CDMA wireless networks, along with a detailed implementation ... We consider wireless mesh networks with nodes located at ..... Cambridge Univ. Press, 2005.
Fast power control for cross-layer optimal resource allocation in DS-CDMA wireless networks Marco Belleschi† , Lapo Balucanti† , Pablo Soldati∗ , Mikael Johansson∗ and Andrea Abrardo† ∗ School
of Electrical Engineering, KTH, SE-10044 Stockholm, Sweden Email: {pablo.soldati | mikael.johansson}@ee.kth.se † University of Siena, Via Roma 56, 53100 Siena, Italy Email: {belleschi | balucanti | abrardo}@dii.unisi.it
Abstract—This paper presents a novel cross-layer design for joint power and end-to-end rate control optimization in DSCDMA wireless networks, along with a detailed implementation and evaluation in the network simulator ns-2. Starting with a network utility maximization formulation of the problem, we derive distributed power control, transport rate and queue management schemes that jointly achieve the optimal network operation. Our solution has several attractive features compared to alternatives: it adheres to the natural time-scale separation between rapid power control updates and slower end-to-end rate adjustments, and uses simplified power control mechanisms with reduced signalling requirements. We argue that these features are critical for a successful real-world implementation. To validate these claims, we present a detailed implementation of a crosslayer adapted networking stack for DS-CSMA ad-hoc networks in ns-2. We describe several critical issues that arise in the implementation, but are typically neglected in the theoretical protocol design, and evaluate the alternatives in extensive simulations.
I. I NTRODUCTION Network utility maximization (NUM) [1], [2] has emerged as a promising framework for the systematic design of networking protocols with performance guarantees. The subject has been widely investigated for almost a decade, covering both layered resource allocation mechanisms (e.g. Internet congestion control [1], [3] and radio resource management [4]) and cross-layer designs which coordinate congestion control with power control, routing, network coding, etc. (see [2] for selected references). While the advances on the theoretical side have been substantial, papers reporting on experience in detailed implementation of NUM-engineered protocols are very scarce, see e.g. [5]. This paper combines new theory development and protocol design with experiences from detailed implementation and evaluation in the network simulator ns-2. We focus on the joint congestion control and radio resource management problem for DS-CDMA wireless networks. The immediate NUM-formulation of this problem is non-convex, and the initial studies used a high-SIR approximation to convexify the problem (examples include [6] for centralized solutions, [4] for distributed protocols). Recently, Papandriopoulos et al. [7] recognized how the original problem, without any approximations, could be transformed to a convex form and distributed mechanisms for congestion control and radio resource management that converges to the optimum network operation could be devised. Although theoretically well-founded, the protocols proposed in [7] present several
implementation challenges. Firstly, the power control mechanisms demand a large amount of signaling overhead, which steals effective bandwidth from the data communication. Secondly, the theory supports end-rate and power-control updates running at the same timescale. In practice, however, power control loops are executed on the millisecond timescale while round-trip times in the transport layer, which dictate the update rates for the congestion control, can be on the scale of seconds. This paper extends our experience on alternative paths for solving the NUM problem [8]. Our theoretical developments separate the operation at PHY/MAC and transport layer while maintaining optimality. The power control subproblem is solved at fast time-scale through a simple distributed mechanism with reduced signalling requirements. We devise two distributed schemes to handle the control signalling and further reduce the traffic overhead, avoiding eventually an explicit message passing. Finally, we present a detailed implementation of a cross-layer adapted protocol stack, including our proposed mechanisms, in the ns-2 simulator. This effort reveals several issues that are neglected in the theoretical protocol design but are critical for the practical implementation. II. T HEORETICAL
SYSTEM MODEL
We consider wireless mesh networks with nodes located at fixed positions. Each node is assumed to have infinite buffering capacity and the ability to transmit, receive and relay data to other nodes over wireless links. We represent the network topology by a directed graph with nodes labelled n = 1, . . . , N and links l = 1, . . . , L. A link is represented by an ordered pair (i, j) of distinct nodes. The presence of link (i, j) means that the network is able to send data from node i to node j. Nodes are assumed to always have data to send to the other nodes, possibly via multi-hop routing. We label the sourcedestination pairs by integers i = 1, . . . , I and let si denote the end-to-end rate for communication between source-destination pair i. Associated with each pair i is a function ui (·), which describes the utility of the pair to communicate at rate si (see [1] for further details). We assume that ui is increasing and strictly concave, with ui → −∞ as si → 0+ . Data is assumed to be routed along a single fixed path. The routing can then be specified by a routing matrix R = [rli ] ∈ RL×I , whose entry rli is 1 if data between pair i is routed across link l, zero otherwise. Letting c = [cl ] denote the vector of transmission
rates, the vector of total traffic across links is given by Rs and the network flow model imposes the following set of constraints on the end-to-end rate vector s Rs c
s0
We consider a CDMA system with nodes equipped with omnidirectional antennas and sharing the same frequency band at the expense of multiple access interference. Preassigned to each link is a matched filter and a CDMA spreading sequence, and we assume perfect self-interference cancellation so that nodes are able to transmit and receive simultaneously. Such assumption is suitable through RF isolators and echocancelers, coupled with base-band digital filtering, see [9] and references therein. Let Glm denote the effective link gain between the transmitter of link m and the receiver of link l (including pathloss, fading, as well as the effects of coding gain, spreading gain and beam-forming, see e.g., [10]), let σl be the thermal noise power at the receiver of link l and Pl be transmission power. The signal to noise and interference ratio of link l is G P P ll l γl (p) = (1) σl + m6=l Glm Pm PL denotes the vector of power where p = P 1 ··· P allocation, and m6=l Glm Pm is the interference experienced at the receiver of link l. We view each link as a single-user Gaussian channel with Shannon capacity cl (p) = W log2 (1 + Kγl (p))
(2)
where W is the system bandwidth and K models the SIR-gap reflecting a specific modulation and coding scheme [11]. In the following, we assume K = 1 for the sake of notation. III. P ROBLEM FORMULATION Our interest is on distributed end-to-end flow control and radio resource management in wireless multi-hop networks. We formulate the problem as one utility maximization (cf. [1]) P P maximize i ui (si ) − ω l Pl (3) subject to Rs c, p, s 0
Unlike [1], the link capacities in (3) are not fixed a priori but depend in a non-trivial way on both the MAC scheme and the allocation of radio resources at PHY layer, resulting into a nonconvex formulation. The optimization (3) aims to maximize the network utility while minimizing the transmitted power, and hence interference. Much like multi-criterion optimization problems, we introduce a fixed weight ω ∈ [0, ∞) to trade these conflicting objectives by a specified amount [7], [12]. An optimal and distributed cross-layer design for PHY and transport layer solving (3) has been proposed in [7]. The solution deals with the general non convex nature of the Shannon capacity in the PHY constraints through an exponential transformation of the variable si ← eesi and e Pl ← ePl and a log-transformation of the PHY constraints. Problem (3) is rewritten in the equivalent form P Pe P si e l maximize i (e ) − ω le i uP (4) si e subject to log r e log cl (epe ) ∀l i li
where the constraint set is now convex. It is argued that the transformed problem (4) is convex if the utility functions are (log, x)-concave over their domain, see [7, Theorem 2]. Utility functions modelling TCP Vegas/Reno, as well as the α − f airness functions, are (log,x)-concave [7]. Under the conditions of [7, Theorem 2], problem (4) can be solved to optimality through standard Lagrange duality, resulting in an iterative algorithm where end-user rate and power control updates run at the same time-scale and exploit a network-wide message passing between two consecutive updates. IV. A PRIMAL DECOMPOSITION APPROACH We have previously investigated alternative paths for solving problem (4) based on primal decomposition techniques [8]. We consider the problem as one in the end-user rates maximize ν(e s) (5) subject to se ∈ Se P e where Se = e s | log( i rli eesi ) ≤ log(cl (epe )), for some p denotes the set of feasible end-to-end user rates, and X ν(e s) = u ei (e si ) − ϕ(e s), (6) i
si e
Here, u ei (e si ) = ui (e ) and ϕ(e s) is the minimum cost in terms of total transmit power for realizing a given e s, i.e. ( ) X e e Pl p ϕ(e s) = min ω e | tl (e s) ≤ log cl (e ) ∀l (7) e p
l
si e and tl (e s) , log models the traffic load per link. i rli e We devise an optimal and distributed protocol design that, for the first time, respects the time-scale separation between the operation at the PHY and networking layers. Let t and k denote the update time at PHY and transport layers respectively. e we rewrite (7) as Physical layer algorithm: Given e s(k) ∈ S, P Pel minimize ω l e (8) subject to tl (e s(k) ) ≤ log(cl (epe )) ∀l P
e and a distributed solution can be Problem (8) is convex in p found via dual decomposition, [8]. Let λ be the Lagrange multipliers for the constraints in (8) and form the Lagrangian X e X L(e p, λ) = ω ePl + λl tl (e s(k) ) − log(cl (epe )) l
l
The corresponding dual function is
g(λ) = inf L(e p, λ) = gp (λ) + e p
X
λl tl (e s(k) )
l
where unconstrained convex minimization problem X e gp (λ) = min ωePl − λl log(cl (epe )) e p
(9)
l
can be solved using equation updates similar to [7], i.e. (t+1)
Pl
(t)
=
ω+
where (t) ∆l
P
∆l
(t)
k6=l
(t)
=
λl
Mk Gkl
(10) (t)
γl (t)
(t)
log(1+γl ) 1+γl
,
(t) Ml
(t)
=
(t) γl ∆l (t) G P ll
l
The dual problem to (8) maximize subject to
g(λ) λ0
(11)
can be solved by the projected gradient iterations n h io+ (t) (t+1) (t) λl = λl + ε tl (e s(k) ) − log cl (epe )
(t+1)
Pl
Unlike [7], here the power and dual variables updates run in parallel until convergence for a fixed rate vector e s(k) . ⋆ (k) Transport layer algorithm: Let now {e p (e s ), λ⋆ (e s(k) )} denote the solution of the RRM subproblem (8) for the given rate vector e s(k) . The solution to problem (5) can be improved using the following gradient ascent iterations (cf. [8]) (k+1)
sei
(k)
= sei
+ ǫ∇i ν(e s(k) ),
∀i
where ν(e s) is defined as in (5) and (k)
∇i ν(e s(k) ) = si
(k)
u′i (si ) −
X l
λ⋆ (e s(k) ) rli Pl (k) j rlj sj
(12)
!
=
γltgt (t) P γl (p(t) ) l
(16)
It is worth mentioning that any alternative power control scheme solving problem (15) may be used to replace (16). ⋆ Let (e p⋆ , λ⋆ ) and (p⋆ , λ(LP) ) denote the optimal primal-dual points for (8) and (15) respectively. The following result holds. Theorem 5.1: The nonlinear power control (8) and the LP formulation (15) are equivalent, i.e. in the sense that Pl⋆ = ⋆ e⋆ ePl ∀l. In addition, λ⋆ and λ(LP) are related as λ⋆l = fl (Pl⋆ , γltgt )λ(LP) l
⋆
∀l
(17)
1+γ tgt
(13)
The end-user rate update placed back to the original space is (k+1) (k) si = si exp ǫ∇i ν(e s(k) ) (14)
The new rate vector is applied to the RRM problem (7) and the procedure is repeated until convergence. Theorem 4.1: Let e s⋆ denote the optimal solution to (5). The gradient iterations produced by (12)-(13) always generate feasible rate vectors, i.e. es(k) ∈ Se ∀k, and lim es(k) = e s⋆ . k→∞ Proof: A detailed proof can be found in [8]. V. A
which can be solved with a distributed power control scheme similar to [13], allowing to replace the power updates (10) with a SIR-based closed-loop power control (CLPC) scheme
LOW SIGNALLING DISTRIBUTED POWER CONTROL
Similarly to [7], the power control (10) relies on networkwide message passing between two consecutive updates. We now demonstrate that in our approach one can replace (10) with a simpler distributed power control scheme a` la Zander [13], which limits the traffic overhead and maintains optimale the constraints in (8) correspond ity. For any fixed e s(k) ∈ S, to require the links’ SIR to exceed a target value, i.e.
where fl (Pl⋆ , γltgt ) = log(1 + γltgt ) γ tgtl Pl⋆ log(2) l Proof: The result follows through direct inspection of the KKT conditions. Details can be found in [8]. A. Limiting the signalling overhead The complete solution to the joint congestion control and resource allocation problem combines the end-user rate update (14) with the distributed power control (16). The optimal ⋆ dual variables λ(LP) for problem (15) are transformed into λ⋆ (e s(k) ) and used to update the source rates. We propose two ⋆ distributed low-signalling schemes to compute λ(LP) . ⋆ 1) Limited messages passing (MP): Let {p⋆ , λ(LP) } denote the optimal primal-dual solution to problem (15). The KKT optimality conditions associated to problem (15) give P ⋆ ⋆ λ(LP) − i6=l λ(LP) Mi(LP) Gil − ω = 0, ∀l i l where (18) tgt (LP) (LP) (LP) γl ∆l = 1 Ml = ∆l Gll ⋆
Therefore, λ(LP) solve a system of linear equations of the ⋆ king A(LP) λ(LP) = 1ω where the system matrix has diagonal (LP) elements A(LP) ll = 1 and off diagonal entries Alj = −Mj Gjl . tl (e s(k) ) ≤ log(cl (epe )) ⇔ γl (p) ≥ γltgt (e s(k) ) ∀l A limited message passing can be used to locally construct the ⋆ (k) P matrix A(LP) at the nodes and find λ(LP) . Compared with [4], [7] tgt (k) W −1 p rlp ese p where γl (e s ) = 2 − 1. For the sake of we observe two main differences. Firstly, Ml(LP) do not depend notation, we will drop the dependence of the SIR target on on SIR measurements, transmit power nor dual variables, e s(k) and we will describe the simplified power control for a but only on the new γ tgt which is immediately available to tgt generic γ vector. We rearrange the previous inequality as the transmitters. Therefore, transmitter-receiver pairs do not X Gli γltgt σl need to communicate extra information to build the messages. tgt tgt γl (p) ≥ γl ⇒ Pl − γl Pi − ≥ 0 ∀l Secondly, as Ml(LP) do not affect the PHY layer but only λ and Gll Gll i6=l the end-user rate update, message passing is required only Let H ∈ RL×L and η ∈ RL be defined as follows sporadically compared to [4], [7] and Ml(LP) can be exchanged # at slow rate while the power control loop attains convergence. " −1, if l = m γltgt σl 2) Fully distributed power control (FD): Alternatively, we H = [hlm ] = η = [ηl ] = γltgt GGlm , if l 6= m Gll ll propose an approach that completely avoids any message passing based on the dual problem to (15) Problem (8) can be reformulated as the linear programming (LP)
minimize subject to
ω1T p Hp −η
p0
(15)
maximize subject to
η T λ(LP) HT λ(LP) −ω1 λ(LP) 0
(19)
We rewrite the inequality constraints explicitly as X Gkl tgt λ(LP) λ(LP) l k − γ ≤1 ω Gkk k ω
∀l
k6=l
We can interpret these constraint as SIR requirements, i.e. γlfc (µ) ,
σl +
µG P l ll σl ≤ γltgt , G µ k6=l kl σk k
∀l
(20)
−1 where µl = λ(LP) , and we reformulate (19) as l ηl ω
maximize ω1T µ subject to γlfc (µ) ≤ γltgt ,
∀l
µ0
j
(21)
For radio cellular systems, the primal-dual problems (15)-(21) can be interpreted in terms of downlink-uplink SIR duality (see, e.g, [14]). More precisely, if problem (15) minimizes the downlink sum-powers subject to SIR constraints, i.e γ dl γ tgt , then the dual variables µ represent the uplink power allocation and the problem (21) maximizes the uplink sumpower subject to maximum SIR requirements, i.e. γ ul γ tgt . In our case, µ represents the power allocation in the feedback control channel used to update the Pl through (16), and can be found through the following distributed iterations (t+1)
µl
(t)
= γltgt γlfc (µ(t) )−1 µl
(22)
⋆
Given µ⋆ , the optimal dual variables λ(LP) can be retrieved as ⋆
λ(LP) = ωµ⋆l ηl−1 l VI. NS-2
A. Transport layer The transport layer implements a TCP variant whose congestion avoidance mechanism is dictated by Equation (14), along with complete mechanisms of acknowledgment (i.e. TCP ACK), packet expiration and retransmissions. The updates are TCP ACK-driven in compliance with the traditional TCP congestion control where the source adjusts its sending rate according to the congestion along the path. Let Λl = λ⋆ (es(k) ) Pl (k) denote the normalized congestion price of link l in
(23)
IMPLEMENTATION
Most theoretical papers on cross-layer design only validate the theory on numerical examples, typically in the Matlab environment. While the conceptual difference between the theoretical studies and reality is small, there is a significant gap between the mathematical descriptions of the derived mechanisms and their real-world implementation. This gap comprises the impact of signalling, protocol dynamics, wireless propagation (the effect of interference, fading and losses) as well as the precise behaviour of the communication layers (queueing, adaptive modulation and coding, acknowledgements, etc.). All these issues could potentially result in significantly reduced spectral efficiency, and it is hard to isolate the most critical components without going all the way to a detailed implementation and evaluation. Thus, a significant contribution of this paper is to describe a detailed implementation of our proposed mechanisms in the network simulator ns-2. To this end, we have implemented a relatively complete cross-layer adapted protocol stack in ns-2. The proposed solution both respects the hierarchical layers-based architecture and let the different layers cooperate as in the spirit of crosslayer design. The stack includes modified data link, network and transport layers and allows asynchronous transmissions, power and rate updates at each node. The stack is publically available upon request from the authors.
rlj sj
Equation (14). These quantities are aggregated along the path and stored in a reserved field within the TCP acknowledgment. Specifically, each intermediate node in the reverse path adds Λl into the reserved field. Once the source retrieves the acknowledgment, the ideal rate update si in (14) expressed in bit/sec Ti is performed. We then calculate the window wi = ⌈ si ×RT ⌉ SZi expressed in units of packets, where RT Ti is the last round trip time experienced and SZi the size of TCP packets. Packet losses (both data and TCP ACK) determine a delay in the rate update and are usually neglected in the theoretical design. B. Network layer The network layer comprises queueing mechanisms and routing. The queueing policy allows parallel transmissions over multiple links at each node in compliance with the DSCDMA based data-link layer. Each node buffers packets in per-destination queues, and selects the next queue to be served in a round robin fashion. This strategy avoids starvation when a node has multiple flows with large discrepancies in the RTT. Since the routing is not included in the optimization framework, we maintain it static and assume the routing tables to be fixed. In alternative, nodes can support any ns-2 module for dynamic routing such as AODV or DSDV. C. Data-link layer Since the underlying theory assumes a DS-CDMA access scheme, the basic ns-2 environment has been extended to incorporate a novel DS-CDMA module. The module assigns different spreading sequences to each logical link, allowing pointto-multipoint transmissions at each node. The module also implements acknowledgment mechanisms (i.e. MAC ACK), packet expiration and retransmissions, as well as MAC ACKdriven transmissions. Each node handles the enqueue/dequeue routines independently without synchronization. The system bandwidth W is shared by a direct channel, used to send data packets and acknowledgments (i.e. TCP ACK and MAC ACK), and a control channel, exclusively used for power control (see Section VI-D for details). The received signals are subject to multiple access interference. All the packets, regardless their type, cause interference in their respective channel and can be subject to losses. Unlike the theoretical scenario, the waste of the bandwidth for the acknowledgments, the delay due to packet losses, the additional interference caused by acknowledgments and retransmissions degrade the network efficiency in terms of utility. We next describe in details the distributed SIR-based CLPC scheme combined with cross-layer signalling mechanisms proposed in Section V.
(a) Total utility. Fig. 2.
(b) Transmission powers.
(a) Total utility. Fig. 3.
Fig. 1.
(c) Experienced end-to-end rates.
Performance evaluation of the distributed cross-layer design with FD-CLPC scheme.
(b) Transmission powers.
(c) Experienced end-to-end rates.
Performance evaluation of the distributed cross-layer design with MP-CLPC scheme.
Linear network topology.
D. Power control implementation In the ns-2 implementation of the CLPC scheme (16), the receivers track the SIR variations and feedback a power control command (PCC) to the intended transmitters through a dedicated control channel (DCC). The DCC is organized in mini-slots of duration T = LPRCC , where LP CC is the number c of bits of PCC commands and Rc is a fixed bit rate. Choosing the appropriate LP CC is crucial. Ideally, the PCC commands should carry the exact ratio between the experienced SIR and the desired target requiring LP CC → ∞. In practice, efficient schemes using a quantized ratio can be designed with only few bits (e.g., see[15]). We propose to use LP CC = 10 bits assuming that such a value allows to get an ideal PCC. To avoid interference, direct (d) and control (c) transmissions occur at different frequencies sharing the system bandwidth W , i.e. two separate bandwidths Wc and Wd = W −Wc are dedicated to the control and direct channels respectively. Different spreading sequences Sd and Sc are assigned to each direct/control link pair. Specifically, to have a stronger protection against noise and interference in the control channel, we set Sc = 4Sd so that no losses of mini-slots can occur. Hence, considering a QPSK modulation without link adaptation, we obtain Rc = 2Wc /Sc . To make the power control effective, the PCC commands must be received with minimum delay. Since
transmitters and receivers are often very close, the propagation delay can be neglected, so that the power control loop delay D mainly depends on the SIR measurement time and the duration T of a PCC command. The estimated SIR is obtained by averaging instantaneous SIRs over the duration of a mini-slot (i.e. ideal interleaving). While measuring the SIR, the receivers transmit the PCC relative to the previous slot, making the ×Sc total loop delay D ≃ 2T , or equivalently D ≃ LP CC . Wc The fast CLPC allows to mitigate both the effect of additional interference and the near-far problem satisfying the required SIR target. Both MP-CLPC and FD-CLPC mechanisms exploit the framework described above. However, while the FD-CLPC scheme implements power control in the DCC channel, the MP-CLPC scheme transmits at fixed power in the DCC. VII. S IMULATION This section presents detailed simulation of our distributed cross-layer design. To achieve proportional fairness we will assume logarithmic utility functions throughout. We adopt a bandwidth Wd = 1MHz in the direct channel which gives 125KHz baseband after employing a spreading gain Sd = 8. A bandwidth of Wc = 50KHz is dedicated to the control channel with Sc = 32, giving T = 3.2ms, i.e. D ≃ 6.4ms. We assume a path loss attenuation factor δ = 4 and a thermal noise power σ = 10−10 W for all links. We somewhat arbitrarily select ω = 1 in the NUM formulation and model the SIR gap K = −1.5/ log(5BER) with bit error rate BER = 10−3 corresponding to MQAM modulation [11]. We consider that the combination of MQAM with an ideal channel coding permits to achieve an effective BER → 0. Packets are acknowledged at RACK = 40Kb/s and PACK = 10mW. In
TRAFFIC OVERHEAD [%]
35 30
Algorithm in [7] MP−CLPC FD−CLPC
25 20 15 10 5 0 1x5
2x5
3x5
4x5
5x5
Grid Topology
Fig. 4.
Utility evolution for FD-CLPC and MP-CLPC in a 5 × 5 grid.
the following figures, values are printed every 0.5s. A. System validation and performance analysis Similarly to [7], we validate our protocols on a 5-node linear network topology with nodes separated 100m apart, see Figure 1. We analyze the evolution of total utility, transit powers and the experienced end-to-end rates for the two variants FDCLPC and MP-CLPC of the distributed cross-layer design, see Figures 2(a) to 2(c) Figures 3(a) to 3(c) respectively. The optimal network operation is obtained solving off-line problem (4) in the Matlab environment. Both FD-CLPC and MP-CLPC converge to the theoretical optimal operation point under idealized conditions, i.e. instantaneous and non-interfering packet acknowledgements, no packet losses or retransmissions, ideal DCC (Wd = W ) and perfect SIR measurements (for FD) and message passing (for MP). Removing these ideal assumptions, we observe a performance loss of approximately 4% for both schemes. Comparing Figures 2(b) and 3(b), higher power fluctuations appear in the MP mechanism due to the extra interference of the message passing, however the fast CLPC algorithm can still track and mitigate the additional interference. Similar convergence properties and performance loss can be observed in Figure 4 for a 5 × 5 grid topology. B. Overhead evaluation We evaluate the traffic overhead in terms of ratio (expressed in units of bytes) between the amount of messages and data packets required by MP-CLPC, FD-CLPC and the solution alternative [7] to converge. The size of the messages Ml and data packets is 64bytes and 1000bytes respectively. Figure 5 shows the percentage of traffic overhead due to explicit signalling for different network sizes. While the FD-CLPC does not require any network-wide message passing, the MP-CLPC variant drastically reduces the traffic overhead compared to solution alternative [7] as the network size increases. VIII. C ONCLUSIONS We have presented a distributed cross-layer design for joint power and end-to-end rate control optimization in DS-CDMA wireless networks. We derived distributed and efficient power control, transport rate and queue management schemes that jointly optimize the network operation. Our solution adheres to the natural time-scale separation between rapid power control
Fig. 5.
Traffic overhead for different algorithms in grid topologies.
updates and slower end-to-end rate adjustments, and exploits simplified power control scheme with reduced signalling requirements. Finally, we proposed two distributed mechanisms to handle the cross-layer signalling. We argued that their features are critical for a successful real-world implementation, and presented a detailed implementation in the ns-2 simulator to validate our claims. We isolated and described several critical issues that arise in the implementation, but are typically neglected in the theoretical protocol design. Although at this stage we did not consider fading, the fast power control is known to be able to efficiently track time-varying channels. However, the impact on fading on system-level performance is left for future studies. R EFERENCES [1] F. P. Kelly, A. K. Maulloo, and D. K. H. Tan. Rate control for communication networks: shadow prices, proportional fairness and stability. Journal of the Oper. Res. Soc., 49(3):237–252, March 1998. [2] M. Chiang, S. H. Low, A. R.Calderbank, and J. C. Doyle. Layering as optimization decomposition: A mathematical theory of network architectures. Proc. IEEE, 95(1):255–312, 2007. [3] S. Low and D. E. Lapsley. Optimization flow control I: basic algorithm and convergence. IEEE Trans. on Networking, 7:861–874, 1999. [4] M. Chiang. Balancing transport and physical layers in wireless multihop networks: jointly optimal congestion control and power control. IEEE Journal on Sel. Areas in Comm., 23(1):104–116, January 2005. [5] V. A. Slavin, M. Wittie, and M. Andrews. Mobile ad hoc networks (MANET) protocols evaluation framework. In IEEE MILCOM, Orlando, FL, October 2007. [6] M. Johansson, L. Xiao, and S. Boyd. Simultaneous routing and power allocation in CDMA wireless data networks. In IEEE ICC, May 2003. [7] J. Papandriopoulos, S. Dey, and J. Evans. Optimal and distributed protocols for cross-layer design of physical and transport layers in MANETs. IEEE Transactions on Networking, 2006. (submitted). [8] P. Soldati and M. Johansson. An optimal and distributed cross-layer design with time-scale separation in MANETs. Technical Report TRITA-EE 2009:008, Royal Institute of Technology KTH, Stockholm, Sweden, February 2009. [9] S. Chen, M. A. Beach, and J. P. McGeehan. Division-free duplex for wireless applications. Electronics Letters, 34(2):147–148, January 1998. [10] S. Toumpis and A. Goldsmith. Capacity region of wireless ad hoc networks. IEEE Trans. on Wireless Comm., 2(4):736–748, July 2002. [11] A. Goldsmith. Wireless Communications. Cambridge Univ. Press, 2005. [12] S. Boyd and L. Vandenberghe. Convex optimization. Cambridge Univ. Press, 2004. [13] J. Zander. Distributed cochannel interference control in cellular radio systems. IEEE Trans. on Vehic. Tech., 41(3):305 – 311, August 1992. [14] M. Codreanu, A. T¨olli, M. Juntti, and M. Latva-Aho. Uplink-downlink SINR duality via Lagrange duality. In IEEE WCNC, March 2008. [15] A. Abrardo, G. Giambene, and D. Sennati. Optimization of power control parameters for DS-CDMA cellular systems. IEEE Transactions on Communications, 49(8), August 2001.
