Minimizing Wireless Connection BER through the Dynamic Distribution of Budgeted Power

 
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  Minimizing Wireless Connection BER through the
      Dynamic Distribution of Budgeted Power
                 Bilal Khan∗            Ghassen Ben Brahim†                  Ala Al-Fuqaha†            Mohsen Guizani†

   Abstract— We develop a new dynamic scheme which contin-                  In this paper, we will not consider mobility-related issues.
uously redistributes a fixed power budget among the wireless                Although our investigation makes the simplifying assumption
nodes participating in a multi-hop wireless connection, with the            of a scenario in which mobility does not greatly impact power
objective of minimizing the end-to-end wireless connection bit
error rate (BER). We compare the efficacy of our scheme with                allocation decisions, the conclusions we present are neverthe-
two static schemes: one that distributes power uniformly, and               less significant in the broader context of power management
one that distributes it proportionally to the square of inter-hop           in wireless and ad-hoc networks.
distances. In our experiments we observed that the dynamic                     The remainder of the paper is organized as follows. We
allocation scheme achieved superior performance, reducing BER               begin in Section II with an exposition of prior related research
by using its ability to distribute the power budget. We quantified
the sensitivity of this performance improvement to various envi-            work. Then, in Sections III and IV we define the problem and
ronmental parameters, including power budget size, geographic               the presumed network model. In Section V, we describe the
distance, and the number of hops.                                           protocol by which power is redistributed dynamically, to attain
   Index Terms— wireless ad-hoc networks, multi-hop path, bit               minimum BER. In Section VI we describe the experimental
error rate, power budget, optimal power distribution.                       setup, and then analyze the results of the simulation study in
                                                                            Section VII, by comparing the proposed protocol against other
                                                                            traditional power distribution schemes.
                         I. I NTRODUCTION
   New distributed computing/communication applications
drive the energy requirements of wireless ad-hoc systems                                         II. R ELATED W ORK
ever upwards, while simultaneously, the batteries which power                  Approaches for efficient power management have been
wireless devices present a hard constraints on the operation of             investigated at various protocol layers by several researchers,
mobile computing systems. Recent developments in devices                    (e.g. see [14], [13], [4]) 1. At the Physical layer: Using
with tunable transmission power enable us to manage the                     directional antennae, applying knowledge of spatial neighbor-
tension of power supply and power demand using dynamic                      hood as a hint in setting transmission power; 2. At the Data-
power redistribution schemes. In this paper, we present results             link layer: Avoiding unnecessary retransmissions, avoiding
of recent investigations along this avenue. Our objective is to             collisions in channel access whenever possible, allocating
optimize the bit error rate (BER) of connections—and hence                  contiguous slots for transmission and reception whenever pos-
the packet-level error rate (PER) experienced at the network                sible; 3. At the Network layer: Considering route-relay load,
layer. Since many applications require a minimal Quality of                 considering battery life in route selection, reducing frequency
Service (QoS) to guarantee acceptable responsiveness, such an               of control messages, optimizing size of control headers, route
improvement can greatly benefit network function.                           reconfiguration; 4. At the Transport layer: Avoiding repeated
   Historically, reconciling the gap between power consump-                 retransmissions, handling packet loss in a localized manner,
tion and supply involved [14] solving the following issues: (i)             using power-efficient error control schemes.
improving the power efficiency in the system; and (ii) prevent-                One broad category of solutions consists of energy aware
ing the system deconstruction due to unfair power usage. In                 routing protocols (e.g. see [13], [6], [8]). In wired networks,
our earlier work [2], [3], we proposed addressing these issues              the emphasis has traditionally been on maximizing end-to-end
through the principle of optimal allocation of budgeted power;              throughput and minimizing delay. To maximize the lifetime
we introduced a model in which every connection request is                  of mobile hosts, however, routing algorithms must select the
assigned a fixed power budget to support its instantiation.                 best path from the viewpoint of power constraints and route
In this paper, we present a scheme which dynamizes these                    stability. Routes requiring lower levels of power transmission
approaches by enabling the redistribution of a power budget                 are generally preferred, but this can adversely affect end-to-
among the constituent nodes in a multi-hop connection, with                 end throughput. Transmission with higher power increases the
the objective of minimizing the wireless connection BER.                    probability of successful transmission, although high power
   Standard models of wireless ad-hoc networks typically con-               strategies also result in more cross-node interference, destroy
sider infrastructure-less networks in which every node assumes              existing transmission bands, and thus cause the network to
the role of both a host and router, and every node is mobile.               have blocked connections. In [5] and [1], Banerjee and Misra
                                                                            showed that energy-aware routing algorithms that are solely
  † Western Michigan University, MI.
  ∗ John Jay College of Criminal Justice, City University of New York, NY   based on the energy spent in a single transmission are not
10019.                                                                      able to find minimum energy paths for end-to-end reliable
packet transmissions, in both End-to-End and Hop-by-Hop             received by node j is given by
retransmission settings.                                                                             Pt (i)
   Our own prior work [3] was a natural extension of Misra                             Prcv (j) =            ,                    (1)
                                                                                                    c × dα
[1] and Banerjee [5], reframed by normalizing experimental                                                ij

scenarios using a fixed power budgets for each connection.          where dij is the distance between nodes i and j. α and c are
In [2], we presented an experimental evaluation of those            both constant, and usually 2 ≤ α ≤ 4 (See [5]). In order to
techniques, showing how data replication along multiple paths       correctly decode the signal at the receiver side, it is required
can be used to lower packet error rate of application layer         that
connections in wireless ad-hoc networks under power budget
                                                                                        P (j) > β0 × N0 ,                         (2)
constraints.
   This work begins at the point where energy aware routing         where β0 is the required signal to noise ratio (SNR) and N0
ends. Here we propose a new dynamic scheme that con-                is the strength of the ambient noise. We denote the minimum
tinuously redistributes the power budget among all nodes            signal power at which node i is able to decode the received
across a multi-hop wireless connection with the objective of        signal as Pmin .
minimizing the wireless connection BER.                                Each link (i, j) has a computable bit error rate BER(i, j),
                                                                    which represents the probability of the occurrence of an
                                                                    error during the data transfer over that link. The relationship
                 III. P ROBLEM D EFINITION
                                                                    between the bit error rate BER over a wireless channel and
   Consider a single connection request between a source node       the received power level Prcv is a function of the modulation
s and a destination node t, and assume that a transmission          scheme. It can be expressed in general as follows [5].
power budget P has been specified for this connection. The                                          s           !
question to be answered is how should P be distributed among                                          Prcv Cte
                                                                                     BER ∝ Q                      ,             (3)
intermediate nodes of the connection if the objective is to                                           f Pnoise
minimize the end-to-end connection bit error rate? We shall
                                                                    where Pnoise is the noise spectral density, f is the raw channel
assume, as assumed in other similar investigations (e.g. [11]),
                                                                    bit error rate, and Q(x) is defined as follows.
that each node has the ability to send with dynamically tunable
                                                                                                    2 x −t2
                                                                                                     Z
transmission power, and that node mobility is insignificant                            Q(x) = 1 −         e     dt.              (4)
when compared to routing convergence times. The proposed                                           π 0
dynamic power distribution protocol is implemented on top of           Since we are only interested in studying the general depen-
a routing protocol that is responsible for providing a multi-hop    dence of the bit error rate on the received signal power, we
path between s and t, within total power budget constraints—        will consider the non coherent binary orthogonal Frequency
designing such an energy-aware routing protocol is beyond the       Shift Keying (FSK) modulation scheme. Other modulation
scope of this paper.                                                schemes can be analyzed in similar way, however closed-
   Our design idea is founded on the simple observation that        form analysis may not be always possible. For this specific
in a multi-hop path the distance between two consecutive            modulation scheme, the instantaneous channel bit error rate
intermediate nodes varies on a hop-by-hop basis. For nodes          BER is given by [9], [10], [7] to be:
which are a short distance from each other, less power can be
                                                                                                 1 − 2PPrcv
allocated while still attaining good channel bit error rate. When                         BER =    e    noise                    (5)
                                                                                                 2
two consecutive nodes are far from each other, a weak trans-
mission power would result in a high wireless channel bit error       A path consisting
                                                                                      Qrof a sequence of links L1 , . . . , Lr has a
rate. We present a dynamic power redistribution scheme based        BER equal to 1 − `=1 1 − BER(L` )
on geographical distance, which allows nodes to negotiate the
amount of power they use (while remaining within connection                             V. DYNAMIC S CHEME
budget constraints) thereby optimizing overall connection bit          The proposed protocol operates on all (overlapping) consec-
error rate.                                                         utive triplets of nodes within the connection (s, t). Within each
                                                                    triplet, we denote the nodes to as the upstream node, the central
                                                                    node, and the downstream node. This naming convention is
                   IV. N ETWORK M ODEL
                                                                    illustrated in Figure 1.
   We consider a wireless ad-hoc network consisting of N               A node enters the protocol by simultaneously sending
nodes equipped with omni-directional antennas that can dy-          an Update message to its upstream and downstream neigh-
namically adjust their transmission power. We model this            bors. The Update message describes its present transmission
network as a linear geometric graph G = (V, E), where V             strength. A node receiving an update uses its contents and the
is the set of nodes and E is the set of edges. Each node is         actual received signal strength to deduce an estimate of the
assigned a unique ID i in {1, . . . , |V |}, and node i can send    distance to the sender of the Update. Thus each node (viewed
data with a dynamically tunable transmission power in the           in its central role) maintains estimates of distance to upstream
range [0, Pmax (i)].                                                and downstream nodes. When the central node receives an
   Wireless propagation suffers severe attenuation [5] and [12].    update message informing it of the transmission power and
If node i transmits with power P (i), the power of the signal       (implicitly) distance to a neighbor, it determines the optimal
Upstream   Central   Downstream
                                                                                Upstream Node                            Central Node                  Downstream Node
                  node      node        node

                                                                                                                                                                         Update from neighbors
                                                                         Get Initial
                                                                                                  Get Initial Signal                     Get Initial Signal
                                                                       Signal Power
                                                                                                  Power strength                         Power strength
                                                                         strength

         s                                                                                        Update message                        Update message
                                                        t

                                                                                                   (1) Estimate the
                                                                                                    distance to the
                                                                                                    upstream and
                                                                                                downstream nodes
                 Fig. 1.   Multi-hop path description                                             (2) Compute best

                                                                                                                                                                          Pow er distribution negotiation
                                                                                                   power allocation
                                                                                                between central and
                                                                                                   upstream nodes
                                                                                                  (3) if a significant

redistribution of power between itself and the upstream node.                                    change is required
                                                                                                          then:

This local optimization is computed on the basis of the analytic
BER model presented in the previous section. In effect the                                       Decrease transmit
                                                                                                   signal power

central node acts greedily to minimize the BER of the two
                                                                                            Power Transfer Message
hop sub-path from its upstream node to the downstream node.
                                                                         Increase
If the local optimization shows that a significant redistribution         transmit
                                                                       signal power
of power is required, and this redistribution will not cause                                         Ack message

                                                                                                                                                                          Update to neighbors
                                                                                                                                         Update Message
                                                                              Update
the received signal strength to drop below Pmin at any node,                 message                                                        Update local
                                                                                                                                             information
then the central node is able push power downstream (Figure                                                                                about neighbor

2) or push power upstream (Figure 3). It accomplishes this
by Power Request and Power Transfer messages, respectively.
Receipt of a Power Request always causes a node to reduce its                 Fig. 2.     Event sequence diagram: pushing power upstream
transmission power and reply with a Power Transfer Message.
Receipt of a Power Transfer Message always causes a node to
increase its transmission power and reply with a Ack Message.       two end points. During the experiment, all network parameters
Receipt of Ack and Update Messages always result in further         involved in the system are kept in the following ranges:
propagation of an Update Message. The power reallocation               • Path Length: We consider path lengths ranging from short
process is negotiated concurrently between all (overlapping)             (5 intermediate nodes) to long (25 intermediate nodes).
triplets of nodes via a distributed protocol. The protocol is          • Power budget: We consider connection power budgets
said to have converged if the total power exchange drop below            ranging from small (1 Watt) to large (10 Watts).
a user specified threshold. In the rest of this paper, we will         • Distance: We consider scenarios in which the two end-
refer to the converged distribution attained by this distributed         points range from nearby (100m) to distant (400m).
protocol as the Dynamic scheme. We compare the performance             • α: A scaling constant is kept fixed at 2, as appropriate to
of the dynamic protocol against two static schemes.                      our connection scales.
                                                                       • SN R: The Signal to Noise Ratio of the wireless channel
                                                                         is kept fixed at 1mW, as appropriate to a typical SN R
A. Uniform Scheme
                                                                         value for wireless channel.
   Given a connection between nodes s and t with length
                                                                       The graphs in the next section depict the average values
k + 1 hops and a total power budget P . The uniform power
                                                                    collected from 104 trial runs of each experiment scenario.
distribution scheme consists of allocating to each of the k
                                                                    We demonstrate how protocol optimally distributes this budget
nodes (excluding the destination node) a uniform fraction of
                                                                    among the nodes of the multi-hop path under consideration.
the total power Punif = Pk .

                                                                                           VII. R ESULTS AND A NALYSIS
B. Sqr Scheme
                                                                       To begin, we study the impact of the variance in inter-node
   Under this power distribution scheme, the power is allocated
                                                                    distances on the improvement (in connection BER) achieved
based on the square of the distance to the next hop along
                                                                    by the Dynamic scheme when compared to the Uniform
the path towards the destination node. Specifically, given a
                                                                    scheme. Intuitively, one might expect that in a high variance
connection between nodes s and t with length N − 1 hops
                                                                    scenario the dynamic power distribution would outperform
and a total power budget P, each node     j will be allocated a
                                    PN −1                           uniform allocation of power, because the negotiation process
power Psqr such that Psqr = P d2j / i=1 d2i , where dj is the
                                                                    would converge to a significantly different power distribution.
distance from node j to node j + 1 along the path.
                                                                    However, Figure 4 shows that the effects are more subtle and
                                                                    cannot be captured by a single parameter of variance. For
                 VI. E XPERIMENTAL S ETUP                           instance, for a variance value of 37m, the improvement varies
  In our simulations, we consider networks where the inter-         from 4% to 24%. Similarly, when the variance is small (say
mediate nodes are randomly distributed along a line between         7m), the improvement varies from 3% to 17%. We conclude
Upstream Node                               Central Node                   Downstream Node                                                                                  Power Distribution Scheme Efficacy
                                                                                                                                                                                 50
                                                                                                                                                                                                                       Dynamic/Sqr
                                                                                                                                                                                                                    Dynamic/Uniform

                                                                                                                   Update from neighbors
    Get Initial
  Signal Power
                                       Get Initial Signal                       Get Initial Signal                                                                               40                                     Sqr/Uniform
                                       Power strength                           Power strength

                                                                                                                                                        Percentage Improvement
    strength

                                                                                                                                                                                 30
                                                                                Update message
                                      Update message
                                                                                                                                                                                 20

                                                                                                                                                                                 10
                                        (1) Estimate the
                                         distance to the
                                         upstream and                                                                                                                             0
                                     downstream nodes
                                    (2) Compute the best
                                        power allocation
                                                                                                                                                                                 -10
                                    between the upstream

                                                                                                                    Power distribution negotiation
                                   and downstream nodes
                                       (3) If a significant
                                                                                                                                                                                 -20
                                      change is required                                                                                                                           1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
                                               then:
                                                                                                                                                                                                       Power (mW)
                                    Power Request Message
                                                                                                                                                         Fig. 5.                       Percentage improvement vs. total connection power budget
     Decrease
      transmit
   signal power
                                    Power Transfer Message
                                                                                                                                                     conducted at that power setting. Similarly, the curve indicates
                                           Increase transmit
                                                 power                                                                                               that with a 5W power budget, Sqr performed almost 20%
                                                                                                                    U pdate to neighbors

                                                                                Update Message
                 Update
                Message
                                               Ack                                                                                                   worse than Uniform.
                                                                                      Update local
                                                                                       information                                                      Figure 5 illustrates the impact of the power budget on the
                                                                                     about neighbor
                                                                                                                                                     performance of each power allocation scheme. The distance
                                                                                                                                                     between endpoints was fixed at 120m, and the number of
                Fig. 3.          Event sequence diagram: drawing power downstream
                                                                                                                                                     intermediate nodes was fixed at 9—thus the average internode
                                                                                                                                                     spacing was approximately 12m, in the range of present
                25
                                                                                                path length = 5
                                                                                                                                                     54M b/s wireless technology. Considering the slopes of these
                                                                                                                                                     curves we conclude that the improvement of the Dynamic
                                                                                                                                                     scheme relative to the Uniform and the Sqr schemes increases
                20
                                                                                                                                                     as the total connection power budget increases. For example,
                                                                                                                                                     comparing Dynamic to Sqr, we see that at 1W power budget
                15                                                                                                                                   Dynamic outperforms Sqr by 8% in terms of BER, while by
  improvement

                                                                                                                                                     9W the improvement rises to 40%. We note, however, that
                10
                                                                                                                                                     the relative performance of Uniform and Sqr schemes is not
                                                                                                                                                     monotone: when the power budget is small, the Sqr scheme
                                                                                                                                                     outperforms the Uniform approach, but as the power budget
                 5
                                                                                                                                                     increases to 10W , the conclusion is reversed. Comparing the
                                                                                                                                                     heights of the curves, we conclude that the proposed dynamic
                 0
                     0       5        10        15          20        25        30         35         40      45   50
                                                                                                                                                     scheme outperforms both of the other power allocation tech-
                                                                   variance                                                                          niques in both fair and good wireless channel conditions.
                                                                                                                                                        Figure 6 illustrates the impact of varying the distance
 Fig. 4.                 Percentage improvement of Dynamic over Uniform vs. variance
                                                                                                                                                     between the connection end points, while keeping constant
                                                                                                                                                     both the number of intermediate hops and the total power
that the performance of the dynamic scheme is not well-                                                                                              budget. The connection power budget was fixed at 2200mW ,
modeled by a coarse measure such as variance.                                                                                                        and the number of intermediate nodes was fixed at 10—
    We compare the performance of our Dynamic scheme with                                                                                            thus the average node transmission power was approximately
both the Uniform and the Sqr schemes. For each of these                                                                                              220mW , in the range of present 54M b/s wireless technology.
schemes, we study the impact of considering different path                                                                                           Considering the slopes of these curves we conclude that the
lengths, connection power budgets, and end point distance.                                                                                           improvement of the Dynamic scheme relative to the Uniform
The legends of each curve indicate the average relative per-                                                                                         and the Sqr schemes decreases as the total distance increases.
formance of two schemes. For example in Figure 5, the curve                                                                                          For example, comparing Dynamic to Sqr, we see that at 100m
titled Dynamic/Sqr shows the average value of the quantity                                                                                           distance Dynamic outperforms Sqr by 16% in terms of BER,
                                                                                                                                                     but at 200m the improvement drops to 3%. We note, however,
                                  BER(Sqr) − BER(Dynamic)
                                                          .                                                                                          that the relative performance of Uniform and Sqr schemes
                                         BER(Sqr)                                                                                                    is not monotone: The lower curve of Figure 6 reaches a
The fact that this curve passes through the point                                                                                                    local minimum at distance 110m. At connection distances
(8000mW, 40%) indicates that when the power budget                                                                                                   below this critical value, the improvement of Uniform over
was 8W , the BER achieved by Dynamic was (on average)                                                                                                Sqr decreases as the distance increase, but this behavior gets
40% lower than what was achieved by Sqr, over the 104 trials                                                                                         reversed for distances bigger than 110m. By comparing the
Power Distribution Scheme Efficacy                         VIII. C ONCLUSION AND F UTURE W ORK
                              60                                                                   In all the experiments, the dynamic allocation scheme
                                                                      Dynamic/Sqr
                              50                                   Dynamic/Uniform              achieved superior performance relative to the uniform and
                                                                       Sqr/Uniform
   Percentage Improvement

                              40                                                                distance-squared proportional schemes. This improvement re-
                                                                                                sulted from the dynamic scheme ability to reduce the BER by
                              30
                                                                                                dynamically allocating the power budget among the interme-
                              20                                                                diate nodes.
                              10                                                                   In all the experiments conducted, the proposed scheme was
                               0                                                                seen to converge in fewer than 10 iterations per node. The
                                                                                                convergence rates and communication overhead was tunable
                             -10
                                                                                                by adjusting the definition of “significant change” in the
                             -20                                                                protocol. Because we were not considering mobility, this
                                   50         100        150        200         250       300
                                                        Distance (meters)                       cost was taken as the one-time initialization cost for the
                                                                                                connection. In future, we intend to extend our consideration to
                            Fig. 6.     Percentage improvement vs. total connection distance    the fully mobile setting. Because our power allocation protocol
                                                                                                is decentralized and dynamic, it can react to node mobility by
                                                Power Distribution Scheme Efficacy
                                                                                                redistributing power in a manner which optimizes the BER. To
                              20                                                                evaluate the efficacy of the protocol in the mobile setting, we
                                                                      Dynamic/Sqr               are presently conducting experiments to quantify the tradeoffs
                              15                                   Dynamic/Uniform
                                                                       Sqr/Uniform              between convergence thresholds, control-traffic overhead, and
   Percentage Improvement

                              10                                                                resultant improvement in BER.
                               5

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