Generalised link-layer optimisation: Application and performance evaluation Virgilio Rodriguez ComNets, RWTH Aachen, Germany email: rodriguez@comnets.rwth-aachen.de Abstract—A wireless communication system work more efﬁ- ciently if link-layer parameters such as modulation order, symbol rate and packet size are (adaptively) optimised. A common criterion is to maximise spectral efﬁciency subject to a very low bit-error constraint. But for systems equipped with strong error detection and a selective packet re-transmission mechanism, a packet-oriented criterion is more appropriate. Recently we showed that the link conﬁguration that maximises bits per second or bits per Joule can be identiﬁed by drawing a tangent from the origin to the scaled graphs of the corresponding packet- success rate functions: the steeper the tangent the better the conﬁguration. We now consider a tight symbol-rate constraint that forces the terminal to switch its conﬁguration from the ideal as channel quality improves, and report on analytically- grounded performance experiments. A terminal with a ﬂexible and unconstrained symbol rate enjoys a growing and overwhelm- ing performance advantage over a similarly-endowed ﬁxed- rate adaptive terminal. And the rate-ﬂexible terminal retains a signiﬁcant performance edge (up to 2-to-1) even when its symbol rate cannot exceed that of the ﬁxed-rate terminal. I. I NTRODUCTION The importance of (adaptively) optimising the link layer conﬁguration of a wireless communication systems has long been recognised. In particular, modulation adaptation has received signiﬁcant attention [1], [2], [3], [4]. However, in these and most studies, the focus is the symbol: for example, to choose bits per symbol in order to maximise bps/Hertz (spectral efﬁciency), while holding the bit error rate under a speciﬁed (very low) level. More recently, it has been recognised that packet-oriented (OSI layer-2) link adaptation is more appropriate under cer- tain interesting scenarios [5]. For example, in many prac- tical communication networks, medium-access-control (MAC) packets are “guaranteed” in the sense that binary data is packetised, strong error-detecting codes (e.g., 16-bit cyclic- redundancy codes (CRC)) are added to each data packet, and an automated repeat-request (ARQ) mechanism is installed, with a highly reliable the feedback ARQ channel. Since a packet is retransmitted until correctly received, the engineer should focus on the system’s post-retransmission performance (e.g., “goodput”). Along these lines, [5] seeks to (adaptively) conﬁgure the link layer parameters for maximal “goodput”. Building upon [5], [6] utilises analytical geometry to con- clude that a set of possible link conﬁgurations can be evaluated by drawing a tangent line from the origin to the graph of a scaled version of the packet-success rate function corres- ponding to each conﬁguration: the steeper the tangent, the better the conﬁguration. The present work complements [6] by comparing the proposed scheme to alternatives, and explicitly considering that the symbol rate constraint may force operation away from the optimum. Below, we ﬁrst describe our system model. Then, we sketch the technical development in [6]. Subsequently, we further discuss the technical development of [5], and propose modiﬁcations that may improve it. We then report and discuss the results of our experiments, after which we make some concluding remarks. II. SYSTEM MODEL • N 0 is the average Gaussian noise spectral density • E is the energy budget, when applicable • ˆ p is the power constraint • H is the channel gain, and h := H/N 0 • R is the symbol rate • p is the transmission power used • b is the no. of bits per symbol • σ s is the signal-to-noise ratio (SNR) per symbol • L-bit packets carrying L − C information bits are used. • For convenience, let ¯ b := b(L − C)/L • For link parameters, a, F (x; a) is the packet-success rate (PSRF) as function of per-symbol SNR, x. • For some technical reasons, f (x; a) := F (x; a) − F (0; a) replaces F [7], and is assumed to satisfy Deﬁnition II.1, i. e., its graph has the S-shape shown in Fig. 1. E. g., in the notation of [5], f (x; a)=[1 − P b (x, b)] L/b − [1/2] L . For convenience, x is used as a generic function argument. Deﬁnition II.1. S : ℜ + → [0, Y ], is an S-curve with unique inﬂexion at x f if (i) S (0)= 0, S is (ii) continuously differ- entiable, (iii) strictly increasing, (iv) convex over [0, x f ) and concave over (x f , ∞), and (v) surjective (see Figure 1). III. LINK ADAPTATION FOR DATA TRAFFIC A. Information transferred over a period of interest Fact III.1. The total number of information bits that a terminal operating with packet-success rate f (·; a) and SNR held at σ s can transfer over time period τ is given by τR L − C L bf (σ s ; a) ≡ τR ¯ bf (σ s ; a) (1)