR based channel prediction under varying conditions such as mobile speed (VRx ),transmit and receive multipath angle spreads (θTx , θRx ), number of multipaths (L), and prediction filter order (p). The remainder of this paper is organized as follows. Section 2 introduces MIMO system model and describes TDD-MIMO channel modeling to be used in the prediction. In Section 3, AR modeling based prediction method is explained. Section 4 presents simulation setups and results. Finally, the concluding remarks are given in Section 5.
2 TDD-MIMO Channel Modeling Consider a MIMO system with MT transmit antennas at the base station (BS) and MR receive antennas at the mobile station (MS). Denoting the MR × MT channel transfer matrix by H, its input–output relation is given by Es y= Hs + n (1) MT where y is the MR × 1 received signal vector, s is the MT × 1 transmitted signal vector, n is the zero mean complex Gaussian noise vector with covariance matrix E{nnH } = N0 IMR and Es is the total average energy available at the transmitter. In case of negligible path delay in the channel, MIMO channel model can be written as, H(t) =
L
T jωl t αl aR,l aT,l e
(2)
l=1
where L is the number of multipaths, αl is the complex attenuation caused by reflections from local scatterers, which can be modeled as a Rayleigh fading parameter, aR,l is the MR × 1 dimensional array response vector for the l-th multipath component for the receive antenna array, aT,l is the MT × 1 dimensional array response vector for the l-th multipath component for the transmit antenna array, and ωl is the phase shift induced by varying path lengths due to mobile movement (Doppler effect). If a uniform linear array (ULA) antenna configuration is used, array response vector at the BS is defined as follows T aT,l = 1 e−jT,l · · · e−j(MT −1)T,l (3) where T,l = kdT sin ϕT,l the angular frequency, k is the wave number 2π/λ, λ is the carrier wavelength in meters, dT is the element-spacing of the transmit antenna array, ϕT,l is the direction of departure (DoD) for l-th multipath with respect to BS broadside. aR,l is defined similarly for the receiver (MS).
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Capacity Improvement for TDD-MIMO Systems via Ar Modeling Based Linear Prediction
We consider a TDD-MIMO system where uplink and downlink channels share the same carrier frequency. The uplink CSI can be directly reused for downlink transmission as long as channel variations remain within an acceptable level. This is not valid for fast fading propagation environments wherein a relative motion exists. In the fast fading mobile environments, using the uplink CSI for the downlink transmission causes degradation in the channel capacity. This degradation can be reduced by updating the downlink CSI using some kind of prediction model as we proposed below. The channel capacity is given by C=
r
log2
i=1
E s γi λi 1+ MT N0
(4)
where r is the rank of channel and λi (i = 1,2,…,r) are the positive eigenvalues of channel covariance matrix HHH , representing the power gain, Es /MT denotes transmit power of r sub-channels. γ i reflects the transmit energy in the i-th sub-channel, which is determined iteratively through the waterfilling algorithm [4,5].
3 Autoregressive (AR) Based Prediction It is known that dynamic propagation environments can be well modeled by time varying autoregressive process [11]. The p-th order AR model of the k-th MIMO channel coefficient is
hk (t) =
p
ak,m (t) hk (t − m) + v(t), k = 1,2,…,MR MT
(5)
m=1
where p is the model or prediction filter order and ak,m is the filter coefficients for the k-th channel coefficient, v(t) is the white noise with zero mean and variance σv2 . These parameters are obtained by solving the Yule-Walker equation [11,12]. For prediction analysis, it is convenient to vectorize the above MIMO channel model in (2) as follows, h = vec {H}
(6)
where vectorization operator vec{H} stacks the columns of H into a vector of length MR MT . In AR modeling, for each complex element of the vectorized MIMO channel matrix, h, the model coefficients with order p is constructed from the first N/2 samples in the uplink interval. Then, in the downlink interval, next N/2 samples are predicted using these AR model coefficients.
4 Simulation and Results 4.1 Performance Measure To test the accuracy of the above AR prediction model, we define a relative capacity improvement (C ) metric given by,
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C (dB) = 20 log10
˜ C(H) − C(H) ˆ C(H) − C(H)
(7)
ˆ are the actual and the predicted channel capacities, respectively, for where C(H) and C(H) ˜ is the channel capacity of the prethe current time slot in the downlink interval, and C(H) vious uplink time slot. C indicates how close the capacity of predicted channel to that of actual MIMO channel, and how much error in capacity can be reduced when using predicted channel rather than outdated (previous time interval) channel. 4.2 Simulation Setup Computer simulations are carried out to evaluate the performance of AR modeling based predictions for TDD-MIMO system under different propagation scenarios. We consider that the BS is stationary and the MS is moving at a speed of VRx . We generate N MIMO channel samples using the model in (2) for the given mobile speed (VRx ), the number (L) and mean DoD (θTx ) and DoA (θRx ) of multipaths, and angle spreads (θTx , θRx ). Since we consider TDD mode of operation, we take duplexing time (time between consecutive samples) as 10/15 ms and to be compatible with UTRA-TDD standard [13] we set N = 30. The carrier frequency is set to 1.8 GHz. Within each 20 ms TDD frame, we assume that L, θTx and θRx are constant, and other parameters such as complex fading attenuation αl and Doppler frequency ωl for each multipath are time dependent variables. Complex attenuation is selected from Rayleigh distribution. The Doppler frequency ωl is given by ωl = 2πk VRx cos (ψl )
(8)
where ψl is the angle between the direction of incoming wave in the l-th multipath and the direction vector of the mobile movement. To obtain statistically conclusive results, multiple simulation runs are performed (1000 times). Each simulation run starts with a random position of the MS and scatterers (i.e., DoDs and DoAs of multipaths randomly change with an uniform distribution) and throughout a simulation run V, L, and θ parameters are assumed unchanged but DoDs and DoAs of multipaths change randomly with a uniform distribution in [θ − θ/2, θ + θ/2] where θ is the mean DoA or DoD of multipaths. We calculate capacity values of TDD-MIMO channel for each TDD slot. We take the signal to noise ratio (SNR) value is 10 dB.Then, these values are averaged over the same interval to obtain their cumulative distributions for 1000 simulation runs. 4.3 Results The effects of varying mobile speeds and prediction filter order on the predictor performance are given in Fig. 1. The predictor provides better relative capacity improvement with increasing VRx and p. As clearly seen that for p = 8 and VRx = 90 km/h parameters, AR modeling has approximately 2.3 dB relative capacity improvement. Figure 2 shows the performance of prediction method with varying p and L parameters. As the number of multipaths is increased, the relative capacity improvement increases. For instance, AR method results in approximately 2.2 dB and 1.3 dB improvement at p = 8 and p = 3, respectively, for L = 10.
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5x5 MIMO, ∆θ =30°, ∆θ =60°, L=10, SNR=10dB Tx
Rx
3
2
∆C (dB)
1
0
−1
p=3 p=8
−2
−3 50
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mobile speed, VRx (km/h) Fig. 1 Mean values of cumulative distributions of C for AR modeling based prediction of a MIMO channel for varying mobile speed (VRx ) and filter order (p)
5x5 MIMO, VRx=90km/h, ∆θTx=30°, ∆θRx=60°, SNR=10dB 3
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∆C (dB)
1
0
−1
−2
p=3 p=8 −3
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multipath number, L Fig. 2 Mean values of cumulative distribution of C for AR modeling based prediction of a MIMO channel for varying filter order (p) and multipath (L)
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5x5 MIMO, VRx=90km/h, ∆θTx=30°, p=8, SNR=10dB 4
3
2
∆C (dB)
1
0
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∆θ =0° Rx ∆θRx=30° ∆θ =60° Rx ∆θ =90°
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−4
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multipath number, L Fig. 3 Mean values of cumulative distribution of C for AR modeling based prediction of a MIMO channel for varying multipath number (L) and angle spread at the receiver (θRx )
5x5 MIMO, VRx=90km/h, ∆θRx=60°, p=8, SNR=10dB 6
4
∆C (dB)
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0
−2
∆θ =0° Tx ∆θ =30° Tx ∆θTx=60° ∆θ =90°
−4
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−6
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multipath number, L Fig. 4 Mean values of cumulative distribution of C for AR modeling based prediction for varying multipath number (L) and angle spread at the transmitter (θTx )
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Capacity Improvement for TDD-MIMO Systems via Ar Modeling Based Linear Prediction
The effects of angle spread at the transmitter and the receiver on the relative capacity improvement of a MIMO channel are given in Figs. 3 and 4. As clearly seen, when the angle spread is large, the capacity improvement is much degraded because in larger angle spread environment, consecutive channel matrix samples might become less correlated.
5 Conclusions For MIMO systems that operate in a time division duplex (TDD) mode, AR modeling based prediction of the uplink MIMO channel for the capacity improvement in fast fading wireless scenarios is studied. The performance of prediction model is investigated for various channel propagation (mobile speed, angle spread, and multipath number) and filter order conditions. The performance measure is relative capacity improvement (C ) that indicates the proximity of the predicted MIMO channel’s capacity to the actual channel’s capacity. We found that for low mobile speeds (i.e., VRx = 65 km/h or below), using AR modeling for MIMO channel prediction has no advantage in terms C . The predictors effect is more prominent under high mobile speeds (i.e., VRx = 90 km/h) and large filter order (i.e., p=8) conditions. The larger the number of multipaths, the more capacity improvement is obtained. When the multipath angle spread at the transmitter and the receiver is small, better relative capacity improvement can be obtained via AR based MIMO channel prediction.
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Author Biographies Halil Yigit received the B.S. and M.S. degrees in Electronics and Computer Education from Kocaeli University, Kocaeli, Turkey, in 2002 and 2005, respectively. He is currently a Ph.D. candidate and a research assistant in Electronics and Computer Education at Kocaeli University. Currently, he is a member of Wireless Communications and Information Systems (WINS) Research Center. His current area of work includes MIMO communications, MIMO channel modeling and prediction, array signal processing, neural networks, and applications to communications, wireless sensor networks.
Adnan Kavak was born in Usak, Turkey, in 1970. He received the B.S. degree from the Electrical and Electronics Engineering Department, Middle East Technical University, Ankara, Turkey, in 1992. He received the M.S. and Ph.D. degrees from the Electrical and Computer Engineering Department, The University of Texas at Austin, TX, USA, in 1996 and 2000, respectively. He was a satellite control engineer with Turksat Satellite Control Center, Ankara, Turkey, from December 1992 to May 1994. He worked as a Senior Research Engineer at Wireless Systems Laboratory, Samsung Telecommunications America in Richardson, TX, USA, from January 2000 to July 2001. He then joined Kocaeli University, Turkey, in August 2001 and worked as an Assistant Professor there until May 2005. Currently, he is the director of Wireless Communications and Information Systems (WINS) Research Center, and an Associate Professor with the Computer Engineering Department, Kocaeli University, Turkey. His current research interests include 3G and beyond wireless networks, software and cognitive radios, smart antenna systems, MIMO communications, resource allocation in wireless networks, and wireless sensor networks.
Kerem Kucuk was born in Izmit, Turkey, in 1979. He received the B.Sc. and M.Sc. degrees from the Electronics and Computer Education Department, Kocaeli University, Kocaeli, Turkey, in 2002 and 2005, respectively. He is currently pursuing his Ph.D. degree at Kocaeli University. Currently, he is a research assistant with the Department of Electronics and Computer Education, and a member of Wireless Communications and Information Systems (WINS) Research Center, University of Kocaeli, Turkey. Kucuk was awarded “Excellence in Signal Processing Award” by Texas Instruments, in May 2006. His current research interests include wireless communication, wireless sensor networks, MIMO systems, software radio, smart antenna implementation, digital signal processor. His URL is http://wins.kocaeli.edu.tr/kkucuk/.
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