We formulate an adaptive power allocation problem where we minimize the energy-per-goodbit (EPG) of a system employing a multiple-input multiple-output maximum ratio combining (MIMO-MRC) scheme. Closed-form results are obtained for the optimum transmit power and minimum EPG as a function of the number of antennas employed and the quality of the channel. To assess the performance of the solution in a statistically varying channel, we obtain the cumulative distribution function (CDF) of the minimum EPG in closed form. We explore the energy-efficiency trade-off between enhanced diversity and the increased circuit power consumption of multiple antennas. In particular, we use the EPG CDF in a numerical example to find the most energy-efficient number of antennas for a given probability of outage. We consider both Rayleigh and Rician MIMO fading channels.

In this paper we formulate a power loading problem for the spatial subchannels (parallel channels) of a single-carrier MIMO-SVD system. The power loading solution is designed to minimize the energy-per-goodbit (EPG) of the MIMO-SVD system. The optimum power loading obtained by solving a nonlinear fractional program, has a closed-form expression and is found by applying a water-filling procedure. It is observed that the optimum total transmit power (water level) depends not only on the MIMO channel realization, but also on the ratio of circuit power cost (which depends on the number of antennas) to transmit power cost (which depends on path loss and other factors). We study the statistical performance (using simulation) of the solution in Rayleigh and Rician flat-fading channels. Using outage EPG as a measure of performance, we determine the MIMO configuration (from a set of allowed configurations) that yields the minimum outage EPG. It is observed that the average number of spatial subchannels utilized (which indicates preference for diversity or multiplexing) depends on the ratio of circuit power cost to transmit power cost and fading type (Rayleigh or Rician). For both cases, the results show that both multiplexing and diversity obtained by MIMO systems are critical for energy efficiency.

In this paper, we develop an energy-efficient power allocation algorithm for the parallel channels of an OFDM system. This algorithm provides the optimum solution to a nonlinear fractional program involving an objective function called energy-per-goodbti (EPG). The EPG objective function models the impact of both transmit power and constant circuit power consumption. The energy minimization problem formulation is quite general and subsumes both maximize rate (MR) and maximize margin (MM) problems as specific cases. As a result, the energy efficiency viewpoint provides a convenient and unified perspective of the various water-filling solutions. Using a numerical example, we show that the energy-efficient solution is quite different from the MM or MR solutions and can provide several dBs of performance improvement. We also study the impact of rounding to discrete constellation sizes.

In this paper, the problem of choosing constellation size and transmit power that minimizes the energy-per-goodbit in a frequency-flat, long-term static fading channel is considered. A goodbit is a bit that is received without error. A low-complexity, near-optimal algorithm to find constellation size and transmit power is presented. Although perfect channel state information (CSI) at the transmitter is assumed, fading can cause situations where the system cannot meet user constraints on acceptable performance. The implications of this type of system outage and the consequent trade-off between energy-efficiency and range are discussed. Assuming that the fading process is ergodic, the average energy-efficient spectral efficiency can be computed for various fading distributions of interest. As an application of the techniques developed, we evaluate, by simulation, the average minimum energy-per-goodbit for a Rayleigh fading channel and note that over a short range of distances (1 m to 10 m), it can cost at most 1 dB more than for the corresponding non-fading AWGN channel. We also show that the restriction of using only a square-QAM constellation does not incur a large penalty in cost.

In this paper, an energy minimization problem for a quadrature amplitude modulation (QAM) system with automatic repeat request (ARQ) is considered. We formulate an optimization problem with constellation size and transmit power as the variables. We give an efficient and accurate geometric programming (GP) approximation to the problem and illustrate the solution using a numerical example. We learn that the transmit power or equivalently bit error rate (BER) should be carefully chosen for minimal energy. Our analysis provides guidelines for setting the BER in an energy optimal way for various packet lengths.