Online Modeling of Wireless Channels with Hidden Markov Models and Channel Impulse Responses for Cognitive Radios

WE2C-2

Online Modeling of Wireless Channels with Hidden Markov Models and Channel Impulse Responses for Cognitive Radios

Thomas W. Rondeau, Christian J. Rieser, Timothy M. Gallagher, and Charles W. Bostian Center for Wireless Telecommunications & Bradley Department of ECE, Virginia Tech,

Blacksburg, Virginia, 24061-01 11, USA

Abslrad

-

A cognitive radio must be able to observe and model the channel in which it operates. As a rust step to creating a truly cognitive radio, we have developed a novel technique to model wireless channels by combining a broadband channel sounder with a Wireless Channel Genetic Algorithm (WCGA). The WCGA receives a sequence of e m r symbols simulated from the impulse response to train a Eidden Markov Model (HMM) with a Genetic Algorithm.

The HMM is a compact representation of the channel that a radio can create online and then use as the input to a cognitive process for intelligent adaptation of the radio.

Index Tenns

-

Genetic Algorithms, Hidden Markov Models, Cognitive Radios, LMDS, Impulse Response.

I. INTRODUCTION

All radios fit into one of three general categories:fid, adaptive, and cognitive. All parameters in a fixed radio are sei at the time of manufacture. Adaptive radios have a limited range of parameter choices that allow them to adapt to a limited set of anticipated events. Cognitive radios [1]-[2], are capable of improved adaptation through intelligent observation of the wireless channel. The intelligence of a cognitive radio, provides it with the capability of responding to an unknown and previously unanticipated channel. Cognitive radios are capable of enhanced performance, improved quality of service, and robust security.

The concept of “perception” is vital to a cognitive radio as it provides the means by which the radio understands its environment. We have developed a method to quickly and accurately model wireless channels wing a Hidden Markov Model

(m

trained by a Genetic Algorithm (GA). A cognitive radio can develop this model of the channel online and then use the model to direct the adaptation process.

This paper draws upon work we have submitted for publication in IEEE Transactions on Wireless Communications [3], where we discuss our approach and framework to a realization of a cognitive radio including a method of modeling a wireless channel with a GA-trained HMM in an algorithm we call the Wireless Channel

Genetic Algorithm (WCGA). This paper extends that work to include a discussion of using a broadband channel sounder, described in [4], in conjunction with the WCGA to improve the performance of modeling a channel online.

Presented in this paper is a brief overview of the WCGA and sounder designs, followed by OUT new methods of wing the two systems together to develop accurate and computationally efficient models of wireless channels that a cognitive process can use to adapt a radio.

We conclude by discussing the future of these techniques and how a cognitive radio can benefit h m them.

11. DESIGN BACKGROUND A . Wireless Channel Genetic Algorithm

The WCGA is based on a Genetic Algorithm [5] that trains an HMM to best represent a wireless channel’s statistical behavior. Rahiner [6] gives a thorough tutorial on HMMs, and the use of HMMs in modeling wireless channels has been previously documented [7]-[9]. To model wireless channels, we combined the effnrts of [7]-

[9] with speech modeling techniques that use GA-trained HMMs [lo]-[12].

As described in [3] the WCGA creates a chromosome (vector) for the GA to work with h m the HMM ma!ices.

The GA operates on the chromosome to compare the statistics of the output sequence generated h m the HMM to an error stream taken hintraining data. The WCGA concludes by choosing the HMM chromosome that most closely matches the statistics of the training data after a certain number of generations has elapsed. The HMM now represents, in a clean and compact form, the wireless channel in which the radio is operating.

B. Broadband Channel Sounder

The broadband channel sounder developed by the Center for Wireless Telecommunications (CWT) is described wholly in [4]. The sounder captures an impulse using a Swept Tune Delay Short Pulse 739

0-7803-8331-1B4/$20.00 Q 2004 IEEE 2004 BEE MTT-S Digest

(SSTDSP) technique to determine the channel's impulse response, which we can then use to characterize and understand the channel's behavior. Fig. 1 shows an impulse response captured by the channel sounder for a Local Multipoint Distribution System (LMDS) 28 GHz line-of-sight (LOS) channel.

1.5

1

0 5 10 15 20 25 30 35 40

Time [na)

Fig. 1. Captured impulse respme from channel sounda for 28 GHz Linedf-Sight link.

The channel impulse response can show multipath, power levels, and spreading of the signal power in time.

These parameters indicate the channel quality, and we can match radio performance such as BER to the impulse response to provide a qualitative measure of the channel.

Furthermore, we can use the information contained in the impulse response to simulate the channel and derive an error sequence that can become the input to the WCGA, thereby allowing the generation of an HMM fiom the channel sounder output.

111. COMBINED " I H O D FOR MODELING WIRELESS cHANNE1.s

We have combined the WCGA with the sounder to produce a method for modehg wireless channels online in a radio. The impulse response of the sounder is used to generate a simulated error stream that closely matches the actual channel. Instead of using a training sequence transmitted between the radios, the simulated error stream acts as the input to the WCGA, which then creates an HhfM to model the channel.

The end-to-end communication system is modeled in software using the captured impulse response data as the channel model. The received signal-to-noise ratio is then monitored to set the thermal noise level. A random bit stream is run through the simulation and the output is monitored for bit errors. The hit ermr stream generated

from this simulation is then used to train the HMM. While the results that follow are based on an ideal channel, the simulation algorithm is independent of the channel impulse response. The simulation treats the chamiel simply as a non-ideal filter with the appropriate characteristics, so that this way, any channel can be characterized and its effect on a data stream reasonably quantized regardless of the environment.

Fig. 2 shows the BER curves for a theoretical (perfect) AWGN channel using QPSK modulation as compared to the simulation results &om the measured impulse response, which shows the close match between simulation and theory.

Fig. 2. Theoretical and simulated BER curves for QPSK modulation h a 28 GHz LOS link.

Running the WCGA given the simulated error sequence output yields very good results for the LOS path. "lie WCGA used a 20 chromosome population with 15 chromosomes replaced every generation. It was run for SO generations with a crossover and mutation rate of 90%

each. The HMM had N equal to 8 states and M equal to 2 to represent binary values. We produce the HMM shoaa in Fig. 3 using the error stream generated for a 2 dB carrier to noise (C/N) as the input to the WCGA.

The HMM is easily compared with the actual channel by comparing the burst eror statistics. The HMh4 and the simulated channel are associated with a histogram showing the hquency of the burst error lengths (i.e. the number of errors in a row). A histog" to compare the

HMM

with the simulated channel is shown in Fig. 4.

As a h a 1 comparison, the BER curve of the

H M E A

versus the simulated channel is created. Data points for CiN values of 2, 5 , and 8 dB define the BER curve shown in Fig. 5. Fig. 5 shows the BER curve given by the HMM and the BER curve for the same CM of the simulated cbamel. Note the close similarities between the two

740

channels, and the close match to the BER curves shown in Fig. 2.

Figs. 2-5 show very close similarities between the actual channel, the simulated channel, and the

HMM

channel, which validates the modelmg of the channel using the channel impulse response with an HMM.

Once generated, the HMM takes very little memory to store. Specifically, the memory s u e of the

HMM

is equal to:

S = b [ ( M V ) + ( N M ) + N ]

Where b is the number of bits used to represent the Hh4M fields, N is the number of states, and M is the number of symbols. If 32-bit floating point values are used with 8 states and 2 symbols, then the memory size of the HMM is 2816 bits, or 352 bytes. The

Hh4M

is then a compact model that can quickly and efficiently represent a statistical channel. A simulation or a cognitive radio can then use the compact

HMM

to simulate channel errors and produce channel statistics to provide a quick means of understanding the radio behavior within a channel.

0:

I

II: 0.2602 I ^0.3616 I 0.3647 1 0.0120 10.0058 I 0.0005 I 0.WW I 0.OW 1

Fig. 3. An HMM hained by the WCGA far a 20 GHr LOS channel with 2dBc/N.

IV. CONCLUSIONS

We have demonstrated a novel method to model wireless channels by using GA-trained HMMs from a broadband channel sounder impulse response. The results show close agreement between the actual channel and the HMM channel trained from data from the channel sounder. The data collected thus far is for line-of-sight AWGN channels only, and we still need to prove the performance for more unique channels, such as diffuse scattering channels, which is the next step in OUT research.

13W

0 4 2 3 4 5

Bun1 E m r Lennh

Fig. 4. B u t ermr statistics of the simulated channel versus the HMM

Channel.

I

(.Ed1

z w m

1 . E Q

1.E-03

2 3 4 5 6 7 0

c(N (dB)

Fig. 5. BER curve8 of simulated channel vmw the HMM channel.

Modeling and understanding the channel is the first step in developing our cognitive radio. It provides the sensing required by the rest of the cognitive system to understand the channel and its surroundings so that the radio can adapt to them. Performing the WCGA online can give disaster systems the knowledge to create and maintain broadband wireless links or allow network devices for wireless networks to adjust their parameters to keep a constant quality of service.

The method described in this paper provides a cognitive radio its “eyes”: to enable the radio to see, understand, and adapt based on the environment in which the radio is operating. The information and techniques described here will become the input to the remaining pieces of the cognitive radio that we described in [3], on which we are currently working.

741

ACKNOWLEDGEMENT

This work was supported in part by the National Science Foundation under awards 9983463 and DGE-9987586.

The authors would like to thank Tapas Kanungo of the University of Maryland, College Park for the GNU General Public Licensed s o h a r e for generating output sequences fiom an

HMM.

We would also like to extend our gratitude to

Dr.

Walling Cyre for his guidance and assistance in our efforts to apply Genetic Algorithms to cognitive wireless systems as well as for providing the basis for the Genetic Algorithm code that is the foundation of OUT cognitive algorithms.

REFERENCES

[l] J. Mitola and G. Q. M a d e , Jr., “Cognitive Radio: Making Software Radios More Personal,” IEEE Personal

Communications, vol. 6 , pp. 13 - 18, Aug. 1999.

[2] 1. Mitola, “Cognitive Radio for Flexible Mobile Multimedia Communications,” IEEE Intenu2fional Workhop on Mobile Multimedia Communications, 1999, pp. 3 - 10.

[31 C. J. Rieser, T. W. Rondeau, and C. W. Bostian, “Cognitive Radio Architecture Based on Genetic Algorithms: A Proposed Architecture and Some Initial Results,” IEEE Trans. Wireless Communications, submitted, 2003.

[4] C. W. Bostian, S. F. Midkiff, W. M. Kwgan, L. W.

Carstensen, D. G. Sweeney, and T. M. Gallaglm,

“Broadband communications for disaster response,” Space Communications, vol. 18, no 3-4, pp. 167-177,2002, [ 5 ] D. E. Goldberg, Genetic Algorlfhms in Searrh,

Optimiznhon, and Machine Learning. Addison-Wesley I’uh Co., 1989.

161 L. R. Rabiner. “A Tutorial on Hidden Markov Models ;md Selected Applications in Speech Recognition,” Proceedi,ngs o f the IEEE. vol. 77. Dn. 257 - 286. Feb. 1989.

[7] W. Turin i d M. M: sbndhi, “Modeling Error Sources in Digital Channels,” IEEE Journal on SelecfedAreas in Communications, vol. 11, pp. 340-347, Apr. 1993.

[SI A. Umbert and P. Dim, “A Generic Radio Channel Emulator to Evaluate Higher Layer Protocols in a CDMA system,” PlMRC congrms, London, Sept 2000.

[9] A. Umbert and P. Dim, “A Radio Channel Emulator for WCDMA Based on Hidden Markov Model (HMM),” IEEE

VTC 5 2 d , vol. 5, pp. 2173 - 2179, Sept 2000.

Algorithm for Training HMM,” Electronics Letiers, vol. 34, pp. 1563 - 1564, Aug. 1998.

[ l l ] C. W. Chau, S. Kwong, C. K. Diu, and W. R. Fahnier,

“OptimiEatioo of HMM by a Genetic Algorithm,” R o c . ICASSP-97.1997, vol. 3, pp. 1727 - 1730.

[12] S. Kwong and C. W. Chau. “Analysis of Parallel Genetic Algorithms on HMM Based Speech Recognition Systerq”

IEEE Trans. Consumer Elecfronics, vol. 43, pp, 1229 - 1233,Nov. 1997.

[IO] F. Sun and G. Hu, “Speech Recognition Based on Genetic

742