Optimal Routing and Power Control for a Single Cell, Dense, Ad Hoc Wireless Network

We consider a dense, ad hoc wireless network, confined to a small region. The wireless network is operated as a single cell, i.e., only one successful transmission is supported at a time. Data packets are sent between sourcedestination pairs by multihop relaying. We assume that nodes self-organise into a multihop network such that all hops are of length d meters, where d is a design parameter. There is a contention based multiaccess scheme, and it is assumed that every node always has data to send, either originated from it or a transit packet (saturation assumption). In this scenario, we seek to maximize a measure of the transport capacity of the network (measured in bit-meters per second) over power controls (in a fading environment) and over the hop distance d, subject to an average power constraint. We first argue that for a dense collection of nodes confined to a small region, single cell operation is efficient for single user decoding transceivers. Then, operating the dense ad hoc wireless network (described above) as a single cell, we study the hop length and power control that maximizes the transport capacity for a given network power constraint.

💡 Research Summary

The paper investigates a dense, ad‑hoc wireless network confined to a small region, where all nodes operate under a single‑cell assumption: at any instant only one transmitter–receiver pair can communicate successfully. Nodes are assumed to be saturated (always have data to send) and to self‑organise so that every hop has the same length d, which is treated as a design variable. The authors adopt a contention‑based MAC (e.g., IEEE 802.11 DCF) with a fixed transmission‑opportunity (TxOP) duration T; after a successful RTS/CTS exchange each transmitter knows the instantaneous fading gain h of its intended link and can adapt its transmit power P(h) for that slot.

The performance metric is transport capacity, defined as the product of aggregate throughput (bits / second) and hop distance (meters), i.e., bit‑meters per second. This metric captures how efficiently data traverses physical space, rather than merely counting bits delivered. The wireless channel is modeled by a distance‑dependent path loss 1/d^η (η is the path‑loss exponent) and a multiplicative fading gain h with a stationary distribution H (pdf a(h), cdf A(h)). The instantaneous Shannon rate is C(h)=W·log₂(1+α·h·P(h)/(σ²·d^η)). Because the TxOP duration T is fixed, the number of bits transmitted in a slot is C(h)·T.

The MAC is abstracted by three probabilities per contention slot: idle (p_i), collision (p_c) and successful transmission (p_s). Under saturation, the average bit rate carried by the system, Θ_T(P(h),d), is given by equation (1) in the paper, which accounts for the payload transmitted in a successful slot and the average time spent in idle, collision and control overhead.

The core optimisation problem is: maximise Θ_T(P(h),d) subject to an average transmit‑power constraint (\bar P_t). Using a Lagrange multiplier λ, the optimal power allocation is derived as a water‑filling (or water‑pouring) solution:

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