Communication networks are often designed and analyzed assuming tight synchronization among nodes. However, in applications that require communication in the energy-efficient regime of low signal-to-noise ratios, establishing tight synchronization among nodes in the network can result in a significant energy overhead. Motivated by a recent result showing that near-optimal energy efficiency can be achieved over the AWGN channel without requiring tight synchronization, we consider the question of whether the potential gains of cooperative communication can be achieved in the absence of synchronization. We focus on the symmetric Gaussian diamond network and establish that cooperative-communication gains are indeed feasible even with unsynchronized nodes. More precisely, we show that the capacity per unit energy of the unsynchronized symmetric Gaussian diamond network is within a constant factor of the capacity per unit energy of the corresponding synchronized network. To this end, we propose a distributed relaying scheme that does not require tight synchronization but nevertheless achieves most of the energy gains of coherent combining.
It is shown that the capacity region of the asynchronous multiple-access channel differs from that of the synchronous channel only by the lack of a convex hull operation. When data traffic in a wireless network is bursty, small amounts of data sporadically become available for transmission, and the energy cost associated with synchronizing the network nodes prior to each communication block is not negligible. Therefore, designing energy-efficient communication schemes for such asynchronous scenarios is of particular importance. In this paper, we show that, for symmetric diamond networks, by performing the tasks of synchronization and communication separately, it is possible to achieve the minimum energy-per-bit to within a factor that ranges from 2 in the synchronous case to 1 in the highly asynchronous regime. An equivalent discrete-time Gaussian channel parametrized by the signal cross-correlations is derived to obtain an equivalent channel model with discrete-time outputs. The main feature introduced by the lack of symbol synchronism is that the channel has memory. This is due to the overlap of each symbol transmitted by a user with two consecutive symbols transmitted by the other user. It is shown that if the transmitters are assigned the same waveform, symbol asynchronism has no effect on the two-user capacity region of the white Gaussian channel which is equal to the Cover-Syner pentagon, whereas if the assigned waveforms are different (e.g., code division multiple access), the symbol-asynchronous capacity region is no longer a pentagon. An alternative representation of the capacity region which results in a particularly compact characterization of the fundamental limits of the multiple-access channel in the region of signal-to-noise ratios is also considered. > This paper considers the optimum method for locating a sync word periodically imbedded in binary data and received over the additive white Gaussian noise channel. It is shown that the optimum rule is to select the location that maximizes the sum of the correlation and a correction term. Simulations are reported that show approximately a 3-dB improvement at interesting signal-to-noise ratios compared to a pure correlation rule. Extensions are given to the "phase-shift keyed (PSK) sync" case where the detector output has a binary ambiguity and to the case of Gaussian data. The capacity per unit cost, or, equivalently, the minimum cost to transmit one bit, is a well-studied quantity under the assumption of full synchrony between the transmitter and the receiver. In many applications, such as sensor networks, transmissions are very bursty, with amounts of bits arriving infrequently at random times. In such scenarios, the cost of acquiring synchronization is significant and one is interested in the fundamental limits on communication without assuming a priori synchronization. In this paper, the minimum cost to transmit B bits of information asynchronously is shown to be equal to (B +H) ksync, where ksync is the synchronous minimum cost per bit and H is a measure of timing uncertainty equal to the entropy for most reasonable arrival time distributions. This result holds when the transmitter can stay idle at no cost and is a particular case of a general result which holds for arbitrary cost functions. The capacity region for the discrete memoryless multiple-access channel without time synchronization at the transmitters and receivers is shown to be the same as the known capacity region for the ordinary multiple-access channel. The proof utilizes time sharing of two optimal codes for the ordinary multiple-access channel and uses maximum likelihood decoding over shifts of the hypothesized transmitter words.