The central design challenge in next generation wireless systems is to have these systems operate at high bandwidths and provide high data rates while being cognizant of the energy consumption levels especially in mobile applications. Since communicating at very high data rates prohibits obtaining high bit resolutions from the analog-to-digital (A/D) converters, analysis of the energy efficiency under the assumption of hard-decision detection is called for to accurately predict the performance levels. In this paper, transmission over the additive white Gaussian noise (AWGN) channel, and coherent and noncoherent fading channels is considered, and the impact of hard-decision detection on the energy efficiency of phase and frequency modulations is investigated. Energy efficiency is analyzed by studying the capacity of these modulation schemes and the energy required to send one bit of information reliably in the low signal-to-noise ratio (SNR) regime. The capacity of hard-decision-detected phase and frequency modulations is characterized at low SNR levels through closed-form expressions for the first and second derivatives of the capacity at zero SNR. Subsequently, bit energy requirements in the low-SNR regime are identified. The increases in the bit energy incurred by hard-decision detection and channel fading are quantified. Moreover, practical design guidelines for the selection of the constellation size are drawn from the analysis of the spectral efficiency--bit energy tradeoff.
Deep Dive into The Impact of Hard-Decision Detection on the Energy Efficiency of Phase and Frequency Modulation.
The central design challenge in next generation wireless systems is to have these systems operate at high bandwidths and provide high data rates while being cognizant of the energy consumption levels especially in mobile applications. Since communicating at very high data rates prohibits obtaining high bit resolutions from the analog-to-digital (A/D) converters, analysis of the energy efficiency under the assumption of hard-decision detection is called for to accurately predict the performance levels. In this paper, transmission over the additive white Gaussian noise (AWGN) channel, and coherent and noncoherent fading channels is considered, and the impact of hard-decision detection on the energy efficiency of phase and frequency modulations is investigated. Energy efficiency is analyzed by studying the capacity of these modulation schemes and the energy required to send one bit of information reliably in the low signal-to-noise ratio (SNR) regime. The capacity of hard-decision-detecte
Energy efficiency is of paramount importance in many communication systems and particularly in mobile wireless systems due to the scarcity of energy resources. Energy efficiency can be measured by the energy required to send one information bit reliably. It is well-known that for Gaussian channels subject to average power constraints, the minimum received bit energy normalized by the noise spectral level is E b N0 min = -1.59 dB regardless of the availability of channel side information (CSI) at the receiver (see e.g., [1] - [5], and [8]). Golay [1] showed that this minimum bit energy can be achieved in the additive white Gaussian noise (AWGN) channel by pulse position modulation (PPM) with Mustafa Cenk Gursoy is with the Department of Electrical Engineering, University of Nebraska-Lincoln, Lincoln, NE 68588 (e-mail : gursoy@engr.unl.edu).
This work was supported in part by the NSF CAREER Grant CCF-0546384. The material in this paper was presented in part at the IEEE International Symposium on Information Theory (ISIT), Nice, France, in June 2007, and at the IEEE International Symposium on Information Theory (ISIT), Toronto, Canada, in July 2008.
vanishing duty cycle when the receiver employs threshold detection. Indeed, Turin [2] proved that any orthogonal Mary modulation scheme with envelope detection at the receiver achieves the normalized bit energy of -1.59 dB in the AWGN channel as M → ∞. It is further shown in [3] and [4] that M -ary orthogonal frequency-shift keying (FSK) achieves this minimum bit energy asymptotically as M → ∞ also in noncoherent fading channels where neither the receiver nor the transmitter knows the fading coefficients. These studies demonstrate the asymptotical high energy efficiency of orthogonal signaling even when the receiver performs harddecision detection. As also well-known by now in the digital communications literature [23], these results are shown by proving that the error probabilities of orthogonal signaling can be made arbitrarily small as M → ∞ as long as the normalized bit energy (or equivalently SNR per bit) is greater than -1.59 dB. As indicated by the unbounded growth of M , the minimum bit energy is in general achieved at infinite bandwidth or equivalently as the spectral efficiency (rate in bits per second divided by bandwidth in Hertz) goes to zero.
Indeed for average power limited channels, the bit energy required for reliable communication decreases monotonically with increasing bandwidth [6], [8]. This is the fundamental bandwidth-power tradeoff. Recently, Verdú [8] has offered a more subtle analysis of the tradeoff of bit energy versus spectral efficiency. In this work, the wideband slope, which is the slope of the spectral efficiency curve at zero spectral efficiency, has emerged as a new analysis tool to measure energy and bandwidth efficiency in the low-power regime. It is shown that if the receiver has perfect knowledge of the fading coefficients, quaternary phase-shift keying (QPSK) is an optimally efficient modulation scheme achieving both the minimum bit energy of -1.59 dB and the optimal wideband slope in the low SNR regime. This indicates that besides orthogonal signaling, phase modulation is also well-suited for energy efficient operation. However, it should be noted that asymptotic efficiency of QPSK holds under the assumption that the receiver performs soft detection. Verdú [8] has also provided expressions for the minimum bit energy and wideband slope of the quantized QPSK. We note that phase modulation is a widely used technique for information transmission, and the performance of coded phase modulation has been of interest in the research community since the 1960s. One of the early works was conducted in [10] where the capacity and error exponents of a continuous-phase modulated system, in which the transmitted phase can assume any value in [-π, π), is studied. More recent studies include [4], [9], and [11]- [14].
As discussed above, high energy efficiency requires operation in the wideband regime in which the spectral efficiencies are low. This is is achieved by either decreasing the data rates or increasing the bandwidth. If the system has large bandwidth, then the data rates are high. For instance, if the total signal power is P = 1 mW and the bandwidth is B = 1 GHz, then the capacity of the AWGN channel is C = B log 2 1 + P N0B ≈ 27.9 Gbits/s 1 . If the bandwidth is increased to B = 10 GHz, the capacity becomes 245.7 Gbits/s. Similarly, high rates are also achieved in fading channels when the available bandwidth is large. For instance, in current practical applications, wideband CDMA and ultrawideband systems offer high data rate services by using large bandwidths [27]. Additionally, operating at high bandwidths and providing high data rates while conserving the energy in mobile applications are the key features of next generation wireless systems which have the goal of offering mobile multimedia access. For instance, one of the fe
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