Underwater Acoustic MIMO Channel Capacity

1. Underwater Acoustic MIMO Channel Capacity Huaihai Guo ECE 776 Spring 2007 Center for Wireless Communications and Signal Processing Research New Jersey Institute of Technology

2. OUTLINE • OUTLINE • Introduction • Review of information theory • MIMO channel capacity • Acoustic MIMO channel capacity • Simulation and Calculation • Summary and Conclusion • Reference

3. Introduction • Underwater Acoustic Channel Characteristic • Multipath channel: Signals are reflected by different scatters. Normally, signals have been reflected by surface and bottom several times. • Fast fading channel: Due to the severe multipath and the shadow water wave, the underwater channel is a time-varying channels under an average power constrain. • Frequency selective fading channel: refection of multipath fading channel. • High delay: Slow propagation speed for acoustic wave (1500m/s), comparing with the optical or electric-magnetic communication.

4. Introduction con’t • The use of multiple antennas can provide gain due to • Antenna gain: more receive antennas means more power is collected. • Interference gain: interference nulling by beamforming (array gain); interference averaging (to zero) due to independent observations. • Diversity gain against fading: receive diversity; transmit diversity. AssumeNt transmit and Nr receive antennae • Channel State Information (CSI) are known for both side • A priority unknown

5. Review of Information Theory • Channel Capacity [1] • Gaussian Channel Entropy • For multivariate, real-valued Gaussian RV’s X1, X2,…, Xn with mean vector μ and covariance matrix K, the differential entropy is [1] • Gaussian distribution maximizes the entropy over all distributions with the same covariance, for any RV’s X1, X2,…, Xn with equality if and only if they are Gaussian [1].

6. Review of Information Theory con’t • Gaussian Channel Capacity [1] • Parallel Gaussian Channels Capacity [2] • MIMO channel is a special case of parallel Gaussian channels

7. MIMO Channel Capacity • MIMO Channel Model [2] • Received signal at jth receiver antenna can be expressed as where is the complex channel impulse response (IR) with normalized energy as 1. • Matrix Formulation where Y(n), X(n) is the signal vector, H(n) is the channel IR matrix. N(n) is the Gaussian noise vector with • The transmitted signal satisfies the average power constraint. (water-filling)

8. MIMO Channel Capacity Con’t • MIMO Channel Capacity [2] • MIMO Channel Capacity for fast fading channel (ergodic channel) has been derived in [3]. With perfect CSI, which is know at the receiver, the channel capacity is where is the average signal-to-noise power ratio at each receiver element. • For non-ergodic channel, the channel capacity does not equal to the average maximum mutual information [4]. In such case, the outage capacity is generally used. The outage capacity is associated with and outage probability which gives the a probability that the channel capacity falls below .

9. Underwater Acoustic MIMO Channel Capacity • Underwater acoustic MIMO Channel Capacity • Basically, the underwater acoustic MIMO channel capacity is the same as the normal MIMO channel capacity [5]. • The spatial and time cross correlation will effect the channel capacity [6]. Because the spatial correlation of channel IR depends on the spacing of the element or antennae and the angle spread of the signals, the channel capacity will also depends on those two factors. • For the second scenario, the channel capacity is represent by outage capacity to reflect the real channel throughput [6].

10. Simulation and Calculation • Channel Impulse Response

11. Simulation and Calculation Con’t • Channel Capacity Vs SNR for Uncorrelated channel IR

12. Simulation and Calculation Con’t • Channel Capacity Vs Number of Antennae for Uncorrelated channel IR

13. Simulation and Calculation Con’t • Spatial Correlation of channel IR

14. Simulation and Calculation Con’t • 10% outage capacity Vs antennae spacing (3X3 MIMO)

15. Simulation and Calculation Con’t • 10% outage capacity Vs angle spread (3X3 MIMO)

16. Conclusion and Future work • In this project, I studied the channel capacity for MIMO communication, especially for the underwater acoustic communication. Then I simulated the channel impulse and calculated the capacity from the given functions. • Apparently, the channel capacity increase with the number of antennae, also with the signal-to-noise ratio. For spatial correlated channel, the channel capacity increase with the antennae spacing and angle spread. That means the channel capacity increase with the decreasing of the cross-correlation of channel. • There are a lot factors which can effect the channel capacity in the underwater environment. We may find more performance for

17. Reference • [1]: T. M. Cover & J. A. Thomas, Elements of Information Theory. JohnWiley & Sons, 1991. • [2]: E. Telatar, “Capacity of multi-antenna Gaussian channels”. European Transactions on Telecommunications, vol. 10, no. 6, pp. 585-595, Nov.-Dec. 1999. • [3]: I. E. Telatar& D. N C. Tse, “Capacity and mutual information of wideband multipathfading channels”. IEEE Transactions on Information Theory, vol. 46, no. 4, pp. 1384-1400, July 2000. • [4]: Henry A. Leinhos, “Capacity Calculations for Rapidly Fading Communication Channels”. IEEE Journal of Oceanic Engineering, vol. 21, no. 2, April 1996 • [5]: Michael Zatman, Brian Tracey, “Underwater Acoustic MIMO Channel Capacity”. Signals, Systems and Computers, 2002. Conference Record of the Thirty-Sixth Asilomar Conference on, Volume 2,  3-6 Nov. 2002 Page(s):1364 - 1368 vol.2 • [6]: Dazhi Piao; Biao Jiang; Huabing Yu; Changyu Sun; Qihu Li;“The effect of space-time joint correlation on the underwater acoustic MIMO capacity”. Oceans 2005 – Europe, Volume 1,  20-23 June 2005 Page(s):413 - 418 Vol. 1 • [7]: Actoolbox by David Duncan