Evaluation and Compensation of Frequency Dependent Path Loss over OFDM Subcarriers in UAC

Transcription

1 Evaluation and Compensation of Frequency Dependent Path Loss over OFDM Subcarriers in UAC Sadia Ahmed Electrical Engineering Department, University of South Florida, Tampa, FL Huseyin Arslan Electrical Engineering Department, University of South Florida, Tampa, FL Abstract The underwater acoustic communication (UAC) channel presents severe time, space, and frequency selectivity that makes it difficult to achieve high data rate communication. In the recent years OFDM is used to resolve primarily frequency selectivity among these problems. Due to high absorbency of water over small frequency range path loss may be highly variable over OFDM subcarriers. This paper will evaluate this varying path loss and present algorithm to compensate such path loss using adaptive power control, adaptive modulation order, and adaptive BW. To the best knowledge of the authors, evaluation and compensation of varying path loss in the proposed method has not been presented before. Thus this research presents a valuable work in this domain. I. INTRODUCTION Underwater acoustic communication (UAC) channel presents severe time, space, and frequency selectivity that pose challenges in achieving high data rate communication. Orthogonal Frequency Division Multiplexing (OFDM) offers an agreeable solution to frequency selectivity by transmitting the data in parallel over multiple subcarrier frequencies [1]. Besides high selectivity, path loss is a major concern that primarily depends on the range between the transmitter (Tx) and the receiver (Rx) and the absorption coefficient, which in turn depends on the transmission frequency. The attenuation caused by path loss limits the useful bandwidth in UAC OFDM in the absence of proper compensation technique. In addition, the high increase of absorbency of water over small frequency range and the frequency compatibility of subcarrier spacing with subcarrier frequencies may cause path loss to vary significantly over OFDM subcarriers. This requires adaptive compensation of path loss over individual subcarriers and optimizing OFDM bandwidth under such condition. Adaptive compensation of path loss can be carried out at the transmitting end using one or all of the following, (i) Adaptive power control over subcarriers, (ii) Adaptive modulation order over subcarriers, and (iii) Adaptive total bandwidth and FFT size. The prior knowledge of the receiver detection threshold and knowledge of path loss derived from the communication environment may allow adjusting power or modulation order on individual subcarriers during Attenuation (db) (,22) (5,22) (1,22) (25,22) (5,14) (75,7.5) (1,6) (15,5) (2,4) (3,3) Fig. 1. Absorption Coefficient.vs. Frequency transmission. This paper will first evaluate the varying path loss over OFDM subcarriers for various channels, range, and frequency and secondly propose an algorithm to adaptively compensate such path loss using adaptive power control, adaptive modulation order, and adaptive BW. To the best knowledge of the authors, the presented varying path loss over OFDM subcarriers and/or its proposed compensation technique in the UAC systems have not been addressed before. Therefore, this analysis and the proposed path loss compensation algorithm present valuable contribution in this area. The rest of the paper is organized as follows. Section II presents the analysis of varying path loss and its compensation technique. Section III presents the performance results through simulation. Section IV addresses the concluding remarks. II. ANALYSIS Channel Model: The water attenuation coefficient of sound presented by Francois-Garrison [1] can be expressed as, α = A 1 P 1 f 1 f 2 f f 2 + A 2P 2 f 2 f 2 f f 2 + A 3P 3 f 2, (1) MTS

2 Subcarrier Amplitudes Subcarrier Index After performing FFT the received signal y(n) <= n <= N 1, in frequency domain can be expressed as Y (k) = N 1 nk n= y(n)e j2π N. If the channel frequency response is denoted as H(k) then the received signal without path loss can be expressed as, Y (k) =X(k) H(k) (3) Using (2) the path loss (db) on the kth subcarrier can be expressed as, TL k (R, α) =2logR + α k R, (4) where α k denotes the attenuation on the kth subcarrier. The SNR k of the kth subcarrier can be presented as, Fig. 2. Amplitudes Arbitrary Subcarrier Amplitude Variation Due to Path Loss Subcarrier Index Fig. 3. AWGN Noise over OFDM Subcarriers where α is the attenuation co-efficient in db/km and f is the transmission frequency. For expressions of A 1 through A 3, P 1, through P 3, and f 1 and f 2, [1] can be referred. In the absence of any reflection, refraction or other noise, the water medium can be considered homogeneous where the transmission loss, TL(R, α) in db depends on α and on transmission range, R (meter). For a reference range at R 1 =1m and R 2 = R, TL(R, α) =2logR + αr. (2) The variation of α with respect to frequency is presented in Fig. 1, where the sets denote the set of (depth, temperature) pairs given in Table I. These values are expected in low to middle latitudes in the ocean. Salinity chosen is 35 p.s.u. Fig. 2 represents varying path loss effect (arbitrary) on OFDM subcarriers and Fig. 3 represents AWGN noise over the subcarriers. OFDM Signal Structure: The nth discrete time sample of the OFDM transmitted signal can be expressed as, x(n) = N 1 nk k= X(k)ej2π N <= n<= N 1, where the real and imaginary components of x(n) are assumed to be i.i.d. Gaussian distributed [2]. SNR k = E Y (k) 2 LS k σ 2, (5) where σ 2 denotes the AWGN noise power and LS k denotes the path loss on the kth subcarrier. The frequency dependent underwater noise is not considered here. Using (4), LS k =1 2logR+α k R 1. (6) Using (5), SNR k in db, ( E Y (k) 2 LS ) k SNR kdb =1log 1 σ 2. (7) Let P tot denote the total transmitted power over N subcarriers and it is assumed fixed for each transmission. Therefore, power over each subcarrier, P sub can be expressed as, P sub = P tot /N. (8) If M denotes the modulation order over each subcarrier then the OFDM data rate R can be expressed as R = N 2 M Δf M =, 1, 2..., (9) where Δf represents the subcarrier spacing. Let SNR TH denote the threshold for accurate detection at the receiver. When SNR KdB falls below SNR TH due to path loss, the power on the Kth subcarrier, P K can be increased such that SNR KdB meets the threshold. If P K is increased, the power on other subcarriers need to be adjusted such that P tot remains fixed. All subcarriers from k +1 to N will be dropped. Therefore, the extra power over those dropped subcarriers can be distributed among the 1st to k 1 subcarriers. The adjustment of powers on K 1 subcarriers must satisfy the condition of SNR (K 1)dB SNR TH. Due to dropped subcarriers the data rate will decrease. To compensate the reduced data rate, the modulation order can be adjusted over the first k subcarriers. If after power adjustment, SNR (K 1)dB <SNR TH then Kth subcarrier will also be dropped and R can be maintained by adjusting the modulation order over the first K 1 subcarriers. The additional power over the K th subcarrier can again be distributed over the first K 1 subcarriers. Let M L represent the adjusted modulation order over the remaining subcarriers

3 and R L represent the adjusted data rate that compensate path loss. Using (9), R L =(K 1) 2 ML Δf M L =, 1, 2... (1) Using (9) and (1), R L R = (K 1) 2ML Δf N 2 M Δf The goal of adjusting the modulation order over the remaining subcarriers will be to, R L (K 1) 2ML = R N 2 M 1 Proposed Algorithm K 1 for K N do Calculate path loss on the Kth carrier Calculate SNR KdB on the Kth carrier K K +1 end for K 1 while K N do if SNR KdB <SNR TH then Boost power on Kth subcarrier, such that SNR KdB = SNR TH {Adjust power on other subcarriers.} Adjust P R, R =, 1, 2...K 1 equally, such that P tot = K 1 R= PR + PK, Recalculate SNR (K 1)dB {Check for lower subcarrier SNR} if SNR (K 1)dB <SNR TH then {Only transmit over K 1 subcarriers} Cannot transmit above K 1 frequency. Adjust modulation order over K-1 subcarriers Exit WHILE loop else {Transmit over K subcarriers} Cannot transmit above K frequency. Adjust modulation order over K subcarriers Exit WHILE loop end if end if K K +1 end while III. SIMULATION RESULTS The simulation is carried out using the parameters of Table I. Fig. 4, Fig. 5, and Fig. 6 show SNR due to path loss in the Hz range. The variation of SNR over OFDM subcarriers is not significant. Although there may be smaller variation, which is not noticeable in the figures due to their condensed nature. All three figures show increase in SNR loss with increase in TABLE I SIMULATION PARAMETERS Parameters in UAC Values Frequency(Hz) (1,2),(5,1) (Minimum,Maximum) (1,2),(2,7) Frequency(KHz) (1,2),(5,1),(1,2) (Minimum,Maximum) (2,7),(1,11) FFT Size 64,128,256,512,124 Range(m) 1,5,1,5,1, 5,1,1 Temperature(deg C) 22,22,22,22,14,7.5,6.,5,4,3 [3] Depth(m),5,1,25,5,75,1 15,2,3 [3] Hz to 2 Hz, FFT = 64,Z =m,t =22 deg C 1m 5m 1m 5m 1m 5m 1m 1m Fig. 4. SNR.vs. Subcarrier Frequency (No Compensation) transmission range. Fig. 7 and Fig. 8 show SNR values due to path loss for frequency in the khz range. Obviously there is high increase in loss compared to the Hz range. Also, the loss varies significantly over frequencies. Some of this variation is not visible in the figures due to the condensed form. It may be noted that the SNR in db in the figures are negative values. Fig. 9 illustrates the SNR for a BW of 1kHz. IV. CONCLUSION This paper presented an evaluation of varying path loss over OFDM subcarriers. A compensation algorithm is proposed to compensate such path loss by adjusting the power, modulation order, and BW. As part of future work, all the possible variables such as power threshold, SNR threshold, modulation order, etc. that influence the variation of path loss and hence the SNR over OFDM subcarriers will be taken into account to formulate an optimization problem. This work will be included in a future paper. REFERENCES [1] X. Lurton, An Introduction to Underwater Acoustics: principles and applications, Springer,Chichester, UK:. Springer, 1996.

4 Hz to 7 Hz, FFT=256, Z=m, T=22 deg C 1m 5m 1m 5m 1m 5m 1m 1m khz to 2 khz, FFT=256,Z=m, T=22 deg C 5m 1m 5m 1m 1m Fig. 5. SNR.vs. Subcarrier Frequency (No Compensation) 2 Hz to 7 Hz, FFT=256, Z=3m,T=3. deg C 1m 5m 1m 5m 1m 5m 1m 1m Fig. 7. 2kHz to 7kHz, FFT=256, Z=m, T=22 deg C 1m 5m 1m Fig [2] I. Capoglu, Y. Li, and A. Swami, Effect of Doppler spread in OFDMbased UWB systems, Wireless Communications, IEEE Transactions on, 15 pp , Sept. 25. [3] [Online]. Available: m 1m 5m Fig. 8.

5 kHz to 11kHz, FFT=124, Z=m, T=22 deg C 1m 5m 1m Fig. 9.