Power-Distortion Optimized Mode Selection for Transmission of VBR Videos in CDMA Systems

Transcription

1 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 51, NO. 4, APRIL Power-Distortion Optimized Mode Selection for Transmission of VBR Videos in CDMA Systems Il-Min Kim, Member, IEEE, Hyung-Myung Kim, Senior Member, IEEE, and Daniel Grobe Sachs Abstract A power-distortion (P-D) optimized coding modeselection scheme is proposed for variable bit rate videos in wireless code-division multiple-access (CDMA) systems. Unlike the conventional rate-distortion (R-D) optimized mode-selection methods, the proposed scheme takes into account time-varying channels. We show that the proposed optimization problem can be represented as the conventional R-D mode-selection problem, in which the Lagrangian multiplier depends on the channel conditions. In the proposed scheme, as the link gain of a user increases, the optimum mode for the user tends to be intramode rather than intermode, and vice versa. Numerical results show that, in CDMA systems, the proposed scheme consumes much less power at the same image quality compared with conventional R-D schemes. Index Terms Code-division multiple access (CDMA), mode selection, power, variable bit rate (VBR). I. INTRODUCTION ACROSS THE WORLD, third-generation cellular communication systems are being introduced. These systems are designed to accommodate various multimedia services, which have a much greater data rate than past voice-only services. However, the greater data rates required by these multimedia services requires a greater transmit power for each mobile terminal. Because the capacity of a code-division multiple-access (CDMA) system is limited by the multiple-access interference (MAI), if the power transmitted by each user is reduced, intracell and intercell interference will be decreased, increasing the total system capacity [1]. Moreover, if the mobile s transmit power is reduced, its battery life can also be extended. It is, therefore, desirable to minimize the amount of signal power transmitted by the mobile, while simultaneously maintaining the desired quality-of-service (QoS) level. Because wireless video offers many opportunities for this type of optimization, there has recently been significant research activity examining power management for wireless video [2] [7]. In particular, [2] [5] have focused on the CDMA systems. In [2], two Paper approved by K.-K. Ma, the Editor for Video and Signal Processing of the IEEE Communications Society. Manuscript received June 22, 2002; revised September 3, 2002 and September 18, I.-M. Kim is with the Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA USA ( ilmin@deas.harvard.edu). H.-M. Kim is with the Department of Electrical and Computer Science, Korea Advanced Institute of Science and Technology, Taegjon , Korea. D. G. Sachs is with the Coordinated Sciences Laboratory, University of Illinois, Urbana, IL USA. Digital Object Identifier /TCOMM efficient power-management schemes have been proposed for wireless video service in CDMA systems. Unlike the conventional scheme which aims for satisfying a fixed target bit-error rate (BER), the two schemes adjust the BER of each video packet according to the importance of the contained video data. Although these schemes considerably outperform the conventional scheme, they have been designed in a heuristic approach and they have not taken into account the image-frame dependency caused by motion compensation. To overcome this problem, in [4], an optimum power-management scheme has been proposed, based on the model of the end-to-end distortion of INTRAframe refreshed image sequences. In [3], a new resource-allocation scheme has been proposed to improve the bandwidth utilization. In [5], Zhang et al. have studied a power-minimized bit-allocation scheme considering both the transmission power and the processing power for source and channel coding. For video encoders, one of the most important optimization tasks is to choose the most efficient encoding mode for each image region. For example, in H.263, each macroblock (MB) can be coded either predictively (intermode) or without dependence on previous frames (intramode). The MB can also simply be skipped and left unchanged from the previous frame; the skip mode can be considered as a special case of intermode. Over the past ten years, many researchers have studied optimum mode-selection schemes [9] [13]. The aim of these schemes is to select the coding mode which minimizes the distortion for any given rate. That is, they optimized the coding mode in the sense of rate-distortion (R-D) tradeoff. This type of algorithm provides good performance for many applications, including wired networks and time-division multiple-access (TDMA) systems, where the capacity is limited by the total transmitted bit rate. However, as stated previously, the capacity of the CDMA system is limited by the total received power rather than the total transmitted bit rate. Thus, the previous R-D optimized scheme may not be efficient in CDMA systems. In this letter, we propose a new optimum mode-selection method which is optimum in the sense of power-distortion (P-D) tradeoff. We will refer to this scheme as the P-D optimized mode-selection scheme. By trading off power against distortion, we can optimize performance for power-limited systems like CDMA. This letter is organized as follows. In Section II, we present our system model. In Section III, the previous R-D and the proposed P-D optimized mode-selection methods are described. In Section IV, we compare the performance of both methods. Finally, conclusions and directions for further work are presented in Section V /03$ IEEE

2 526 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 51, NO. 4, APRIL 2003 II. SYSTEM MODEL A. Channel Model and the Signal-to-Interference Plus Noise Ratio (SINR) We assume Nakagami- distribution. Let be the channel power gain between the desired mobile terminal (MT) and the base station (BS). Then where is the channel power gain due to multipath fading on the th path. Assume are independently, identically distributed (i.i.d.) random variables with where reflects the rate at which decay occurs. The probability density function (pdf) of is then given by [15] where,, and are defined in [15]. For the wideband CDMA (W-CDMA) uplink that we consider, inner-loop power control is directed by the BS. For each power control interval, the BS measures the received SINR from a given MT, compares it to a prescribed target SINR, and generates binary transmit power-control commands every ms to raise or lower the power transmitted by the MT. Let,, and be the transmit power, the link gain, and the bit rate, respectively, used by an MT for the th power-control period. Let be the MAI plus thermal noise power received by the desired MT. Under the assumption of ideal power control, the SINR after despreading of the desired MT is constant and given by where is the spreading bandwidth. B. Variable Bit Rate (VBR) Transmission In this letter, we assume a VBR mode in which no rate control is employed; each frame is encoded with a fixed quantization step size. To accommodate the VBR data over the wireless CDMA channel, a variable processing gain CDMA system [3], [16] is used. We assume that the video encoder used is based on the H.263 standard, which allows the encoder to choose intra-, inter-, or skip mode encoding independently for each MB. Each MB is allocated the same amount of time for transmission; this transmission time is, where is the number of MBs per frame, and the number of frames per second. For example, the MB duration of a quarter common intermediate format (QCIF) video is ms at, which is approximately equal to the power-control interval. For simplicity, in this letter, we will assume the MB duration is equal to. III. OPTIMUM MODE SELECTION A. R-D Optimized Mode Selection Let be the coding mode for the th MB and power-control period. Let and be the induced distortion and the incurred rate, respectively, when mode is (1) (2) (3) chosen for th MB. When the video data is transmitted over error-prone channels, can be expressed as follows [10]: where depends on the coding mode of the th MB: for intracoded MBs, is the same as the error-free coding distortion; for skip- and intercoded MBs, is the quantization distortion plus the expected concealment distortion of the th MB from which it is predicted. is the expected distortion induced by concealing an error decoding the th MB using the concealment method assumed by the encoder, and is independent of the coding mode used. denotes the probability of error decoding the th MB. The conventional R-D optimized mode-selection methods [8] [12] are based on the following theorem [18]: Theorem 1: For any, the solution to the unconstrained problem (5) is also the solution to the constrained problem subject to (6) where and. If the other optional modes, such as inter4v mode, are used, must be modified so that it includes the additional modes. The proof of Theorem 1 can be found in [18]. This theorem states that if happens to be equal to the bit-rate constraint, then the choice of mode is optimal; it is the mode with the least distortion for which the encoded bit rate is less than or equal to [19]. Thus, for a given value, it is necessary to find which makes equal to. Over the past ten years, many methods have been proposed for determination of. For an error-free environment, Sullivan and Wiegand [9] obtained using the quantization step size. Côté et al. [10] extended Sullivan and Wiegand s work by showing that a value obtained in this way is still appropriate for an error-prone channel, and this method has been widely adopted [13]. Therefore, we will use this quantization-based method in this letter. Because we are using a VBR encoding with a fixed quantization step size, for any,. Thus, the Lagrangian multiplier is fixed and given by [9], [10] where is a constant. The R-D optimized modes are given by (8) B. P-D Optimized Mode Selection in CDMA Systems In this section, we extend the R-D optimization scheme above to a P-D optimized mode-selection algorithm for CDMA systems. Let be the transmit power of the desired user with mode during the th power control period or the th MB. Then (9) (4) (7)

3 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 51, NO. 4, APRIL where (10) Now, as in Theorem 1, we can prove the following lemma: Lemma 2: Assume the VBR mode presented in Section II. For any, the solution to the unconstrained problem (11) is also the solution to the constrained problem subject to (12) where. Using this lemma, we can find the optimum mode for a given power constraint, which is fixed when and are given. However, it is necessary to find an appropriate for a given value. Recall that, for Theorem 1, the quantization step size could be used instead of to find the appropriate Lagrangian multiplier. Similarly, we can use and to find the appropriate Lagrangian multiplier. Let, and rewrite (11) as (13) Note that plays the role of the Lagrangian multiplier for the unconstrained R-D optimization problem. Because varies with the link gain, varies with the time index,evenifthe quantization step size is fixed. However, if the channel is fixed, is also fixed, and (13) becomes the unconstrained R-D optimized mode-selection problem with a fixed Lagrangian multiplier. Because we have already determined that is the appropriate Lagrangian multiplier for this problem, we can find by setting the expected value of to be equal to Because the constant is given by satisfying (14) is given as Finally, the P-D optimized modes are given by (14) (15) (16) (17) where. Remark 3: As the link gain of a user increases, the power distortion-optimized mode for the user tends to be intramode rather than intermode, and vice versa, where we regard the skip mode as the special case of the intermode. The proof is given in the Appendix. IV. PERFORMANCE COMPARISON In this section, we compare the performance of the R-D optimized and P-D optimized mode-selection methods for CDMA systems. We assume Rayleigh flat fading environment Fig. 1. Intramode and intermode percentages of the R-D and the P-D schemes versus H =E[H ]. Q = 10. BER = 10. Foreman. with and. To model the Rayleigh fading, we use the Jakes model with a 1.8-GHz carrier frequency and assume the MT moves at a typical pedestrian speed of 4 km/h. We simulate a convolutionally-encoded CDMA system with code rate 1/2 and free distance 10. Also,,, and. 100 frames of two well-known QCIF image sequences are coded at 15 frames per second: the low-motion sequence Mother and Daughter, and the high-motion sequence Foreman. Because each frame consists of 99 MBs, the total number of MBs encoded is As in [10], the constant is set to For these simulations, we used a motion-compensated temporal error-concealment scheme. We set the motion vector of the missing MBs to the median value of the motion vectors of the adjacent blocks. If no surrounding motion vectors are available, the motion vector of the missing MB is set to zero. The simulation results are averaged across 50 independent trials. Finally, to determine the coding mode of an MB, the encoder must compute before the MB is transmitted. Because the actual value for is unavailable before the MB is transmitted, we estimate the current link gain using the link gain measured for the last MB. That is, we estimate using the delayed channel side information (CSI) (18) Fig. 1 shows the percentage of the intercoded and intracoded MBs for the R-D and the P-D optimum schemes when and the BER is. As predicted by Remark 3, for the P-D optimized scheme, the percentage of the intracoded MBs increases as the channel improves. Let denote the peak signal-to-noise ratio (PSNR) degradation from the error-free PSNR of the R-D scheme. For,, and, respectively, the error-free PSNRs for the Foreman sequence were 35.4, 31.2, and 27.2 db. For Mother and Daughter, the error-free PSNR values were 37.5, 33.7, and 30.6 db. In order to compare the total transmit

4 528 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 51, NO. 4, APRIL 2003 Fig. 2. scheme over the P-D scheme versus 1PSNR with delayed CSI. Foreman. Transmit power-use ratio G and interference ratio G of the R-D Fig. 4. Transmit power-use ratio G of the R-D scheme over the P-D scheme versus 1PSNR with perfect CSI and delayed CSI. Foreman. Fig. 3. Transmit power-use ratio G and interference ratio G of the R-D scheme over the P-D scheme versus 1PSNR with delayed CSI. Mother and Daughter. power by the R-D and P-D schemes for the same delivered distortion, we define the transmit power-usage ratio over the MBs as follows: (19) where the SINRs of the R-D scheme and the P-D scheme are chosen so that the values are equal. (In the simulations, we chose the SINR values to ensure that the differences between the values for the R-D and P-D schemes was less than 0.1 db.) Figs. 2 and 3 show the power-use ratio versus for Foreman and Mother and Daughter, respec- tively. We observe that, for CDMA systems, the P-D scheme provides significant power savings when compared to the R-D scheme. For example, Fig. 2 shows that, for the Foreman sequence, the total transmit power is reduced by over 10 db when db and. Thus, the P-D scheme saves the battery life of each mobile terminal considerably. Because the capacity of the CDMA system is limited by the MAI, the total interference (intracell interference plus the intercell interference) is another important criterion for performance comparison. In the P-D scheme, the mode selection depends on the channel gain, and thus, the transmit power is correlated with the channel. Therefore, the amount of intracell interference is not linearly proportional to the transmit power. On the contrary, the intercell interference is proportional to the transmit power because the transmit power of a mobile in the desired cell is generally independent of the channel gains from the mobile to the BSs in other cells. In CDMA systems, the intercell interference to intracell interference ratio,, depends on the path loss, shadowing effect, and the handoff scheme [21]. In general, the path loss is modeled as the product of th power of distance and the shadowing is modeled as the log-normal variable with zero mean and standard deviation. When and db, which are typical values, the ratio is given as follows: for hard handoff; for soft handoff reception by the better of the two nearest cells; and for soft handoff reception by the better of the three nearest cells [21]. Let and denote the total interference at the same values incurred by the R-D and P-D optimum mode-selection methods. Figs. 2 and 3 provide the ratio for various values. Numerical results demonstrate that the P-D scheme reduces the interference considerably, which results in the increased CDMA system capacity. Finally, we consider the transmit power-gain penalty associated with the delayed channel knowledge as in (18). For both the perfect CSI and the delayed CSI cases, we ran simulations. Fig. 4 demonstrates that the gain penalty increases as the mobile speed increases, and thus, the P-D scheme is particularly efficient when the mobile speed is low.

5 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 51, NO. 4, APRIL V. CONCLUSION AND FURTHER WORK Because the capacity of a CDMA system is interference limited, it is important to minimize the total transmit power of the mobile terminals. However, this must be done without compromising QoS. To realize this, we have proposed an optimum mode-selection algorithm for transmitting digital video over a CDMA channel, which minimizes the distortion for a given power consumption value. Unlike previous optimum mode-selection methods, this scheme takes into account time-varying channel conditions. Furthermore, our scheme remains simple and can be implemented on resource-constrained MTs at minimal cost. Numerical results show that optimizing encoding for current channel conditions allows for greatly reduced transmit power while achieving the same average QoS as conventional schemes. In this letter, we have assumed no rate control because we have focused on VBR transmission. For constant bit-rate (CBR) transmission, however, rate control must be considered in order to achieve a target bit rate. To this end, in many R-D schemes [8], [11], [12], the Lagrange multiplier is chosen so that the target bit rate is satisfied while preserving R-D optimality. However, past systems have considered only R-D optimality, and not P-D optimality. Further work extending this type of P-D optimization to CBR video streams in CDMA systems would, therefore, be desirable. In addition, the power consumption for media processing should be also considered as further work because the power consumption may be considerable, especially when the intercoding method is used. APPENDIX Proof of Remark 3: In the following, we drop the subscript for simplicity. Let be the solution to and let Then be the solution to (B.1) (B.2) (B.3) (B.4) Because in (16) and are positive, and. Then we can show the following: (B.5) Therefore, if, then. In addition, for an MB,, where and represent the intramode and intermode, respectively. Thus, we can say that as decreases, i.e., the link gain increases, the optimum mode tends to be intramode rather than intermode. ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers for helpful comments, improving the presentation of the letter. REFERENCES [1] N. Bambos, Toward power-sensitive network architectures in wireless communications: concepts, issues, and design aspects, IEEE Pers. Commun. Mag., vol. 5, pp , June [2] I.-M. Kim and H.-M. Kim, Efficient power-management schemes for video service in CDMA systems, Electron. Lett., vol. 36, pp , June [3], A new resource allocation scheme based on a PSNR criterion for wireless video transmission to stationary over Gaussian channels, IEEE Trans. Wireless Commun., vol. 1, pp , July [4], An optimum power management scheme for wireless video service in CDMA systems, IEEE Trans. Wireless Commun., vol. 2, pp , Jan [5] Q. Zhang, Z. Ji, W. Zhu, and Y.-Q Zhang, Power-minimized bit allocation for video communication over wireless channels, IEEE Trans. Circuits Syst. Video Technol., vol. 12, pp , June [6] J. Lervik and T. Fischer, Robust subband image coding for waveform channels with optimum power and bandwidth allocation, in Proc. ICASSP, 1997, pp [7] C. E. Luna, Y. Eisenberg, T. Pappas, and A. K. Katsaggelos, Transmission energy minimization in wireless video streaming applications, in Proc. Asilomar Conf., 2001, pp [8] T. Wiegand, M. Kightstone, D. Mukherjee, T. George, and S. K. Mitra, Rate-distortion optimized mode selection for very low bit rate video coding and the emerging H.263 standard, IEEE Trans. Circuits Syst. Video Technol., vol. 6, pp , Apr [9] G. J. Sullivan and T. Wiegand, Rate-distortion optimization for video compression, IEEE Signal Processing Mag., vol. 15, pp , Nov [10] G. Côté, S. Shirani, and F. Kossentini, Optimal mode selection and synchronization for robust communications over error-prone networks, IEEE J. Select. Areas Commun., vol. 18, pp , June [11] R. Zhang, S. L. Regunathan, and K. Rose, Video coding with optimal inter/intra-mode switching for packet loss resilience, IEEE J. Select. Areas Commun., vol. 18, pp , June [12] D. Wu, Y. T. Hou, B. Ki, W. Zhu, Y.-Q. Zhang, and H. J. Chao, An end-to-end approach for optimal mode selection in internet video communication: theory and application, IEEE J. Select. Areas Commun., vol. 18, pp , June [13] M. Gallant and F. Kossentini, Rate-distortion optimized layered coding with unequal error protection for robust internet video, IEEE Trans. Circuits Syst. Video Technol., vol. 11, pp , Mar [14] H. Suzuki, A statistical model for urban multipath propagation, IEEE Trans. Commun., vol. 25, pp , July [15] M. Nakagami, The m-distribution a general formula of intensity distribution of rapid fading, in Statistical Methods in Radio Wave Propagation. New York: Pergamon, 1960, pp [16] C. L. I and R. D. Gitlin, Variable spreading gain CDMA with adaptive control for true packet switching wireless networks, in Proc. ICC 95, 1995, pp [17] I.-M. Kim and H.-M. Kim, Scheme for enhancing performance of smart antennas in variable processing gain packet CDMA systems, Electron. Lett., vol. 35, pp , Apr [18] H. Everett, III, Generalized Lagrange multiplier method for solving problems of optimum allocation of resources, Oper. Res., vol. 11, pp , [19] Y. Shohan and Al Gersho, Efficient bit allocation for an arbitrary set of quantizers, IEEE Trans. Acoustics, Speech, Signal Processing, vol. 36, pp , Sept [20] K. Ramchandran and M. Vetterli, Best wavelet packet bases in a ratedistortion sense, IEEE Trans. Image Processing, vol. 2, pp , Apr [21] A. J. Viterbi, CDMA: Principles of Spread Spectrum Communication. Reading, MA: Addison-Wesley, 1995.