This paper is focused on the cross-layer design problem of joint multiuser detection and power control for energy-efficiency optimization in a wireless data network through a game-theoretic approach. Building on work of Meshkati, et al., wherein the tools of game-theory are used in order to achieve energy-efficiency in a simple synchronous code division multiple access system, system asynchronism, the use of bandlimited chip-pulses, and the multipath distortion induced by the wireless channel are explicitly incorporated into the analysis. Several non-cooperative games are proposed wherein users may vary their transmit power and their uplink receiver in order to maximize their utility, which is defined here as the ratio of data throughput to transmit power. In particular, the case in which a linear multiuser detector is adopted at the receiver is considered first, and then, the more challenging case in which non-linear decision feedback multiuser detectors are employed is considered. The proposed games are shown to admit a unique Nash equilibrium point, while simulation results show the effectiveness of the proposed solutions, as well as that the use of a decision-feedback multiuser receiver brings remarkable performance improvements.
Deep Dive into Power control and receiver design for energy efficiency in multipath CDMA channels with bandlimited waveforms.
This paper is focused on the cross-layer design problem of joint multiuser detection and power control for energy-efficiency optimization in a wireless data network through a game-theoretic approach. Building on work of Meshkati, et al., wherein the tools of game-theory are used in order to achieve energy-efficiency in a simple synchronous code division multiple access system, system asynchronism, the use of bandlimited chip-pulses, and the multipath distortion induced by the wireless channel are explicitly incorporated into the analysis. Several non-cooperative games are proposed wherein users may vary their transmit power and their uplink receiver in order to maximize their utility, which is defined here as the ratio of data throughput to transmit power. In particular, the case in which a linear multiuser detector is adopted at the receiver is considered first, and then, the more challenging case in which non-linear decision feedback multiuser detectors are employed is considered. Th
Game theory [1] is a branch of mathematics that has been applied primarily to social science and economics to study the interactions among several autonomous subjects with contrasting interests. Recently, it has been discovered that it can also be used for the design and analysis of communication systems, mostly with application to resource allocation algorithms [2], and, in particular, to power control [3]. As examples, the reader is referred to [4], [5]. Here, for a multiple access wireless data network, noncooperative and cooperative games are introduced, wherein users choose their transmit powers in order to maximize their own utilities, defined as the ratio of the throughput to transmit power. While the above studies consider the issue of power control assuming that a conventional matched filter is available at the receiver, the recent paper [6] considers for the first time the problem of joint linear receiver design and power control so as to maximize the utility of each user. In particular, it is shown here that the inclusion of receiver design in the considered game brings remarkable advantages, and, also, results based on the powerful large-system analysis are presented.
All of the cited studies, while laying the foundations of the game-theoretic approach to utility maximization in wireless data networks, focus on a very simple model, i.e. a synchronous direct sequence code division multiple access (DS/CDMA) channel subject to flat-fading. In this paper, instead, we extend the game-theoretic framework to a more practical and challenging scenario, namely we explicitly take into account (a) the possible system asynchrony across users; (b) the use of bandlimited chip-pulses; and (c) the multipath distortion induced by the wireless propagation channel. Note that in such a scenario intersymbol and interchip interference arises, thus implying that the appealing mathematical relationships between the signal-to-interference plus noise ratio (SINR) and the transmit power (as revealed in [6]) do not hold any longer, and this makes system analysis much more involved than it is for the case in which no self-interference exists. A further contribution of this paper is the consideration of non-linear multiuser receivers. Indeed, while previous studies have considered the case in which either a matched filter (see, e.g., [5]) or a linear multiuser detector [6] is adopted at the uplink receiver, here we also consider the case in which a non-linear decision feedback receiver is employed at the receiver. Notation: (•) T denotes transpose, while * and × denote linear convolution and ordinary product, respectively.
Consider the uplink of an asynchronous DS/CDMA system with K users, employing bandlimited chip pulses and operating over a frequency-selective fading channel. The received signal at the access point (AP) may be written as1
In the above expression, B is the transmitted frame or packet length, T b is the bit-interval duration, p k and τ k ≥ 0 denote the transmit power and timing offset of the k-th user, b k (p) ∈ {+1, -1} is the k-th user’s information symbol in the pth signaling interval (extension to modulations with a larger cardinality is straightforward). Moreover, c k (t) is the impulse response modeling the channel effects between the receiver and the k-th user’s transmitter, while w(t) is the additive noise term, which is assumed to be a zero-mean, Wide-Sense Stationary (WSS) white Gaussian process with Power Spectral Density (PSD) N 0 /2. It is also assumed that the channel coherence time exceeds the packet duration BT b , so that the channel impulse responses c 0 (t), . . . , c K-1 (t) may be assumed to be time-invariant over each transmitted frame. As to s ′ k (t), it is the k-th user’s signature waveform and is written
user’s spreading sequence, N the processing gain, T c = T b /N the chip interval, and h SRRC (•) a square-root raised cosine waveform with roll-off factor α ∈ [0, 1]. We assume here that h SRRC (t) is zero outside the interval [0, 4T c ] and attains its maximum value in t = 2T c . The receiver front-end consists of a filter with impulse response h SRRC (-t), followed by a sampler at rate M/T c ; in our simulations we will assume that M = 2. Denoting by y(t) the signal at the output of the receiver matched filter, it can be easily shown that
and h RC (t) = h SRRC (t) * h SRRC (-t).
Denoting by h k (t) = s k (t-τ k ) * c k (t) the effective signature waveform for the k-th user in the p-th signaling interval, the signal (2) can be expressed as
Notice that the waveform h k (t) is supported in the interval
where T m denotes the maximum channel multipath delay spread over the K active users.
Assuming that τ k + T m < T b , the support of the waveform
thus implying that, for a system with processing gain larger than 7, in the symbol interval I p = [pT b , (p + 2)T b ] the contribution from at most four symbols for each user (i.e. the p-th, the (p -1)-th, the (p -2)-th and the (p
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