Fading Channel Prediction for Mobile Radio Adaptive Transmission Systems

Transcription

1 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 1 Fading Channel Prediction for Mobile Radio Adaptive Transmission Systems Alexandra Duel-Hallen, Senior Member, IEEE Abstract Adaptive transmission methods can potentially aid the achievement of high data rates required for mobile radio multimedia services. To realize this potential, the transmitter needs accurate channel state information (CSI) for the upcoming transmission frame. In most mobile radio systems the CSI is estimated at the receiver and fed back to the transmitter. However, unless the mobile speed is very low, the estimated CSI cannot be used directly to select the parameters of adaptive transmission systems, since it quickly becomes outdated due to the rapid channel variation caused by multipath fading. To enable adaptive transmission for mobile radio systems, prediction of future fading channel samples is required. Several fundamental issues arise in the design and testing of fading prediction algorithms for adaptive transmission systems. These include complexity, robustness, choice of an appropriate channel model for algorithm validation, channel estimation and noise reduction required for reliable prediction, and design and analysis of adaptive transmission methods aided by fading prediction algorithms. We use these criteria in the review of recent advances in the area of fading channel prediction. We also demonstrate that reliable fading prediction makes adaptive transmission feasible in diverse wireless communication systems. Index Terms Fading Channel Prediction, Adaptive Transmission, Adaptive Modulation, Adaptive MIMO Systems, Adaptive OFDM, Adaptive Spread Spectrum Systems. I. INTRODUCTION. Fading prediction algorithms are motivated by the following idea illustrated in Figure 1 for the adaptive transmitter antenna selection method. The transmitter selects the stronger antenna based on the channel gain information sent from the receiver. As the vehicle moves, the channel gain (determined by the interference pattern that causes fading) rapidly varies. Thus, due to the feedback delay and other system constraints, the channel state information observed by the receiver is outdated at the time of the transmission. An antenna choice based on this outdated CSI is not likely to correspond to the stronger channel. Thus, the channel needs to be predicted sufficiently far ahead for reliable transmission. As illustrated in Figure 2, the interference pattern that causes fading arises due to multiple reflections of the Manuscript received Dec. 15, This research was supported by NSF grant CCR and ARO grant W911NF Alexandra Duel-Hallen is with the Department of Electrical and Computer Engineering, Box 7911, North Carolina State University, Raleigh, NC, , USA, sasha@ncsu.edu transmitted signal from objects in the environment. If an unmodulated carrier at the frequency f c is transmitted over a fading channel, the complex envelope (the equivalent lowpass signal) [1,2,3] of the received noiseless signal is given by N c(t) = A n e j(2πf nt+φ n ), (1) n=1 where N is the number of reflectors, sometimes termed scatterers. For the n th reflector, A n is the amplitude, f n is the Doppler frequency shift and φ n is the phase. The Doppler frequency shift is given by: f n = f c v c cosθ n = f dm cosθ n (2) where v is the vehicle speed, c is the speed of light, θ n is the incident radio wave angle with respect to the motion of the mobile, and f dm is the maximum Doppler frequency shift. In (1), the n th complex exponential term is contributed by an individual reflector [2,3,4]. The parameters A n, f n, and φ n vary slowly (on the order of 0.1 sec [4,5]), and can be viewed as fixed on the time scale of a few milliseconds. Thus, the signal c(t) in (1) is a superposition of complex sinusoids and is highly time-variant if the mobile speed is significant. The superposition of terms in (1) can result in destructive or constructive interference, causing deep fades or peaks in the received signal, respectively, as illustrated in Figure 3. As a result, the power of the fading signal can change dramatically, by as much as 30-40dB. Rayleigh stationary uncorrelated scattering random process [1] and the deterministic Jakes model [6] are popular channel models for fading signals without the line of sight. In narrowband communication systems, the complex envelope of the received signal sampled at the rate f s is given by y n =c n x n +z n, (3) where c n, x n and z n are the samples of the time-varying flat fading [1] channel coefficient c(t) in (1), the transmitted symbols, and the additive white Gaussian noise, respectively. We assume that the power of the fading process is normalized to one. Since the channel coefficient is rapidly time variant for fast vehicle speeds, the channel quality estimated by the receiver and fed back to the transmitter differs from that actually experienced during the transmission of the following frame. This degrades the achievable performance gain. Even in open loop systems where the Channel State information (CSI) is obtained directly at the transmitter, e.g., in the time

2 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 2 division duplex (TDD) operation, the current CSI is not sufficient, since the knowledge of the future channel conditions is required to adapt the transmission parameters. To realize the potential of adaptive transmission, the channel variations have to be reliably predicted for the upcoming transmission frame. A review of fading prediction approaches for adaptive transmission was presented in [4]. This field has grown significantly since then. While fading prediction has been primarily applied in narrowband systems [7,8,9,10,11,12,13,14,15] (see also references in [4]), recent work has focused on enabling mobile radio wideband, multiuser and multiple antenna systems [16,11,17,18,19,20,21,22,23,24,25,26, 27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43] by utilizing mobile channel prediction. This paper assumes familiarity with the earlier prediction literature (e.g., the review in [4]) and describes recent advances in the area of fading prediction. The goals are to review the signal processing approaches for reliable prediction and to demonstrate that accurate fading prediction enables adaptive transmission in various applications. The rest of this paper is organized as follows. In Section II, fading prediction algorithms, channel modeling issues, noise reduction methods, and performance bounds are reviewed. In Section III, the benefits and trade-offs of prediction techniques for several practical adaptive transmission systems are discussed. Section IV concludes the paper. II. FADING PREDICTION METHODS. To enable adaptive transmission, a fading prediction algorithm must predict the fading signal (e.g., c n in (3)) for the upcoming transmission frame. The desired prediction range τ can vary from a fraction of a ms to many ms, depending on the application. Since prediction ranges in adaptive transmission applications are typically much larger than in channel estimation and other receiver-based methods (on the order of a symbol interval), we refer to the techniques discussed in the paper as the long range prediction. When the carrier frequency and the propagation conditions are fixed, one can predict reliably twice as far for a vehicle speed of 50 km/h than for 100 km/h. To normalize the prediction range, it is often expressed in spatial units: wavelengths, λ. (The spatial nature of fading is illustrated in Figure 1.) When the maximum Doppler shift is f dm (2), prediction τ sec ahead corresponds to f dm τ wavelengths, and the desired spatial prediction range varies from a fraction of a wavelength for most adaptive transmission systems to about one wavelength for systems that require fixed transmission parameters over long data frames. The prediction mean square error, MSE=E[ c n -c^n 2 ], where c^n is the predicted channel coefficient, is often used as a measure of prediction reliability. However, the sensitivity of various adaptive transmission systems to the MSE level varies significantly. For example, transmission antenna selection is very robust to the prediction error [24,25], while adaptive modulation (AM) is more sensitive [8,37]. Therefore, it is important to measure overall system performance (e.g., the bit error rate or the throughput) when assessing prediction reliability. While prediction of the complex fading coefficient in (3) is often employed and will be implied in the subsequent discussion, it is often desirable to forecast the power of predicted samples, since it determines the parameters of many adaptive transmission techniques. Since the estimate of future power gain computed from the predicted complex coefficient c n in (3) is biased, direct power prediction approaches were developed and utilized in [7,8,25,38]. Moreover, past and predicted channel estimates can be located at multiple frequencies, diversity branches or antenna elements in wideband channels or Multiple Input Multiple Output (MIMO) systems as discussed in Sections II.D and III. The performance issues discussed below extend to the prediction of power and to diverse applications. A. Prediction Algorithms The theory of estimation, tracking and prediction of random processes with slowly time-varying statistics is very well developed [1, 44, 45, 46, 47]. Since fading signal in (1) can be modeled successfully using such random process characterization [1,2,3], these standard techniques have been exploited by researchers on fading signal prediction. Most fading prediction methods in the literature fall into one of three categories: (i) auto-regressive (AR) model-based techniques; (ii) sum-of-sinusoids (SOS) model-based methods; (iii) band-limited process model-based and other basis expansion algorithms. (i) AR model-based methods In the AR model-based algorithms, the prediction of the future channel sample c^n is given by: p c^n = d j (n) c n-j (4) j=1 where p is the AR model order, and c n-1,..., c n-p are p previous channel samples. The AR model-based prediction methods are also often referred to linear predictors (LP). The slowly timevariant AR coefficients d j (n) are computed using the Minimum Mean Square Error criterion (MMSE) [1]. When the signal samples are jointly Gaussian, as in the Rayleigh fading process that corresponds to N= in (1), the linear MMSE predictor in (4) is the optimal MMSE predictor [44,45]. Since empirical distributions of fading signals obtained from measurements are modeled well by the Gaussian distribution even when number of reflectors is modest [4,5,6], the linear predictor is expected to have excellent performance, provided that the prediction coefficients can be correctly identified and tracked. The ARmodel based Long Range Fading Prediction method (LRP) was discussed in [4]. In the LRP algorithm, the sampling rate f s in (4) (given by 1/T s, where T s is the time interval between the fading samples c n used by the predictor) is chosen higher

3 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 3 that the Nyquist rate of the fading signal given by twice the maximum Doppler frequency f dm, but much lower than the data rate. Given fixed filter length p, this low sampling rate increases the memory span in (4) and utilizes large sidelobes of the channel autocorrelation function, resulting in prediction farther into the future than for symbol sampling rate-based prediction methods, usually employed in the receiver for channel estimation and demodulation. The equation (4) can also be easily extended to directly accommodate an arbitrary prediction range. To simplify the implementation in those cases when several predicted samples are required, iterative multi-step prediction can be employed. This technique is useful when predicted low rate samples are interpolated to forecast the fading signal at the data rate [4]. The computation of the AR coefficients d j (n) in (4) requires the knowledge of the correlation function of the channel coefficients. (Throughout the paper, an empirical correlation function is implied when discussing the deterministic fading signals [4,6,28,33].) Since this function is unknown and slowly time-variant in practice, it has to be estimated from noise-corrupted channel observations. The Burg method was employed in [27, 48, 49] and the Modified Covariance method was utilized in [48] to estimate these coefficients. These techniques are based on Least Squares minimization [45]. Moreover, efficient adaptive filtering techniques, Least Mean Squares (LMS), Normalized LMS (N-LMS), Recursive Least Squares (RLS), QR-Decomposition based RLS (QR-RLS), and Affine Projection algorithms [46] were used to track the changes of predictor coefficients in [4,5,48,28,29,50]. (ii) SOS model-based prediction While fading prediction methods are based on modeling the fading signal as a random process, the deterministic fading description (1) provides an intuitive justification of their utilization and effectiveness. For example, the SOS modelbased approaches can be explained using the following idea: if the parameters associated with the complex exponentials in (1) (the amplitudes, Doppler shifts and phases) are known perfectly and remain fixed, the individual complex sinusoids can be extrapolated into the future and superimposed to produce reliable prediction of the fading signal. Whereas the AR-model based methods directly estimate the coefficients d j (n) in (4), the SOS approaches employ spectral estimation methods to determine the parameters associated with individual sinusoids in (1), e.g. MUSIC and ESPRIT algorithms [27,39,48,51,52,53] to accomplish the extrapolation of the fading process. A reduced complexity ESPRIT algorithm was proposed in [39] to overcome the high computational load of SOS techniques for realistic channels with time-variant parameters. A combined SOS and LP approach was recently proposed and tested for measured data in [53]. (iii) Basis expansion techniques Band-limited process model-based prediction algorithms were investigated in [54,55,56]. In these methods, the basis functions of the subspace of time-concentrated and bandlimited sequences are determined using the autocorrelation function of the fading channel. The extrapolated basis functions are then used to construct predicted fading coefficients. A related modal expansion method based on a physical equation for wave propagation was employed in [57]. While reliable performance has been demonstrated for the synthetic radio channels with stationary parameters, performance-complexity trade-offs for realistic or measured channels have not been investigated for these methods. (iv) Performance comparison for measured channels Performance of several AR and SOS model-based prediction methods was compared in [48]. A normalized mean square error threshold of -20dB was employed to determine whether various prediction methods provide reliable prediction performance for a given prediction range. For the synthetic radio channel (the Jakes model), the SOS algorithms root-music and ESPRIT achieve a prediction range of several wavelengths and outperform the AR-model based techniques. However, the performance expectation of the SOS methods is not fulfilled when tested with realistic statistical model or measured signals. Figure 4 illustrates the comparison of envelope prediction for these two SOS methods and several AR model-based techniques for measured data. It is demonstrated the AR model-based Modified Covariance and QR-RLS method are the most attractive in this case, since they provide reliable performance beyond one wavelength. It is also discussed in [48] that RLS with an adaptive forgetting factor also performs well for measured channels. Prediction results for measured channels in [53] confirm the superiority and robustness of the AR model-based linear prediction approach. (v) Advantages of AR model-based algorithms In summary, the AR-model based methods are more appropriate than SOS techniques for realistic channels. As stated in [48], This is a welcome result since exactly these algorithms are of considerably less computational complexity as compared with the subspace-based parameter estimation schemes. The difference in performance between the data produced by the Jakes model and the realistically modeled or measured data sets can be explained as follows. In the Jakes model, the parameters associated with the reflectors (the amplitudes, the Doppler shifts and the phases) in (1), and the resulting correlation function of the fading process, are timeinvariant. Therefore, when the Jakes model is employed, the SOS-based methods are able to resolve the sinusoids in the signal spectrum. However, in real mobile radio environments, the parameters of the reflectors and, thus, the correlation function, are slowly time-variant. This variation is caused by many position-dependent factors as the mobile proceeds along its route: the number and the locations of the reflectors, the vehicle speed, the carrier frequency, the distance between the transmitter and the receiver, etc [4,5,48,58]. To enable adaptive transmission, the channel has to be predicted far

4 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 4 ahead, and thus requires a much longer memory span than conventional channel estimation and tracking algorithms [4,40]. Due to this large memory span, the performance of the prediction algorithms is affected by the slow variation in time of the parameters associated with the reflectors. The spectral resolution required for the SOS methods is very sensitive to these time-varying effects, while several AR model-based algorithms can maintain reliable prediction, since they employ direct estimation and fast tracking of the model coefficients in (4). B. Channel Modeling Issues The performance comparison in [48] illustrates the importance of using realistic models for testing prediction methods for adaptive transmission. Testing of prediction algorithms requires a model that creates the slow parameter variation discussed above in a physically realistic manner. The Jakes model is sufficient for verifying techniques that span shorter data frames, such as channel estimation at the receiver. We employed a physical channel model based on the method of images and augmented with diffraction [4,5,58] to test the AR-model based LRP algorithm and its application in adaptive transmission schemes. It has been demonstrated that this physical model generates datasets with time-variant statistical characterization and results of the prediction performance similar to those for measured data, and differing significantly from those for Jakes model data. In addition, this model s insights allow classification of scenarios into typical and challenging cases for testing fading prediction methods. This classification is more difficult to make a-priori with measured data. Figure 5 illustrates the MSE comparison of the LRP with p=40 in (4) that utilizes adaptive RLS and LMS tracking of the AR coefficients. A Jakes model and a typical data set generated by realistic physical model are employed [5,58]. As in [48], utilization of the Jakes model results in overoptimistic estimate of the MSE. Moreover, RLS significantly outperforms LMS. Its gain is on the order of 10dB for realistic prediction ranges for the physical model. This result can be explained by the superior convergence properties of the RLS algorithm [1,46]. The correlation matrices of the fading signals have large eigenvalue spreads, and, therefore, the LMS is not sufficient for tracking these signals. The reliable prediction range in this figure is smaller than that reported in [48] (see Figure 4), mostly due to the fact that only two of many possible prediction methods are compared in Figure 5. However, it clearly illustrates that both fast tracking and realistic modeling are necessary for successful design and validation of long range fading prediction. Note that the complex envelope of the measured and physical model-generated data often has a non-zero timevarying mean that is due to a line-of sight component and/or to non-equal strengths of dominant reflectors. The Rician model [1] is often employed to include this mean. To make a fair comparison with the Jakes model, the local mean (computed using a sliding window) was subtracted from the measured and model-generated data sets in Fig. 5, the results in Section III.B below, and in [4,5,28,58]. The resulting data sets had approximately Rayleigh fading distributions. The non-zero mean would potentially improve prediction accuracy. However, it is worth noting that even when the mean is not removed, as in the results of Section III.C and [32,33,48], prediction MSE for the measured or realistically modeled signal is worse than for the zero mean Jakes model. Thus, in practice, the non-zero mean cannot compensate for the detrimental effect of the time-varying parameters associated with the reflectors. C. Noise Reduction For the AR model-based prediction, the prediction MSE saturates to the theoretical value derived in [37] as the number of taps p in (4) increases. Most of the gain is achieved by p=30 for the Jakes model [4,59]. The MSE strongly depends on the additive noise variance, or the Signal-to-Noise ratio (SNR) in the past observations in (4). For example, when predicting 0.2λ ahead, the theoretical MMSE rises from about -30dB to -10dB as the SNR decreases from 60 to 20 db [4,7]. This amounts to about 1.5 bits/symbol loss for adaptive modulation methods [7,8,37]. Thus, prediction quality is degraded for realistic received SNR values in (3) if raw channel observations are employed for prediction. Noise reduction techniques that use over-sampling in (3) to average out the noise and to increase the effective SNR in the past observations have been proposed [4,7,29,49,59]. These approaches are effective, since the variation of the fading signal in (3) is much slower that that of the noise when the sampling rate significantly exceeds the maximum Doppler shift. Noise reduction produces a reliable estimate of the fading coefficient c n that replaces the raw observation in (3). The benefit of the noise reduction diminishes as the prediction range grows [7]. For prediction ranges of over half a wavelength, the prediction error (computed for the noiseless observations) dominates the MSE. In [7,49], highly over-sampled pilots were employed in a single carrier system. In [7], these pilots were smoothed using a Wiener filter, producing a channel estimate with reduced additive noise variance. For example, for a raw SNR=20dB, a pilot rate of 100f dm and a prediction range of 0.2λ, the MSE is reduced by 5dB relative to using raw pilots, thus increasing the achievable bit rate of AM by about 0.5 bps [8,37]. In [49], the pilot sequences are filtered by a band-pass filter with a cut-off frequency determined by the maximum Doppler shift. The trade-offs of pilot symbol allocation were examined in [9,60]. Since over-sampled pilots degrade spectral efficiency, decision directed noise reduction has been proposed in [4,29,59]. While this approach can potentially enhance the noise reduction, since the over-sampling is performed at the data rate, decision errors can degrade performance. Noise reduction that involves both decisions and pilots is under investigation [61]. Sufficient noise reduction and the resulting

5 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 5 high effective observation SNR is assumed in most numerical results presented in this paper. D. The Cramer-Rao Bound and the Prediction Gain for MIMO systems The Cramer-Rao bound (CRB) [44] on the prediction MSE was derived in [40,41,51,62,63] for several adaptive transmission systems. Moreover, it was shown in [40] that the CRB is much lower for MIMO than for a Single Input Single Output (SISO) channels. Figure 6 shows the prediction length, defined as the maximum prediction horizon (obtained from the CRB) in units of wavelength with an average normalized prediction error less than 0.05, versus measurement length, for MIMO systems with M t input and M r output antennas separated by λ/2 [40] and N=10 in (1). Since noise reduction (over-sampling) is not utilized, the prediction results for the SISO case are worse than for high-snr scenarios presented in previous figures, but are consistent with the investigations in [4,7,59]. Reliable prediction of at least several wavelengths is demonstrated for MIMO systems in the CRB results of Fig. 6. In addition, the optimal two-dimensional MIMO MMSE prediction algorithm and a suboptimal MIMO approach were presented in [35], and it was demonstrated that when the antenna correlations are taken into account, there is performance gain relative to SISO methods, especially when both the additive noise and the spatial correlation are significant. It is also discussed in [40] that the reliability of prediction decreases as the number of reflectors N in (1) grows. Beamforming that projects the signal in (1) onto several angular regions, thus resolving the signal with N complex sinusoids into several components with a smaller number of rays, is exploited to improve prediction accuracy [40]. The dependency of the prediction reliability on N is also addressed in the CRB results in [51], in the MIMO predictor presented in [42], and the investigation in [59] where it is demonstrated that as N decreases, the sidelobes of the channel autocorrelation function increase, and more reliable prediction results. This gain is the most dramatic for modest values of N. Measurements and realistic channel modeling [4,26,64] demonstrate that a relatively small number of strong reflectors often dominate wireless signals. Numerous sinusoidal components that result from diffuse scattering quickly weaken away from the object, and can usually be ignored. However, we emphasize that reliable prediction is achievable for the continuous scattering model, as discussed for the Rayleigh fading random process corresponding to infinite N in (1) in [4,59], and for the physics-based models in [57,62]. III. ENABLING ADAPTIVE TRANSMISSION IN MOBILE RADIO SYSTEMS USING FADING PREDICTION To justify the implemention complexity of a fading prediction method, it is useful to compare system performance with and without prediction. In this section, we first discuss the benefits of fading prediction in 3 rd generation Wideband Code Division Multiple Access (W-CDMA) systems with transmitter antenna selection, and the relationship between multipath diversity and the prediction gain. Second, we demonstrate that AR model-based RLS fading prediction achieves near-optimal bit rates in mobile radio Adaptive Orthogonal Frequency Division Multiplexing (AOFDM) systems. Finally, we show that fading prediction makes adaptive modulation possible in Frequency Hopping Systems. A. Transmitter Antenna Diversity in W-CDMA Systems Systems that utilize diversity combining exploit several uncorrelated (or partially correlated) fading channels, termed diversity branches. Since it is unlikely that these channels will experience deep fades simultaneously, a diversity gain, or improved SNR, is obtained [1]. A simple and efficient closed loop transmit antenna diversity technique selective transmit diversity (STD) is illustrated in Figure 1. STD and other transmit diversity techniques that require knowledge of the CSI at the transmitter have better potential performance than methods that do not rely on this knowledge (e.g., space-time codes). However, as discussed in the Introduction, fading prediction is needed to realize the potential of these closed loop methods. (i) W-CDMA with Selective Transmit Diversity The implementation of STD enabled by LRP in W-CDMA systems was investigated in [20]. In addition to STD, several other diversity approaches are utilized in W-CDMA. Channel coding with interleaving exploits time diversity [1]. Moreover, CDMA systems usually employ waveforms with a transmission bandwidth that is much larger than the symbol rate. Thus, they typically experience significant frequency (multipath) diversity achieved using a RAKE correlator. We assume using the Maximal Ratio Combining (MRC), and, thus, the total power at the output of the RAKE correlator is given by the sum of powers of independent flat fading multipath components [1]. The STD system chooses the transmitter antenna that corresponds to the downlink channel with the largest total received power. To predict the total received power for each channel, we employ the LP method (LRP) in (4) to forecast the individual flat fading complex RAKE taps. These predictions are then combined to forecast the total channel power [25]. The following parameters were used in the simulation of the W-CDMA system with two transmitter antennas [20]. Halfrate constraint length nine convolutional coding is used with generator polynomial parameters 561 and 753 in octal form. The minimum distance of the code is 12. The interleaving depth is 10ms. The orthogonal codes are obtained with the tree structure [65]. The Jakes model with 9 oscillators is employed. The carrier frequency is 2 GHz, the vehicle speed is 60 MPH, f dm =200 Hz, the chip rate is Mcps, and the bit rate is 128 kbps [20]. The sampling rate of the LRP algorithm f s is chosen as the slot rate of 1.6 khz, and p=50 in (4). This results in at least ms delay for calculating the channel state information. The multi-step LRP [4] is used at

6 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 6 the receiver to obtain the predicted values of the channel coeffients in the next few slots, given the delayed channel samples. For STD, these coefficients are used to choose the antenna with the largest received power, and in other closedloop approaches they are used to determine the transmitter antenna weights [20]. Note that the feedback load is very low for the STD method, since only the index of the selected antenna needs to be fed back. The number of predicted samples depends on the switching frequency, as discussed below. In W-CDMA with adaptive tranmsission, the desired prediction range can vary from 0.625ms (1 slot) to 10 ms (the frame length) [65]. (ii) Numerical results and the relationship between system diversity order and the benefit from prediction In Figure 7, the Bit Error Rate (BER) of the STD method is compared for different antenna switching frequencies 1.6 KHz (at the slot rate) and 400Hz (once every four slots). Thus, the prediction ranges are 1 slot, or 0.125λ, and 4 slots, or 0.5 λ. A single predicted sample per antenna is sufficient for the higher switching rate. However, for the lower switching rate, average predicted channel state information for the duration of the entire future switching interval is utilized. When prediction is not employed, the channel sample delayed by one slot relative to the beginning of the switching interval is used to select the antenna for downlink transmission. Results for the flat fading channel (in the absence of multipath) are presented in Figure 7 (a). It is observed that significant performance improvement is possible when prediction is used. Note that the performance of STD with the higher switching rate approaches the ideal performance (STD Every bit) and is very close to the theoretical lower bound (Tx AA with perfect CSI and 2 path MRC). Although the prediction error increases as the switching frequency decreases, the gain due to employing prediction instead of using the outdated CSI increases from about 1 db to 2.5 db as the switching frequency changes from 1.6KHz to 400Hz. Figure 7 (b) shows the comparison between STD with a RAKE receiver and a more complex space-time closed loop precoding method (STPR) method [20] for a 4-path channel. The gain due to prediction is lower here than in Figure 7(a) (around 0.5 db for 1.6 khz, and about 1 db for 400 Hz switching, respectively). This can be explained as follows: the total power at the output of the RAKE receiver is used to select the transmit antenna in the Figure 7 (b) case. This power is less time-variant than the power of the flat fading signal in (1), used for antenna selection in Figure 7 (a). Thus, the outdated channel estimate is more reliable for the multipath channel, and prediction is less helpful. This result generalizes to systems with various forms of diversity at the transmitter and the receiver. As the diversity order increases, the performance for the fading channel saturates and approaches that of the Additive White Gaussian Noise Channel (AWGN) [1]. The channel becomes less time-variant, resulting in reduced benefit from prediction. This observation does not diminish the importance of accurate fading prediction, since in most practical mobile radio systems, the outdated CSI is not sufficient for enabling efficient adaptive transmission techniques (including adaptive transmit diversity methods). B Adaptive Channel Loading for Multicarrier Systems. (i) System model Consider an Orthogonal Frequency Division Multiplexing (OFDM) signal with K subcarriers (tones). While the OFDM channel is wideband and, therefore, frequency selective, the bandwidth of each subcarrier is usually much smaller than the coherence bandwidth of the channel, and, thus, the signal associated with each subcarrier is flat fading [1,2,3]. Denote the flat fading complex channel gain at the n th symbol block and i th subcarrier (with center frequency f i ) as H[n,i]. Setting f c =f i in (1), we express H[n,i] as the n th sample of the complex fading channel c(f i N,t) = Am exp{j(2πf m t+φ i m}, i = 1,2 K. (5) m=1 Note that the signals c(f i,t) have approximately the same Doppler shifts and amplitudes, but different phases [2,3]. For the m th path, and the subcarriers i and j, the phase offset φ i m φ j m = 2π fτ m, where f = f j f i and τ m is the excess propagation delay, usually characterized by the exponential distribution with rms delay spread σ [3,6]. In an uncoded AOFDM system aided by LRP and reduced feedback, the input data is allocated to the subcarriers according to the CSI fed back from the receiver as illustrated in Figure 8. At the receiver, we estimate the complex fading gains H[n,k]. Denote these accurate, noise-reduced estimates as H ~ [n, k], where n refers to the low sampling rate used in the prediction [4,28]. To assess the performance of fading predictors in AOFDM, we employed two models of the frequency selective channel in (5). First, we used the random phase model (RMP) with N=34 reflectors [28]. The RPM is similar to the conventional Jakes model, but utilizes independent and uniformly distributed incident angles in (2). While the RPM model is more realistic, it has the same shortcomings as the Jakes model when used for testing fading prediction methods, as discussed in Section II.B. Therefore, our realistic physical model [4,5,58] was used for performance validation. The geometry for generating the model data set is shown in Figure 2. The scattering objects are arranged approximately to the side of (group A) and in front of (group B) the direction of the mobile. The fading amplitude is shown in Figure 3. The fading signal is dominated by the reflectors that are closer. This is group A for the first 600 samples, and group B thereafter. Taking into account the direction of the mobile, away from group A and towards group B, we expect that the dominant paths change from group A reflections to group B reflections, and the Doppler shifts of the dominant paths will rapidly change in both magnitude and sign in the vicinity of sample 600 (the transition interval). This is evident in Figure 3 as a faster fading rate when the Doppler shifts are larger, for points >600, when group B reflections dominate. We use this

7 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 7 data set to test the robustness of the LRP to parameter variation. In the numerical results, the carrier frequency is 900MHz, the maximum Doppler shift is 100Hz, and the rms delay spread is approximately 1µs in both channel models. To construct an OFDM symbol, the entire channel bandwidth, 800kHz, is divided into 128 subcarriers. The symbol duration is 160µs, and the guard interval is 5µs, resulting in a total block length of 165µs and a subcarrier symbol rate of approximately 6 KHz. For each subcarrier, the fading signal is sampled at the low rate of 466Hz for the AR-model based LRP described below. The prediction range is at least one sample ahead, 1/466Hz 2ms, or 0.2 λ. This prediction interval is sufficient to compensate for the feedback delay and other system constraints. The multi-step predictor is employed to accommodate interpolation at the symbol rate [4]. (ii) AR model-based fading prediction for multicarrier systems The optimum linear K-dimensional Minimum Mean Square Error (MMSE) prediction algorithm that utilizes previous symbols of all subcarriers was investigated in [28,29]. However, this method is very complex. It can be shown that a simplified approach investigated in [27,28] is near-optimal. In addition, low complexity prediction and reduced feedback approaches that utilize time domain channel taps instead of the frequency domain gains were investigated in [29,30] and [28], respectively. Prediction for adaptive OFDM was also investigated in [31]. As for the narrowband case in equation (4), we use only previous observations of subcarrier k for predicting its CSI H[n,k]: p H^ [n, k] = d j (n) H ~ [n j, k] k = 1,2,,K. (6) j=1 We employ the near optimal prediction filter length p=50 in (6) [4,59]. In practice, significantly lower filter lengths can be used, resulting in modest performance degradation. The general model implies that the coefficient vector d(n) = [d 1 (n) d 2 (n) d p (n)] in (6) needs to be computed and adapted individually for each subcarrier. However, the frequencyselective channel characterization in (5) allows simplification of this calculation. It is sufficient to employ the same filter coefficient vector d(n) to predict the future CSI for each subcarrier due to the fact that the taps d j (n) are determined by the Doppler shifts f m, m=1 N [66], that are tone-invariant for realistic OFDM systems. Hence, the filter coefficient vector d(n) in (6) is also tone-invariant. This property allows a reduction in the computational complexity relative to the optimal K-dimensional predictor and a significant improvement in the convergence of the LMS and RLS adaptive prediction methods relative to single carrier adaptive prediction [5,28,48]. The improvement is due to the fact that observations of all subcarriers can be used jointly to update the coefficient vector d(n). We refer to this method as the simplified multiple carrier prediction (SMCP). In addition, robustness to additive noise relative to single carrier prediction can be improved by extending (6) to include observations of several adjacent subcarriers. While the RLS method has higher computational complexity than the LMS algorithm, its convergence speed and MSE are significantly better than those of LMS for both the RPM and physical models [28]. This is due to the superior tracking capabilities of RLS as discussed in Section II. Note that in our simulations, the parameters of both adaptive methods were carefully chosen to improve convergence. Figure 9 illustrates that SMCP aided by the RLS algorithm is suitable for predicting the realistic fading channel. It is robust to the transition period shown in figure 3 and recovers rapidly after the transition. The tracking results for the LMS algorithm are much worse, with relatively high MSE throughout the physical model data set. (iii) Bit rate of prediction-enabled adaptive channel loading The SMCP prediction was utilized to enable AOFDM. Rectangular variable power and rate Quadrature Amplitude Modulation (M-QAM) is employed for each subcarrier, with M=0 (outage) or 2 i, i=1 6. Channel loading optimization under the bit rate maximization criterion was employed, where the goal was to allocate the limited energy among the subcarriers to maximize the overall bit rate subject to a target bit error rate constraint BER tg. In particular, we utilized a simplified near-optimal loading method [28] similar to the loading algorithm in [67]. This method maintains the target bit error rate even when the predicted CSI is not perfect [28]. The modulation levels (or bits per symbol) and the transmitted powers allocated to all subcarriers depend on the predicted fading coefficients H^ [n, k] in (6) and the reliability of the prediction measured by the correlation between the actual fading coefficient H[n,k] and the predicted CSI H^ [n, k] [28]. This method follows the principle of adaptive modulation design with statistical CSI uncertainty as described in [68] (see also [13,69]). For very low correlation values, the performance is the same as for non-adaptive transmission for a given target BER. As the correlation approaches one, the reliability increases, and ideal performance with perfect CSI is approached. The average bit rate, or Bits per Symbol (BPS), of the AOFDM versus the total SNR constraint for different prediction algorithms and the RPM or physical channel model is plotted in Figure 10. While the LMS method is acceptable for the RPM model, LMS cannot track the physical model data set as illustrated in figure 9, and results in a BPS loss on the order of 1 bit/symbol relative to the ideal case, when the knowledge of the CSI at the transmitter is perfect. The performance of the RLS algorithm for the RPM is nearoptimal (not shown), whereas the loss is less than 0.25 BPS for the physical model compared to perfect knowledge of CSI. The performance of the AOFDM using outdated CSI samples (1 ms delay) without long range prediction for the RPM is also shown in Figure 10. The calculation of thresholds for this case was studied in [68]. This method is equivalent to the LRP

8 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 8 with a single observation (p=1 in (4)) delayed by 1 ms. We found that even very small delay causes significant loss of the bit rate for fast vehicle speeds when accurate LRP is not utilized. Our results demonstrate feasibility of AOFDM for rapidly varying mobile radio channels when prediction is employed, with bit rates approaching those for channels with the ideal knowledge of the CSI. C. Adaptive Modulation in Frequency Hopping Systems (i) AR-model based prediction with observations at different frequencies Joint adaptive modulation (AM) and adaptive frequency diversity, aided by prediction of fading and narrowband interference, for slow Frequency Hopping (SFH), spread spectrum mobile radio systems was exploited in [32,33,34]. Consider the SFH system that employs coherent detection [1,3,70] with the total number of frequencies q and the hopping rate f h. The dwell interval is given by the time between the hops. Thus, the carrier frequency is fixed during each dwell interval. Let f denote the frequency separation between adjacent carrier frequencies. We employ a randomly chosen periodic hopping pattern, although the proposed methods also apply to non-periodic hopping patterns [33]. Figure 11 illustrates an LP approach (the LRP) for SFH systems. Reliable observations at past hopping frequencies of given user are fed back from the receiver to the transmitter. The transmitter employs the LRP to predict the future CSI for the upcoming frequency determined by the hopping pattern, and adapts the transmission parameters to the channel variation. Suppose the predictor employs the sampling rate f s =1/T s. Note that each dwell interval contains several low rate samples used for prediction, i.e. f h <f s. The equivalent lowpass complex sample of the fading channel at time nt s and carrier frequency f(nt s ), where f(nt s ) is the hopping frequency occupied at the time nt s, is c n =c(f(nt s ),nt s ). Assume that the fading is flat during each dwell interval and c(f(nt s ),nt s ) are the samples of the frequency selective fading channel in (5), where the carrier f c =f(nt s ). We employ the optimal MMSE linear prediction method with p coefficients. The prediction of a future sample c n+m =c(f((n+m)t s ),(n+m)t s ) is given by p-1 ĉ n+m = dj(n)c n-j (7) j=0 In narrowband and OFDM systems, the observations and the predictions were at the same carrier frequency. The prediction coefficients in (4,6) were determined by the channel correlation function at that frequency, and thus were very slowly varying. However, in SFH systems, the frequencies associated with the observations depend on the hopping pattern. Thus, observations at a different set of frequencies are used for predicting c n+m-1 than for predicting c n+m in (7). The prediction coefficient vector d(n) of this predictor is determined by the spaced-time spaced-frequency channel correlation function [1] sampled at a different set of frequencies for each predicted sample. Therefore, the filter d(n) of the LP in (7) changes completely with every consecutive predicted sample. The MSE for SFH systems is computed as the average over all LP filters. We have employed pilot symbol-aided channel estimation to track and update the time varying channel correlation function [33]. It was shown in [37] that the required update rate is significantly lower that the low sampling rate f s, and does not significantly affect the bandwidth requirements and computational complexity. The optimal MMSE LRP described above is complex, because it requires inversion of large matrices at the sampling rate. Simplified prediction techniques were explored in [33,34] and found to be insufficient for enabling AM is SFH systems. To reduce the computational load of the optimal MMSE method, a recursive matrix update method was utilized in [32,33,34]. (ii) Numerical results We assume a typical slow hopping rate f h =500 hops/second, LRP filter length p=50, and the feedback delay of at least 1ms. To enable AM, several samples are predicted for each dwell interval, and the average prediction range is 2ms. We employ the sampling rate f s =2 khz since it results in near-optimal performance [33]. Figure 12 shows the MMSE vs. normalized frequency separation fσ for various maximum Doppler shifts for this prediction range. The parameter fσ is the product of the frequency separation between two adjacent hopping frequencies and the rms delay spread of the fading channel [1,3]. We observe that the prediction MMSE increases as the normalized frequency separation grows since the observations and the prediction become less correlated. LRP is employed to enable AM for each upcoming dwell interval. We employ adaptive discrete power discrete rate MQAM with M=2, 2 2(i-1), i=2,3,4 [71]. As in Section III.B, reliable performance is maintained by incorporating the accuracy of the predicted CSI into the AM design [32,68]. The symbol rate is 20Ksps (symbols per second), and the target BER is While we compared performance with and without prediction in previous results (Figures 7, 10), this comparison is meaningless in adaptive SFH systems. The delay associated with the feedback and other system constraints is comparable with the dwell interval duration, so the channel estimates obtained during current dwell interval cannot be employed. A single outdated estimate at a different frequency (as dictated by the hopping pattern) is not helpful for enabling AM. Thus, the only practical alternative to using fading prediction for SFH is to resort to non-adaptive modulation. Therefore, we compare the BPS of AM enabled by the LRP with that of non-adaptive MQAM at the same average SNR and target BER constraints [1]. In Figure 13, we plot the spectral efficiency (BPS) of AM vs. average SNR for the standard Jakes model. The maximum Doppler shift is 50Hz. We observe that significant gain can be achieved relative to non-adaptive modulation (Binary and

9 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 9 Quaternary Phase Shift Keying (BPSK, QPSK)). The gain depends on the normalized frequency separation. For fσ=0.01, the BPS with prediction approaches the BPS with perfect CSI [33]. For fσ=0.1, the gain relative to the nonadaptive modulation is about 3dB, or 1 BPS. In Figure 14, we employed the physical model discussed in Sections II.B and III.B to investigate the performance of AM for SFH systems in realistic fading channels. A typical and a challenging model scenarios are created. Since prediction for SFH systems involves multiple frequencies, the prediction coefficients are affected by both the Doppler shifts and the delays that determine the phases in (5). While the maximum Doppler shift is 50 Hz, and the average rms delay spread σ=1µs for all curves in Figure 14, the Doppler shifts and the delays do not vary in the Jakes model, and their variation is much more significant for the challenging model scenario than for the typical physical model scenario [5,32,34,58]. Thus, the prediction accuracy is worse for the challenging case. While the BPS gain is lower for the physical model than for the Jakes model due to the channel parameter variation, significant improvement is still achieved relative to nonadaptive modulation. (iii) Limitations of fading prediction for FH systems Our results demonstrate that the spectral efficiency of adaptive transmission degrades as fσ increases due to decreased correlation between fading signals at different hopping frequencies. The FH system benefits from adaptive transmission primarily when fσ does not significantly exceed 0.1. Typical values of the delay spread are on the order of microseconds in outdoor radio channels [3]. Suppose σ is 1µs, representative of suburban areas. Then a SFH system would benefit from adaptive transmission when the frequency separation is as large as 100 KHz ( fσ 0.1). If σ is 10µs, the frequency separation has to decrease to 10 khz to obtain good performance. In realistic SFH systems [1,3,70], the symbol rate is on the order of tens Ksps. Thus, the frequency separation of SFH systems is often less than 100 KHz. Therefore, adaptive transmission aided by the proposed channel prediction method is feasible for these systems. Other factors that degrade prediction accuracy are the number of frequencies q and the f dm [34]. AM is feasible when the total normalized bandwidth (TNB) is q fσ is on the order of 3 or lower, and the f dm is modest (under 100Hz). As the TNB grows, the spectral efficiency saturates and approaches that of non-adaptive modulation, and adaptive transmission becomes less useful. On the other hand, frequency diversity is usually exploited in FH communications [1], and its benefit increases as the TNB grows. Thus, adaptive transmission and diversity combining compliment each other over the practical range of frequency correlations in SFH systems. The relationship between prediction, adaptive transmission and diversity was also discussed in Section III.A for direct sequence CDMA systems, and exploited in mitigation of narrowband interference in SFH systems [32,33], as well as in adaptive coded systems [72]. Our results demonstrate that fading prediction is less accurate for SFH systems than for narrowband transmission, OFDM, direct sequence CDMA and even open loop Frequency Division Duplex systems [37]. This loss is further enhanced when the realistic physical model is employed. In non-fh channels, we can employ fast adaptive tracking combined with LRP to achieve near-ideal spectral efficiency for realistic channels, as demonstrated for the AOFDM in Figure 10. The reason why we have not achieved similar gains for FH systems is that the observations were constrained by the hopping pattern, and, thus, widely distributed in frequency. This constraint degrades prediction accuracy, and hampers utilization of fast and efficient adaptive tracking techniques. However, we note that fading prediction is critical in this application, since adaptive transmission would not be possible without prediction in FH systems. IV. CONCLUSION Recently proposed fading prediction methods for mobile radio adaptive transmission were reviewed and compared. The suitability and robustness of an AR-model based linear prediction method that utilizes fast tracking of channel coefficients was demonstrated for realistic channel conditions. Noise reduction and modeling issues, performance bounds, prediction gains in MIMO systems, and enabling adaptive transmission using fading prediction in diverse wireless systems were discussed. To summarize, reliable fading prediction beyond one wavelength is achievable in measured channels. Moreover, when fading prediction is employed jointly with adaptive transmission, significant performance gains are obtained relative to using outdated CSI and to non-adaptive transmission methods. These gains are observed even in challenging cases when prediction accuracy is limited due to channel impairments or system constraints. It was also discussed that the benefit from prediction decreases as the system diversity order grows, and adaptive transmission enabled by fading prediction complements conventional diversity combining as an effective fading mitigation technique. On-going investigation and future research directions include comprehensive examination of performance and complexity trade-offs of utilizing fading prediction in modern wireless systems. ACKNOWLEDGMENT The author is grateful to Hans Hallen, Tao Jia, Tung-Sheng Yang, Ming Lei and Secin Guncavdi. This paper would not be possible without their efforts. REFERENCES [1] J. G. Proakis, Digital Communications. Fourth Edition, McGraw-Hill, 2001.

10 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 10 [2] A. Duel-Hallen, Fading Channels, the Wiley Encyclopedia of Telecommunications, John Wiley&Sons, Inc., J. G. Proakis, Editor, 2003, pp [3] T. S. Rappaport, Wireless Communications: Principles and Practice, 2nd edition, Prentice-Hall, [4] A. Duel-Hallen, S. Hu, H. Hallen, Long-range Prediction of Fading Signals: Enabling Adaptive Transmission for Mobile Radio Channels, IEEE Signal Processing Magazine, Special Issue on Advances in Wireless and Mobile Communications, Vol. 17, No.3, May 2000, pp [5] H. Hallen, A. Duel-Hallen, S. Hu, T.-S. Yang, and M. Lei, A Physical Model for Wireless Channels to Provide Insights for Long Range Prediction, Proc. MILCOM 02,Oct. 2002, vol.1, pp [6] W. C. Jakes, Microwave Mobile Communications. Wiley, New York, [7] T. Ekman, "Prediction of mobile radio channels : modeling and design," Ph. D. Dissertation, Uppsala Univ., Sweden, 2002 [8] S. Falahati, A. Svensson, T. Ekman and M. Sternad, "Adaptive modulation systems for predicted wireless Channels," IEEE Trans. Commun., vol. 52, pp , Feb [9] X. Cai and G. B. Giannakis, "Adaptive PSAM accounting for channel estimation and prediction errors," IEEE Trans. Wireless Commun., vol. 4, pp , Jan [10] S. Falahati, A. Svensson, M. Sternad and H. Mei, "Adaptive trellis-coded modulation over predicted flat fading channels," in Proc. IEEE VTC, Fall, pp , Orlando, FL [11] S. Zhou and G. B. Giannakis, "How accurate channel prediction needs to be for transmit-beamforming with adaptive modulation over Rayleigh MIMO channels?" IEEE Trans. Wireless Commun., vol. 3, pp , July [12] G. E. Oien, H. Holm and K. J. Hole, "Impact of channel prediction on adaptive coded modulation performance in Rayleigh Fading," IEEE Trans. Veh. Technol., vol. 53, pp , May [13] A. Svensson, An Overview of Adaptive Modulation Schemes for Known and Predicted Channels, this issue. [14] Andersen, J.B, Jensen, J., Jensen, S.H., Frederiksen, F., "Prediction of Future Fading Based on Past Measurements", Proceedings of the Vehicular Technology Conference, Vol.1., pp , Delft, The Netherlands, September [15] "Testing the Multipath Model - the Prediction of Short Term fading", Chapter 7.5, pp , in Vaughan, R.G., Bach Andersen, J., "Channels, Propagation and Antennas for Mobile and Personal Communications", IEE/Peregrinus, [16] M. Sternad and S. Falahati, Maximizing throughput with adaptive M- QAM based on imperfect channel predictions, Proc. IEEE PIMRC, 2004, vol. 3, pp , Barcelona, Spain [17] A. Alsawah, I. Fijalkow, and C. R. Johnson. Improving minimum rate maximization link adaptation strategy using channel prediction, Proc. IEEE ICASSP, 2006, vol. 4, pp , Toulouse, France [18] Y. Takei, and T. Ohtsuki, Uplink pre-equalization using MMSE prediction for TDD/MC-CDMA systems, Proc. IEEE PIMRC, 2005, vol. 1, pp , Berlin, Germany [19] B. Hu, W. Liu, L. L. Yang and L. Hanzo, "Multiuser decorrelating based long-range frequency-domain channel transfer function prediction in multicarrier DS-CDMA systems," Proc. IEEE ISSSTA, Aug. 2006, pp , Manaus, Brazil. [20] S. Guncavdi, A. Duel-Hallen, Performance Analysis of Space-Time Transmitter Diversity Techniques for W-CDMA Using Long Range Prediction, IEEE Transactions on Wireless Communications, Vol. 4, No. 1, Jan. 2005, pp [21] J. Liu and A. Duel-Hallen, Performance Analysis of Tomlinson- Harashima Multiuser Precoding in Multipath CDMA Channels, Proc. 4GMF'05, July 07-08, [22] Y. Takei, and T. Ohtsuki, Throughput maximization transmission control scheme using channel prediction for MIMO systems, Proc. IEEE Globecom, 2005, vol. 4, St. Louis, MO [23] S. Hu, A. Duel-Hallen, Combined Adaptive Modulation and Transmitter Diversity Using Long Range Prediction for Flat Fading Mobile Radio Channels, Proceedings of IEEE Globecom, 2001, San Antonio, Texas, Nov , vol. 1, pp [24] S. Guncavdi and A. Duel-Hallen, Space-Time Pre-RAKE Multiuser Transmitter Precoding for DS/CDMA System, Proceedings of VTC 03, MUD and Signal Proc. Issues Session, pp. 1-5, Orlando, FL, Oct. 03. [25] S. Hu, T. Eyceoz, A. Duel-Hallen, H. Hallen, Transmitter Antenna Diversity and Adaptive Signaling Using Long Range Prediction For Fast fading DS/CDMA Mobile Radio Channels, Proc. of IEEE WCNC 99, Vol. 2, 1999, pp [26] A. Arredondo, K.R. Dandekar, Guanghan Xu, Vector Channel Modeling and Prediction for the Improvement of Downlink Received Power, IEEE Trans. Commun., vol. 50, no. 7, pp , July [27] I. C. Wong and B. L. Evans, "Joint channel estimation and prediction for OFDM systems," in Proc. IEEE Globecom, 2005, pp [28] A. Duel-Hallen, H. Hallen, T. S. Yang, Long Range Prediction and Reduced Feedback for Mobile Radio Adaptive OFDM Systems, IEEE Transactions on Wireless Communications, Vol. 5,No. 10, Oct. 2006, pp [29] D. Schafhuber and G. Matz, "MMSE and adaptive prediction of timevarying channels for OFDM systems," IEEE Trans. Wireless Commun., vol. 4, pp , Mar [30] I. C. Wong, A. Forenza, R. W. Heath, Jr., and B. L. Evans, "Long range channel prediction for adaptive OFDM systems," in Proc. IEEE Asilomar Conference, 2004, pp , Pacific Grove, CA [31] M. Sternad and D. Aronsson, "Channel estimation and prediction for adaptive OFDM downlinks," in Proc. IEEE VTC, 2003-Fall, vol. 2, pp , Orlando, Florida.

11 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 11 [32] M. Lei, A. Duel-Hallen, H. Hallen Enabling Adaptive Modulation and Interference Mitigation for Slow Frequency Hopping Communications, proceeding of IEEE SPAWC 2005, June, 2005, pp [33] M. Lei, Performance Analysis of Reliable Adaptive Transmission for Mobile Radio Slow Frequency Hopping Channels Aided by Long Range Prediction, Ph.D. dissertation, NC State University, Fall [34] M. Lei, A. Duel-Hallen, Long Range Channel Prediction and Adaptive Transmission For Frequency Hopping Communications, Proc. of 41th Annual Allerton conference on Comm., Control, and Computing, Oct. 1-3, 2003, pp [35] I. C. Wong and B. L. Evans, "Exploiting Spatio-Temporal Correlations in MIMO Wireless Channel Prediction," Proc. IEEE Global Telecom. Conf., Nov. 2006, San Francisco, CA. [36] M. Guilland and D. Slock, A Specular Approach to MIMO Frequency- Selective Channel Tracking and Prediction, In Proc. IEEE Signal Proc. Advances in Wireless Comm., July 2004, pp [37] T. S. Yang, A. Duel-Hallen, H. Hallen, Reliable Adaptive Modulation Aided by Observations of Another Fading Channel, IEEE Transactions on Communications, Vol. 52, No. 4, Apr. 2004, pp [38] T. Ekman, M. Sternad, and A. Ahlen, Unbiased power prediction on broadband channel, Proc. IEEE VTC, Vol. 1, Sept 2002, pp [39] I. C. Wong and B. L. Evans, "Low-complexity adaptive high-resolution channel prediction for OFDM systems," in Proc. IEEE Globecom, 2006, San Francisco, CA [40] T. Svantesson and A. L. Swindlehurst, "A performance bound for prediction of MIMO channels," IEEE Trans. Signal Processing, vol. 54, pp , Feb [41] I. C. Wong and B. L. Evans, "Performance bounds in OFDM channel prediction," in Proc. IEEE Asilomar Conference, 2005, pp , Pacific Grove, CA [42] M. Guilland and D. Slock, A Specular Approach to MIMO Frequency- Selective Channel Tracking and Prediction, In Proc. IEEE Signal Proc. Advances in Wireless Comm., July 2004, pp [43] H. T. Nguyen, G. Leus, N. Khaled, Prediction of the Eigenvectors for Spatial Multiplexing MIMO systems in Time-Varying Channels, Proc. Of IEEE Symposium on Signal Processing and Information Technology, 2005, pp [44] S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. Upper Saddle River: Prentice Hall, 1993 [45] S. M. Kay, Modern Spectral Estimation: Theory & Application. Englewood Cliffs, New Jersey: Prentice-Hall, 1988 [46] S. Haykin, Adaptive Filter Theory, 3 rd edition. Prentice-Hall, [47] P. Stoica and R. Moses, Spectral Analysis of Signals. Upper Saddle River, NJ: Prentice Hall, 2005 [48] S. Semmelrodt and R. Kattenbach, "Investigation of different fading forecast schemes for flat fading radio channels," in Proc. IEEE VTC, 2003, pp [49] K. E. Baddour and N. C. Beaulieu, "Improved pilot-assisted prediction of unknown time-selective Rayleigh channels," in Proc. IEEE ICC, 2006 [50] W. Liu, L. L. Yang, and L. Hanzo, "Wideband channel estimation and prediction in single-carrier wireless systems," Proc. IEEE VTC-Spring, June 2005, vol. 1, pp , Stockholm, Sweden. [51] P. D. Teal and R. G. Vaughan, "Simulation and performance bounds for real-time prediction of the mobile multipath channel," Proceeding of the 11th IEEE Signal Processing Workshop on Statistical Signal Processing, 2001, vol. 1, pp , Singapore. [52] R. Vaughan, P. Teal, and R. Raich. Short-term mobile channel prediction using discrete scatterer propagation model and subspace signal processing algorithms. In Proc. IEEE Vehicular Technology Conference, vol. 2, pages , Fall, Boston, Sep [53] M. Chen, T. Ekman and M. Viberg, "New Approaches for Channel Prediction Based on Sinusoidal Modeling," EURASIP Journal on Advances in Signal Processing, [54] T. Zemen and B. H. Fleury, "Time-variant channel prediction using timeconcentrated and band-limited sequences," in Proc. IEEE ICC, 2006, Istanbul,Turkey [55] R. J. Lyman, "Linear prediction of continuous-time, bandlimited processes, with applications to fading in mobile radio," Ph. D. Dissertation, University of Florida, 2000 [56] R. J. Lyman and A. Sikora, "Prediction of fading envelopes with diffuse spectra," in Proc, IEEE ICASSP, 2005, pp , Philadelphia, PA [57] M. Williams, G. Dickins, R. Kennedy, T. Pollock, T. Abhayapala, Novel Scheme for spatial extrapolation of multipath, Proc 11th Asia Pacific Conference on Communications, APCC, Perth, Oct 2005, pp [58] H. Hallen, S. Hu, M. Lei and A. Duel-Hallen, A Physical Model for Wireless Channels to Understand and Test Long Range Prediction of Flat Fading, Proceedings of WIRELESS, 2001, Calgary, Canada, July 9-11, 2001, pp [59] T. Eyceoz, S. Hu, and A. Duel-Hallen, Performance Analysis of Long Range Prediction for Fast Fading Channels, Proc. 33 rd Annual Conference on Information Sciences and Systems CISS 99, March 1999, Volume II, pp [60] X. Cai and G. B. Giannakis, Adaptive Modulation with Adaptive Pilot Symbol Assisted Estimation and Prediction of Rapidly Fading Channels, Proc. CISS [61] T. Jia, Ph. D. Thesis, ECE Dept., NC State Univ., in preparation. [62] P. Teal and R. Kennedy, Bounds on extrapolation of field knowledge for long-range prediction of mobile signals, IEEE Trans. Wireless Communications 3(2): , March 2004 [63] S. Barbarossa and A. Scaglione, "Theoretical bounds on the estimation and prediction of multipath time-varying channels," in Proc. IEEE ICASSP, 2000, vol. 5, pp , Istanbul, Turkey [64] J. E. Berg and H. Asplund, private communication. [65] IEEE Communications Magazine, Wideband CDMA issue, pp , September 1998.

12 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 12 [66] T. Eyceoz, A. Duel-Hallen, H. Hallen, Deterministic Channel Modeling and Long Range Prediction of Fast Fading Mobile Radio Channels, IEEE Commun. Lett., Vol. 2, No. 9, Sept. 1998, pp [67] A. Czylwik, Adaptive OFDM for Wideband Radio Channels, Proc. IEEE GLOBECOM, 2006, pp [68] D.L. Goeckel, Adaptive Coding for Time-Varying Channels Using Outdated Channel Estimates, IEEE Trans. Comm., 47 (6), 1999, [69] H. Zhang, G. Amariucai, S. Wei, G. Ananthaswamy, D. Goeckel, Adaptive Signaling under Statistical Measurement Uncertainty in Wireless Communications, this issue. [70] S. Tomisato, K. Fukawa, and H. Suzuki, Coherent Frequency Hopping Multiple Access (CFHMA) with Multiuser Detection for Mobile Communication Systems, IEEE Trans. Vehic. Tech., vol. 49, Issue: 2, March 2000, pp [71] A.J. Goldsmith and S.G. Chua, Variable-Rate Variable-power MQAM for Fading Channels, IEEE Trans. Comm., 45 (10), 1997, [72] P. Ormeci, X. Liu, D. L. Goeckel and R. D. Wesel, "Adaptive bitinterleaved coded modulation," IEEE Trans. Commun., vol. 49, pp , Sep A B amplitude channel predictor Figure 1. Transmitter antenna selection enabled by long range fading prediction symbol Figure 3. Fading signal amplitude for the physical model data set in Figure 2; the symbol interval is 0.2λ. Figure 2. Multiple reflectors cause multipath fading. Figure 4 Comparison of reliable envelope prediction for several fading prediction methods when using measurements (reprinted from [48], Fig. 3(a)).

13 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < MSE RLS Jakes model LMS Jakes model RLS Physical model LMS Physical model Prediction Length (wavelengths) Figure 5. Comparison of prediction mean square error for AR model-based prediction with RLS and LMS tracking of model coefficients for Jakes model and physical model data. (b) Multipath fading (4 paths). Figure 7 Performance of the transmitter antenna selection (STD), 2 transmitter antennas, f dm =200Hz, coded W-CDMA. Prediction ranges: STD 1.6 KHz: 1 slot=0.125λ; STD 400 Hz: 4 slots = 0.5 λ. Figure 8. Block diagram of an adaptive OFDM system with fading prediction. Figure 6 Prediction length for M t xm r MIMO systems versus measurement length, N=10 reflectors, noise power = -20dB. (reprinted from [40], Fig. 2) LMS µ = MSE LMS µ = 0.05 RLS ξ = RLS ξ = OFDM symbol (a) Flat fading. Figure 9. Performance of adaptive SMCP prediction methods in an OFDM system for the physical model data set of Fig. 2 and 3. Prediction range is 0.2λ. ξ is forgetting factor in RLS, and µ is step size in LMS.