Abstract
Identifying the start time of a sequence of symbols received at the receiver, commonly referred to as frame synchronization, is a critical task for achieving good performance in digital communications systems employing time-multiplexed transmission. In this work we focus on frame synchronization for linear channels with memory, in which the channel impulse response is periodic and the additive Gaussian noise is correlated and cyclostationary. Such channels appear in many communications scenarios, including narrowband power line communications and interference-limited wireless communications. We derive frame synchronization algorithms based on simplifications of the optimal likelihood-ratio test, assuming the channel impulse response is unknown at the receiver, which is applicable to many practical scenarios. The computational complexity of each of the derived algorithms is characterized, and a procedure for selecting nearly optimal synchronization sequences is proposed. The algorithms derived in this work achieve better performance than the noncoherent correlation detector, and, in fact, facilitate a controlled tradeoff between complexity and performance.
Highlights
In digital communications, blocks of information bits are mapped into sequences of symbols taken from a finite constellation set
In [6], we considered the joint estimation of the carrier frequency offset and the channel impulse response for this channel model, and proposed a compressed-sensing based approximate joint maximum likelihood estimator for these quantities
The work in [20] presented a sequential frame synchronization (FS) algorithm based on hypothesis testing, for pilot-symbol assisted modulation (PSAM) transmission [25], in which the pilot and the data symbols are selected from disjoint sets, and the signal is received over a memoryless additive white Gaussian noise (AWGN) channel such that the channel gain has an unknown random phase and frequency offsets
Summary
Blocks of information bits are mapped into sequences of symbols taken from a finite constellation set. The work in [20] presented a sequential FS algorithm based on hypothesis testing, for pilot-symbol assisted modulation (PSAM) transmission [25], in which the pilot and the data symbols are selected from disjoint sets, and the signal is received over a memoryless AWGN channel such that the channel gain has an unknown random phase and frequency offsets. Main Contributions: In this work we derive a sequential FS algorithm for channels with linear, periodically time-varying CIR and with ACGN, based on the likelihood ratio test (LRT) metric. It should be noted that in this work we do not consider designing new low-correlation sequences, since an important insight which arises from the simulations is that once the CIR has memory and the noise has correlation, the low-correlation property becomes less relevant for frame synchronization performance This point is clearly demonstrated by the numerical evaluations, which include an exhaustive search over all SWs, whose conclusion is that the good SWs for the considered channels have a relatively large correlation.
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