# Complexity-bounded Power Control in Video Transmission over a CDMA Wireless Network

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3 C. Maximizing Utility for Given Complexity Maximizing Utility for Given Bit Rate: Given complexity β [β,β 2,,β N ] and rate R s [R s,,r s,2,,r s,n ], we can determine the corresponding SINR requirement ΓR s [γ R, γ 2 R 2,, γ N R N ] that satisfies the quality constraint at each terminal. We would like to determine the maximum utility achievable by each user. The problem can be formulated as: Maximize U i fr Minimize, i,,n, subject to Eb h i N 0 i R i j i h jp j + σ 2 γ ir i 0 <,max 2 D i R s,i,β i,γ i D i,0 3 where D i,0 is distortion corresponding to the target quality, and,max is the maximum possible transmission power for the i th user. The minimal power Pi satisfying the above requirements, 2, 3 when SINonstraints are met with equality, [7]. This results in Pi h i σ 2 R + iγ ir i j 4 Rc R j γ j R j + The minimal power P i is feasible only if 0 <P i,max, which yields N j R + < [ σ2 ] R iγ ir i min i h i P c i,max R + iγ ir i 5 When there is no maximum power constraint, the feasibility condition reduces to N < 6 R jγ jr j + j Therefore, for given β i, we can search through all possible R i and find the pairs R i, γ i that satisfy both the distortion constraint 3 and the feasibility conditions i.e., 5 or 6. For each feasible pairs, we determine the corresponding minimal power Pi. The combination that achieves the minimal is the optimal R i, γ i pair for the given β i. 2 Quality factor q i : Equation 4 indicates the minimal transmission power required for given R s and corresponding ΓR s that satisfies the quality requirement. We would like to find the pair R s, ΓR s that can lead to minimal transmission power at each user among all feasible R i, γ i sets satisfying 3 and 5 or 6. Assume R s, ΓR s is one feasible set and Pi is the corresponding minimal transmission power at each user. Now consider another set R s, ΓR s with corresponding. When R s,i γ i R i R s,i γ i R i,from4 we observe that { R s,i, γ i R s,i } is also feasible if {R s,i,γ i R s,i } is feasible, and quality factor Mother_daughter.qcif 20% 56% 99% foreman.qcif Bit rate kbps Fig. 3. Quality factor q i for received distortion D i,0 50at different INTER rates β i for video sequences mother daughter.qcif and foreman.qcif. TABLE I SIMULATION PARAMETERS. chip rate 8.92 MHz compression complexity β i {20, 56, 99}% Maximum Distortion D i, The minimum power determined by { R s,i, γ i R i } is less than that by {R s,i, γ i R i }, i.e., Pi. We see that R i γ i R i is an important parameter for our work and define q i 7 R i γ i R i as quality factor. The larger the quality factor is, the less the power is consumed for the same quality, or the higher the utility function is. Hence a larger q i is preferred. The power ratio between using the largest quality factor q i,max and other q i is,min q i + q i,max + j j q j+ q j,max+ 8 In Fig. 3 we show how the quality factor q i changes as a function of bit rate when QCIF video sequences mother daughter.qcif and foreman.qcif are compressed at different INTER rates for distortion constraint of D i,0 50 this corresponds to PSNR 3dB. The chip rate is set to chips/s as described in Table I. Stuhlmüller s models [8] are used to describe distortion from both lossy source compression and transmission errors. It shows that q i decreases as bit rate increases, given the INTER rate; and 2 The range of q i is quite large. This provides an opportunity to reduce the transmission power significantly. Now we see that for each complexity, there exists a bit rate and a corresponding SINR achieving the maximum quality factor and consequently maximum utility. In other words, for There is a small interval during which q i stays about the same in the beginning part of the feasible rate range. Globecom /04/\$ IEEE

4 TABLE II MAXIMUM QUALITY FACTORS AT DIFFERENT INTER RATES INTER mother daughter.qcif foreman.qcif rate γ R s q γ R s q 20% % % certain video sequence, the optimal bit rate, SINR and quality factor are determined by the compression complexity. This simplicity is because we have the distortion constraint at each user, which constraints γ i equivalently givenr i.inthe conventional power control problem, R i and γ i or are two independent variables. D. Maximizing Utility Over a Range of Complexity We observe from Fig. 3 that the largest quality factor, q i,max, occurs at the highest compression complexity. It is reasonable that the video encoder works at the highest possible complexity to reduce transmission power, in other words, larger utility is achieved at the expense of more compression computation. Since keeping working on a high complexity imposes a high volume of computation on the video compression and consumes a large amount of signal processing power, bound is set for compression complexity to prohibit the video encoder from draining too much battery. This complexity bound determines the optimal operating point. Such an algorithm is referred to as a complexity-bounded power control method. E. Influence of Source Statistics Different video sequences have different end-to-end distortion when compression algorithms and channel conditions are exactly the same. Fast-moving pictures require more bits for the same distortion than slow-moving pictures due to less correlation between adjacent video frames. In other words, for the same source compression algorithm, channel conditions and same video quality, minimum SINR requirements are different for different sequences for the same quality requirement, hence the transmission power is also different. It is clearly shown in Fig. 3 that the quality factor is larger for a slowmoving video sequence mother daughter.qcif than for a fastmoving sequence foreman.qcif. Since a higher q i has the advantage of lowering transmission power,aslow-moving video sequence consumes less transmission power than a fastmoving video sequence given the same desired end-to-end quality. To summarize, we observe that when only transmission power is considered, the source encoder works at its largest quality factor q i,max. Usually this forces the terminal to work with the highest possible complexity. The other two optimal parameters: the bit rate and required SINR are set to reach such q i,max while satisfying the feasibility criterion which depends on other terminal s operating points. Hence this optimal pair for a video sequence is determined by the video characteristics, video codec and the modem, but is independent of path gain h i. One way to implement this complexity-bounded algorithm TABLE III NUMBER OF USERS. INTER rates 20% 56% 99% mother daughter.qcif slow-moving foreman.qcif fast-moving would be the following: The central base station collects algorithms for the video codec when one terminal is admitted, and upon the change of video scene or after a predetermined period, q i,max is updated as well as bit rate and required SINR while satisfying the feasibility criterion. Then the required transmission power is computed from 4. III. PERFORMANCE STUDY An example system is used to examine the properties of our algorithm. We assume the same source compression algorithm H.263 [5] in this paper and the same compression complexity choice are used in all terminals. This can be true if video transmission is standardized for a certain application. Stuhlmüller s models [8] are used to describe distortion from both lossy source compression and transmission errors. A. Number of users It is important to know how many users can be accommodated in one cell. Not considering the constraint on maximum transmission power, from 6 we get the maximum number of users N max argmax N N q j,max + < j It is seen that to maximize the number of users we need select the maximum possible q j,max for all users, the same criterion as maximizing utility. We first examine how many users of the same characteristics either slow-moving or fast-moving, represented by mother daughter.qcif and foreman.qcif, respectively can be supported simultaneously. Then we assume the video distributes evenly between fast-moving and slow-moving sequences. The choice of parameters is summarized in Table I. The capacity of the system is shown in Table III. It is clear that a system can accommodate more slow-moving video sequences than fast-moving ones. B. Utility ratio In this section, we try to analyze the system performance with N terminals. For simplicity, we assume the video sequences transmitted by all terminals have the same characteristics, and the complexity at all terminals is bounded by the same complexity, with a corresponding maximum quality factor q max. We compare the gain from all terminals using q max versus using some lower q<q max. From 4, the optimal utility function for the i th user working at quality factor q is U i f r P i 9 h if r q + N. 0 σ2 Globecom /04/\$ IEEE

5 utility ratio number of users Fig. 4. Utility ratio between algorithms using q max and q. Equation 0 indicates that as more users enter the system, the utility of each user decreases. This is because higher transmission power must be used by each user to combat interference from others. For a fixed number of users, a terminal which is far away from the base station with a small h i, higher transmission power is required to achieve the same quality, and hence this user achieves lower utility than terminals that are closer with larger h i. The ratio between utility functions by using q max and other q is written as U i,max U i q max + N q + N. This ratio is an increasing function of number of users in one cell as described in Fig. 4. As the number of users approaches the limit of the system, the utility ratio becomes significant. This means that the power savings from using optimal operating point at each user i.e. working at q max increases as the number of user increases. C. Overall system utility We define the overall system utility as the total number of frames transmitted per Joule of transmission power consumed by all the users. Assuming N users, this utility can be written as i U tot,n f r i P Nf r i i Q N hi f r σ 2 Nq + N i h i 2 where Q N h i σ2 q+ N.ForafixedN, the total utility increases with q linearly, as in the case of single user utility. Hence when the number of users is given, the maximized overall system utility occurs at the highest quality factor q max. At follows, we let the system work at q max to maximize utility. However, the overall utility is not necessarily an monotonic function of the number of users in the system. To observe how this term varies with the number of users, we look at U tot,n U tot,n i h i N q max + N N 3 N q max +2 N i h i [ ] + q max 2N N q max +2 N h N N i h i Overall system utility can be used to decide whether to admit a new user. In order to improve system utility by addition of one user we need Utot,N U tot,n, which results in q max 2N 0, orn qmax 2 + Nmax 2, i.e., the number of users should not exceed half of the capacity to get a maximized total utility. IV. DISCUSSION In this work, we propose an algorithm that determines the video encoder bit rate and received SINR to maximize the number of received picture frames per Joule, or to minimize transmission power in a CDMA cell, under a certain quality constraint. We find that these parameters depend on algorithms used in video codec, modem and the characteristics of video scene under transmission.for each possible compression complexity, there is a unique optimal operating point. When there exists multiple choices of complexity, a video encoder is usually forced to work on the highest complexity. This is reasonable since the minimized transmission power comes at the expense of a high volume of computation on the video codec and a large amount of compression power. To prohibit the video encoder from draining too much battery, we set bound for compression complexity. This complexity bound determines the optimal operating point. Thus, we refer to the developed algorithm a complexity-controlled power control method. Capacity and utility function are studied by an example system. We show that using the optimal operating point can improve the utility of individual terminals significantly compared to using non-optimal operating points, especially when the number of terminals is large. When compression power consumption is also taken into consideration, we can determine the optimal operating point that minimizes the sum of the transmission and compression power consumption by searching in the complexity space instead of the space of {bit rate, complexity, SINR}. This is a very nice property, especially when a large number of users are in the system. This work is in progress. REFERENCES [] D. Goodman and N. Mandayam, Network assisted power control for wireless data, Mobile Networks and Applications, vol. 2, pp , 200. [2] V. Rodriguez, Resource management for scalably encoded information: The case of image transmission over wireless networks, in IEEE International Conference on Multimedia and Expo ICME, vol., 2003, pp [3] V. Rodriguez, D. Goodman, and Y. Wang, Optimal coding rate and power allocation for the streaming of scalably encoded video over a wireless link, in IEEE International Conference on Acoustics, Speech and Signal Processing ICASSP, [4] X. Lu, Y. Wang, E. Erkip, and D. Goodman, Power efficient multimedia communications over wireless channels, IEEE Journal on Selected Areas in Communications, vol. 2, no. 0, pp , [5] ITU-T Recommendation H.263: Video Coding for Low Bit Rate Communication, 998. [6] Y. Wang, J. Ostermann, and Y. Q. Zhang, Video Processing and Communications. Prentice Hall, [7] A. Sampath, P. S. Kuma, and J. M. Holtzman, Power control and resource management for a multimedia CDMA wireless system, in Personal, Indoor and Mobile Radio Communications, vol., 995, pp [8] K. Stuhlmüller, N. Färber, M. Link and B. Girod, Analysis of video transmission over lossy channels, IEEE Journal on Selected Areas in Communications, vol. 8, no. 6, pp , Globecom /04/\$ IEEE

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