L. Li and A. Goldsmith. Capacity and optimal resource allocation for fading broadcast channels--Part II: Outage capacity. IEEE Trans. Inform. Theory, 47(3):1103--1127, March 2001.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....must be completed by a deadline. Resource allocation for fading multi user broadcast channels is a popular topic in information theory. However, the resource being allocated is usually average power or bandwidth, and the quantity to be maximized is most often Shannon capacity. Goldsmith and Li [11] [8] and Tse and Hanly [14] have found capacity limits and optimal resource allocation policies for such channels. Biglieri et al. 1] have examined power allocation schemes for the block fading Gaussian channel. Tse and Hanly [10] have also studied channel allocations in multi access fading ....

L. Li, A. Goldsmith, "Capacity and optimal resource allocation for fading broadcast channels," in Proceedings, Thiry-Sixth Annual Allerton Conference on Communication, Control, and Computing. (1998, pp.516-25).

....operating under energy constraints. Resource allocation for fading multi user broadcast channels is a popular topic in information theory. However, the resource being allocated is usually average power or bandwidth, and the quantity to be maximized is most often Shannon capacity. Goldsmith and Li [17] [10] and Tse and Hanly [22] found capacity limits and optimal resource allocation policies for such channels. Biglieri et al. 2] examined power allocation schemes for the block fading Gaussian channel. Tse and Hanly [12] also studied channel allocations in multi access fading channels that ....

L. Li, A. Goldsmith, "Capacity and optimal resource allocation for fading broadcast channels," in Proceedings, Thiry-Sixth Annual Allerton Conference on Communication, Control, and Computing. (1998, pp.516-25).

....must be completed by a deadline. Resource allocation for fading multi user broadcast channels is a popular topic in information theory. However, the resource being allocated is usually average power or bandwidth, and the quantity to be maximized is most often Shannon capacity. Goldsmith and Li [12] [9] and Tse and Hanly [15] found capacity limits and optimal resource allocation policies for such channels. Biglieri et al. 2] examined power allocation schemes for the block fading Gaussian channel. Tse and Hanly [11] also studied channel allocations in multi access fading channels that ....

L. Li, A. Goldsmith, "Capacity and optimal resource allocation for fading broadcast channels," in Proceedings, Thiry-Sixth Annual Allerton Conference on Communication, Control, and Computing. (1998, pp.51625) .

.... in wireless data networks, both optimal routing and optimal resource allocation problems have been studied in isolation: routing in data networks has a long tradition, e.g. 1, 5, 6] while optimal resource allocation problems for wireless systems have been considered more recently, e.g. [9, 10, 11]. Joint optimization of routing and link capacities has been studied in the context of design and provisioning of IP networks. In this case the capacities take one of several discrete values (corresponding to, say, the number of transmission lines between two routers) and the routing is often ....

....optimization problem in section 4. Figure 2: Resource sharing among outgoing links at a node. 3. 2 Examples of communications resource constraints Capacity formulas of many important communication channel models satisfy the concavity and monotonicity assumptions of the generic model (see, e.g. [14, 9]) Here we will only illustrate how the Gaussian broadcast channels with FDMA (frequency division multiple access) and TDMA (time division multiple access) fit into this framework. 3.2.1 Gaussian broadcast channel with FDMA In the Gaussian broadcast channel using FDMA, the transmitters at node n ....

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L. Li and A. J. Goldsmith. Capacity and optimal resource allocation for fading broadcast channels part I: ergodie capacity and part II: outage capacity. IEEE Trans. Inform. Theory, 47(3):1083 1127, March 2001.

....of the capacity region and choose the set of rates on this boundary that is optimal according to whatever definition of transport capacity happens to be of interest. Our solution turns out to be a special case of the optimal power allocation solution for fading broadcast channels as presented in [8]. However, while [8] only presents an algorithm for determining what the optimal power allocation scheme should be in any given case, we give a completely explicit solution. This allows us to obtain insights and make conclusions which would be di#cult to make on the basis of the results in [8] ....

....and choose the set of rates on this boundary that is optimal according to whatever definition of transport capacity happens to be of interest. Our solution turns out to be a special case of the optimal power allocation solution for fading broadcast channels as presented in [8] However, while [8] only presents an algorithm for determining what the optimal power allocation scheme should be in any given case, we give a completely explicit solution. This allows us to obtain insights and make conclusions which would be di#cult to make on the basis of the results in [8] The paper is ....

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Lifang Li and Andrea J. Goldsmith. Capacity and optimal resource allocation for fading broadcast channels - part I: Ergodic capacity. IEEE Transactions on Information Theory, IT-47:1083--1102, March 2001.

....to achieve a given set of target rates. At the end of the paper, we will briefly mention the application of some of these results in the context of power control for the downlink of a wireless fading channel. A more comprehensive study, using some of the results described here, can be found in [8]. After the conference presentation of this work [11] we were informed that a similar optimal power allocation solution was obtained in earlier unpublished work [6] Our solution and proofs are presented in a simpler form, emphasizing the greedy structure of the optimal solution as well as the ....

....in Section 3.5 can readily applied to this problem. In the case when there is no average power constraint at all, the power price # is simply set to be zero. In this case, the strategy that maximizes the total throughput is simply to allocate power P to the user with the best channel. In [8], some of the results described here are used to study the fading channel in greater depth, comparing the performance of the optimal strategy with sub optimal schemes such as TDMA and FDMA. Acknowledgment We would like to thank Professor Andrea Goldsmith for informing us about the work [6] ....

L. Li and A. Goldsmith , " Capacity and Optimal Resource Allocation for Fading Broadcast Channels", presented at the Allerton Conf. on Communication, Control, and Computing, Sept. 1998.

....The second set of constraints describe resource limits, such as the total available transmitting power for the links outgoing from the same node. Capacity formulas of many important communication channel models satisfy the convexity and monotonic ity assumptions of the generic model (see, e.g. [6, 7]) Here we will only illustrate how the Gaussian broad cast channel with FDMA fits into this framework. 3.1 Gaussian broadcast channel with FDMA In this channel model, the transmitters at node n send data to receivers at the end nodes of its outgoing links. The outgoing links 1 O(n) are ....

L. Li and A. J. Goldsmith. Capacity and optimal resource allocation for fading broadcast channels: Part I: Ergodic capacity. IEEE Transactions on In- formation Theory, 47(3):1103 1127, March 2001.

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L. Li and A. Goldsmith. Capacity and optimal resource allocation for fading broadcast channels--Part II: Outage capacity. IEEE Trans. Inform. Theory, 47(3):1103--1127, March 2001.

No context found.

L. Li and A. Goldsmith. Capacity and optimal resource allocation for fading broadcast channels--Part I: Ergodic capacity. IEEE Trans. Inform. Theory, 47(3):1083--1102, March 2001.

No context found.

L. Li and A. Goldsmith, "Capacity and optimal resource allocation for fading broadcast channels: Part II: Outage capacity", IEEE Trans. Inform. Theory, vol. 47, pp 1103-1127, March 2001.

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L. Li and A. J. Goldsmith, "Capacity and optimal resource allocation for fading broadcast channels: Part II: Outage capacity," IEEE Trans. Inform. Theory, vol. 47, pp. 1103--1127, March 2001.

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L. Li and A. J. Goldsmith, "Capacity and optimal resource allocation for fading broadcast channels: Part I: Ergodic capacity," IEEE Trans. Inform. Theory, vol. 47, pp. 1083--1102, March 2001.

....we show that duality holds for the ergodic capacity region of fading channels as well. We also show that the relationship in (2) holds for fading channels. Duality also holds for outage capacity and minimum rate capacity. Though the ergodic capacity regions [2] 3] and outage capacity regions [4], 5] of both the MAC and BC have previously been found, duality ties these results together. Minimum rate capacity has only been found for the BC [6] but using duality we can find the minimum rate capacity of the MAC as well. Duality is an exciting new concept that gives great insight into the ....

....regions. V. DUALITY OF OUTAGE CAPACITY In this section, we show that duality holds for the outage capacity of fading channels. The outage capacity region (denoted and ) is defined as the set of rates that can be maintained for user for a fraction of the time, or in all but of the fading states [4], 5] Outage capacity is concerned with situations in which each user (in either the BC or MAC) desires a constant rate a certain percentage of the time. The zero outage capacity [4] 16] is a special case of outage capacity where a constant rate must be maintained in all fading states, or ....

[Article contains additional citation context not shown here]

L. Li and A. Goldsmith, "Capacity and optimal resource allocation for fading broadcast channels--Part II: Outage capacity," IEEE Trans. Inform. Theory, vol. 47, pp. 1103--1127, Mar. 2001.

....of constant channels established in (1) we show that duality holds for the ergodic capacity region of fading channels as well. We also show that the relationship in (2) holds for fading channels. Duality also holds for outage capacity and minimum rate capacity. Though the ergodic capacity regions [2], 3] and outage capacity regions [4] 5] of both the MAC and BC have previously been found, duality ties these results together. Minimum rate capacity has only been found for the BC [6] but using duality we can find the minimum rate capacity of the MAC as well. Duality is an exciting new ....

....the points where the MAC and BC capacity region boundaries touch, we find that there is also a fundamental relationship between the power policies used to achieve these points. The optimal power policies (i.e. boundary achieving power policies) for the fading MAC and BC are established in [3] and [2], respectively. Given a priority vector , it is possible to find the optimal power policy that maximizes in both the MAC and the BC. Due to the duality of these channels, the optimal power policies derived independently for the BC and MAC are related by the MAC BC (12) and BC MAC (13) ....

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L. Li and A. Goldsmith, "Capacity and optimal resource allocation for fading broadcast channels--Part I: Ergodic capacity," IEEE Trans. Inform. Theory, vol. 47, pp. 1083--1102, Mar. 2001.

....length, i.e. the channel is constant during transmission of a codeword. Two notions of Shannon capacity have been developed for multiuser fading channels: ergodic capacity and outage capacity. Ergodic capacity is concerned with achieving long term rates averaged over all fading states [1] [3], while outage capacity achieves a constant rate in all non outage fading states subject to an outage probability [4] 5] Zero outage capacity refers to outage capacity with zero outage probability [6] Manuscript received October 4, 2001; revised December 13, 2002. This work was supported by ....

....for Communications. Digital Object Identifier 10.1109 TIT.2003.819328 The ergodic capacity of a fading broadcast channel determines the maximum achievable long term rates averaged over all fading states. The optimal resource allocation scheme for rates in the ergodic capacity region is found in [3], 7] and corresponds to multilevel water filling over both time (i.e. fading states) and users. As intuition would suggest, users are allocated the most power when their channels are strong, and little, if any, power when their channels are weak. Such an allocation scheme maximizes long term ....

[Article contains additional citation context not shown here]

L. Li and A. Goldsmith, "Capacity and optimal resource allocation for fading broadcast channels-Part I: Ergodic capacity," IEEE Trans. Inform. Theory, vol. 47, pp. 1083--1102, Mar. 2001.

....l Vi, limited by separate or total power constraints, and a total bandwidth constraint. Variations and extensions Channels with time varying gain variations (fading) as well as rate constraints based on bit error rates (with or without coding) can be formulated in a similar manner; see, e.g. [7]. We can also combine the channel models de scribed above to model more complex communication systems, where different groups of channels may have separate or total power and bandwidth constraints. 4 Resource allocation for fixed linear system In this section, we assume that the linear system ....

L. Li and A. J. Goldsmith. Capacity and optimal resource allocation for fading broadcast channels: Part I: Ergodie capacity. IEEE Transactions on Information The- ory, 47(3):1103 1127, March 2001.

....W i , limited by separate or total power constraints, and a total bandwidth constraint. Variations and extensions Channels with timevarying gain variations (fading) as well as rate constraints based on bit error rates (with or without coding) can be formulated in a similar manner; see, e.g. [7]. We can also combine the channel models described above to model more complex communication systems, where di#erent groups of channels may have separate or total power and bandwidth constraints. 4 Resource allocation for fixed linear system In this section, we assume that the linear system is ....

L. Li and A. J. Goldsmith. Capacity and optimal resource allocation for fading broadcast channels: Part I: Ergodic capacity. IEEE Transactions on Information Theory, 47(3):1103--1127, March 2001.

....scheme with minimum rates reduces to first allocating the minimum power required to meet the minimum rates and then allocating the excess power according to a multi level water filling scheme relative to effective noise. Minimum rate capacity is essentially a combination of outage capacity [3] and ergodic capacity: some power is used to maintain the minimum rates in all fading states, similar to outage capacity with zero outage probability, while the remaining power is used to maximize the average rates in excess of the minimum rates, similar to ergodic capacity. Minimum rate capacity ....

....indicator function. For simplicity, we assume B = 1. In this paper we impose minimum rate constraints R = R 1 ; R M ) which must be maintained in all fading states, or R j (n) R j ; j = 1; M , for all n. Clearly, R must be in the zero outage capacity region [3] of the channel in order for the minimum rates to be achievable in all fading states. III. SINGLE USER FADING CHANNEL Before analyzing the broadcast channel, we first find the capacity achieving scheme for a single user fading channel subject to minimum rate constraints. We must find the optimal ....

L. Li and A. Goldsmith, "Capacity and optimal resource allocation for fading broadcast channels: Part II: Outage capacity", IEEE Trans. Inform. Theory, pp. 1103-1127, March 2001.

....fading broadcast channel models. I. INTRODUCTION The ergodic capacity of fading broadcast channels determines the maximum average rates achievable in the downlink of a single cell. Ergodic capacity is achieved via multi level water filling of power over time and users using superposition coding [1,2]. An unfortunate consequence of the optimal power allocation scheme is that users with poor channels may receive no data for large periods of time, depending on the duration of channel fades. Such a situation may be unacceptable in delayconstrained applications such as video transmission. With the ....

....B. The signal intended for user j at time i is denoted by X j (i) and has power P j (i) Each receiver has additive white Gaussian noise (AWGN) with noise density v j . The time varying channel gain of user j is denoted by p g j (i) By incorporating the channel gain into the noise term as in [2], we define an effective noise density n j (i) v j =g j (i) and get an equivalent form for the received signal: Y j (i) M X k=1 X k (i) z j (i) 1) where z j (i) N(0; n j (i)B) We assume that the noise density vector n(i) n 1 (i) nM (i) is known to the transmitter and ....

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L. Li and A. Goldsmith, "Capacity and optimal resource allocation for fading broadcast channels: Part I: Ergodic capacity", IEEE Trans. Inform. Theory, pp. 1083-1102, March 2001.

....channels as well. Each joint channel state becomes a multi user component channel in the corresponding parallel channel. The optimal power allocation schemes for single user and multi user parallel channels are well known for various different capacity definitions and power constraints [7] 8] [9] [11] Therefore, we apply these known results to the delay constrained channel with known channel states. Caire et al. 5] studied the single user optimal power allocation problem under a stringent delay constraint with various power constraints and objective functions. Caire s solution was ....

....high SNR. V. TWO USER BROADCAST CHANNEL A broadcast channel has one transmitter sending information to many receivers (down link in a cellular system) The capacity region of the BC channel is known to be convex and the optimal coding scheme is superposition coding with interference cancellation [9]. The decoding order only depends on the noise level at receivers. The user with the best channel is decoded last. Since the base station is the only transmitter in a broadcast channel, there is only one power constraint. We solve the one dimensional optimization problem (2) via dynamic ....

L. Li, A. Goldsmith, "Capacity and Optimal Resource Allocation for Fading Broadcast Channels: Part I: Ergodic Capacity, " IEEE Trans on Information Theory, Jan 2000.

....for multi user fading channels: ergodic capacity and outage capacity. Ergodic capacity is concerned with achieving long term rates averaged over all fading states [7] 8] 4] while outage capacity achieves a constant rate in all non outage fading states subject to an outage probability [5], 6] Zero outage capacity refers to outage capacity with zero outage probability [9] The ergodic capacity of a fading broadcast channel determines the maximum achievable longterm rates averaged over all fading states. The optimal resource allocation scheme for rates in 3 the ergodic capacity ....

....assume that the fading state 6 has some joint distribution. As the noise density vector incorporates the effects of the channel gain, we will alternatively refer to 6 as the fading state throughout this paper. III. ERGODIC ZERO OUTAGE CAPACITY REGIONS In this section we present results from [4, 5] on the ergodic and zero outage capacity of the fading broadcast channel. A. Ergodic Capacity Region In [4] the ergodic capacity region and optimal power allocation scheme for the fading broadcast channel is found by decomposing the fading channel into a parallel set of constant broadcast ....

[Article contains additional citation context not shown here]

L. Li and A. Goldsmith, "Capacity and optimal resource allocation for fading broadcast channels: Part II: Outage capacity", IEEE Trans. Inform. Theory, vol. 47, pp 1103-1127, March 2001.

....length, i.e. the channel is constant during transmission of a codeword. Two notions of Shannon capacity have been developed for multi user fading channels: ergodic capacity and outage capacity. Ergodic capacity is concerned with achieving long term rates averaged over all fading states [7] 8] [4], while outage capacity achieves a constant rate in all non outage fading states subject to an outage probability [5] 6] Zero outage capacity refers to outage capacity with zero outage probability [9] The ergodic capacity of a fading broadcast channel determines the maximum achievable longterm ....

....capacity refers to outage capacity with zero outage probability [9] The ergodic capacity of a fading broadcast channel determines the maximum achievable longterm rates averaged over all fading states. The optimal resource allocation scheme for rates in 3 the ergodic capacity region is found in [3, 4] and corresponds to multi level water filling over both time (i.e. fading states) and users. As intuition would suggest, users are allocated the most power when their channels are strong, and little, if any, power when their channels are weak. Such an allocation scheme maximizes long term average ....

[Article contains additional citation context not shown here]

L. Li and A. Goldsmith, "Capacity and optimal resource allocation for fading broadcast channels: Part I: Ergodic capacity", IEEE Trans. Inform. Theory, vol. 47, pp 1083-1102, March 2001.

....function. For simplicity, we assume B = 1. In this paper we impose a vector minimum rate constraint R = R 1 ; R 2 ) which specifies rates to be maintained in all fading states, or R j (n) R j ; j = 1; 2, for all n. Clearly, R must be in the zero outage capacity region [3] of the channel in order for the minimum rate conditions to be achievable in all fading states. III. SINGLE USER FADING CHANNEL Before analyzing the broadcast channel, we first find the capacity achieving scheme for a single user fading channel subject to minimum rate constraints. We must find ....

L. Li and A. Goldsmith, "Capacity and optimal resource allocation for fading broadcast channels: Part II: Outage capacity", IEEE Trans. Inform. Theory, March 2001.

No context found.

L. Li and A. Goldsmith, "Capacity and optimal resource allocation for fading broadbacast channels, part I: ergodic capacity," IEEE Trans. Inform. Theory, vol. 47, no. 3, pp. 1083-1102, March 2001.

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L. Li and A. Goldsmith, "Capacity and Optimal Resource Allocation for Fading Broadcast Channels - Part I: Ergodic Capacity," Information Theory, IEEE Transactions, vol. 47, pp. 1083--1102, March 2001.

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