Mobile Lattice-Coded Physical-Layer Network Coding with Practical Channel Alignment

Abstract

Physical-layer network coding (PNC) is a communications paradigm that exploits overlapped transmissions to boost the throughput of wireless relay networks. A high point of PNC research was a theoretical proof that PNC that makes use of nested lattice codes could approach the information-theoretic capacity of a two-way relay network (TWRN), where two end nodes communicate via a relay node. The capacity cannot be achieved by conventional methods of time-division or straightforward network coding. Many practical challenges, however, remain to be addressed before the full potential of lattice-coded PNC can be realized. Two major challenges are: (1) for good performance in lattice-coded PNC, channels of simultaneously transmitting nodes must be aligned; (2) for lattice-coded PNC to be practical, the complexity of lattice encoding at the transmitters and lattice decoding at the receiver must be reduced. We address these challenges and implement a first lattice-coded PNC system on a software-defined radio (SDR) platform. Specifically, we design and implement a low-overhead channel precoding system that accurately aligns the channels of distributed nodes. In our implementation, the nodes only use low-cost temperature-compensated oscillators (TCXO)-a consequent challenge is that the channel alignment must be done more frequently and more accurately compared with the use of expensive oscillators. The low overhead and accurate channel alignment are achieved by (1) a channel precoding system implemented over FPGA to realize fast feedback of channel state information; (2) a highly-accurate carrier frequency offset (CFO) estimation method; and (3) a partial-feedback channel estimation method that significantly reduces the amount of feedback information from the receiver to the transmitters for channel precoding at the transmitters. To reduce lattice encoding and decoding complexities, we adapt the low-density lattice code (LDLC) for use in PNC systems. Experiments show that our implemented lattice-coded PNC achieves better bit error rate performance compared with time-division and straightforward network coding systems. It also has good throughput performance in mobile non-LoS scenarios.

Coherent Detection for Short-Packet Physical-Layer Network Coding With Binary FSK Modulation

“…The signal vector can be expressed as In practice, we should have a rough idea of the range of the CFOs f RF A and f RF B . This can be acquired through equipment testing beforehand [16] [29]. The range of CFO investigated in this paper is f RF u ∈ [−10Hz, 10kHz] for u ∈ {A, B} (the oscillators in software-defined radio boards, for example, have CFO smaller than this range [16] [29]).…”

“…The analysis in the rest of this paper is based on the system model described by (13) and (16), and the detector in (17). Note that, after the transformation of the channels shown above, the detector does not need to estimate the initial phase offsets of users A and B separately from their channels since the initial phase offsets are incorporated into the channels.…”

“…In particular, h u for u ∈ {A, B} is complex Gaussian random variable with zero mean and variance σ 2 hu . Since after phase rotation on the channel in (16), the distribution of the channels is unchanged, h n , n = 0, · · · , N − 1, are still Rayleigh distributed with zero mean and…”

“…Accurate channel information at the relay is a must. Much prior work used preambles to estimate the channel [14] [15] [16] [17] [18] [19]. For long packets, the preamble overhead is low because of the large data payload.…”

Buffer-Aided Relaying Network With Hybrid BNC for the Internet of Things: Protocol and Performance Analysis

“…Proof: Substitute (11) into (14) and (15), we can derive the expression of the queue length and queuing delay under the symmetric situation as follows:…”