1 Resource allocation for frequency-selective multiple access channels with adaptive QAM modulation Th. Sartenaer, L. Vandendorpe Communications and Remote Sensing Laboratory, Universit´ e catholique de Louvain, Place du Levant, 2 - 1348 Louvain-la-Neuve, Belgium, sartenaer@tele.ucl.ac.be Keywords: Multiple Access, DMT, OFDMA, CDMA, Joint Detection, Powerline Communications. Abstract— This paper addresses the problem of resource allo- cation in a general multiple access scenario. Powers are supposed to be fixed and maximization of the bit rate is put as an objective, with a number of fairness constraints that provide each user with individual bit rates in proportion with their needs. Linear programming algorithms give the solution for the matched filter bound. As soon as the channels are frequency-selective, the use of joint detectors is proposed. An adapted allocation algorithm is given, that implies the update of the joint detector performance for each iteration. A fast update algorithm is also proposed. Results are given for a 5-users powerline access network. I. I NTRODUCTION In multiple access channels, a single physical medium has to be shared by a set of users requesting different bit rates. Whatever the selected multiple access technique, it can be expressed as the partitioning of the available bandwidth into a set of parallel subchannels, defined through their signature waveforms. Orthogonality between each pair of signature waveforms has to be ensured in order to allow easy signal separation at the receiver. This general scenario includes ad- vanced techniques like CAP-CDMA (Carrierless Amplitude- Phase CDMA, where waveforms are codes) and DMT-FDMA (Discrete MultiTone FDMA, where waveforms are tones) [2]. Adaptive modulation is an elegant way to get high spectral efficiency in bandlimited systems: on each subchannel, a QAM (Quadrature Amplitude Modulation) modulation can be used, with a constellation size depending on the available signal to noise ratio at the receiver. If the transmitted power on each subchannel is fixed (which is the case if there is a constraint on the total transmitted power spectral density), the throughput on each subchannel only depends on the channel conditions. Allocation of the waveform set to the user set has a large influence on the resulting system performance. Indeed, different users undergo different channel conditions, depending on their distance from the central office and other relevant parameters. As a given waveform will provide a different contribution to the total system bit rate according to the allocation scheme, a careful selection has to be performed to best match the available resources to the user-specific channels. This throughput maximization has to take into account a number of fairness constraints: indeed, QoS (Quality of Service) requirements of each user have to be fulfilled, and at least one signature waveform has to be allocated to each user. As the bit rates requested by the users are known and can be different, and as the channels can present various kinds of performance, it could seem impossible to meet all these user requirements. A solution to this problem is to choose the size of the waveform set much higher than the number of users. In this scenario, many waveforms can be allocated to each user, and unequal channel performance can be compensated for by the allocation of a different number of waveforms to different users. An alternative solution would make use of variable length signature waveforms (as also investigated in UMTS, the Universal Mobile Telecommunications System), but this is not investigated here. This allocation problem can be reformulated as a linear programming problem that can be solved by standard optimization techniques. If the channels are frequency-selective, orthogonality among the resources is lost and Inter-Symbol Interference (ISI) and Multiple Access Interference (MAI) will arise, which severely degrade the system performance. The size of the QAM constellations not only depends on channel attenuation and additive noise captured by the different waveforms, but also on these inter-waveforms interactions. To ensure acceptable performance, more advanced detectors have to be designed, that will compensate for the channel dispersiveness. Linear and decision-feedback MMSE Joint-Detectors (JD) are in- vestigated, and their influence on the waveform allocation procedure is addressed. An initial allocation scheme is calculated, based on the Matched Filter Bound (MFB). A first JD is computed, along with the corresponding performance (including ISI and MAI). The allocation scheme is then progressively updated in order to meet the fairness constraints between the users. A fast method is proposed to update the JD performance computation at each iteration. Results are proposed in the context of high-speed powerline communications in the access network. II. TRANSMISSION MODEL In this paper, we focus on the baseband transmission of signals from a K u -sized user set towards a common central office. We suppose that a set of K r signature waveforms are available to ensure multiple access. Each user is provided with the ability to modulate any subset of these waveforms. A resource allocation algorithm, located at the central office, will select the appropriate subsets and transmit that information