A noncoherent two-way relaying system is developed using physical-layer network coding for improved throughput over conventional relaying in a fading channel. Energy-efficient noncoherent operation is achieved using multitone frequency shift keying (FSK). A novel soft-output demodulator is developed for the relay, and corresponding achievable exchange rates are found for Rayleigh fading and AWGN channels. Bit-error rate performance approaching the achievable rate is realized using a capacity-approaching channel code and a receiver architecture, which iterates between demodulation and channel decoding. Iterative decoding is performed feeding information back from the channel decoder to the demodulator. In addition, the error-rate performance is made to approach the achievable rate more closely by optimizing LDPC codes for this system. The energy efficiency improvement obtained by increasing the modulation order is more dramatic for the proposed physical-layer network coding scheme than it is for a conventional point-to-point system. Using optimized LDPC codes, the bit-error rate performance is improved by as much as 1.1 dB over a widely known standardized LDPC code, and comes to within 0.7 dB of the limit corresponding to the achievable rate. Throughout this paper, the performance for physical-layer network coding is compared with conventional network coding. When noncoherent FSK is used, physical-layer network coding enables higher achievable rates, and conventional network coding exhibits better energy efficiency at low rates.

Analog network coding (ANC) is a throughput increasing technique for the two-way relay channel (TWRC) whereby two end nodes transmit simultaneously to a relay at the same time and band, followed by the relay broadcasting the received sum of signals to the end nodes. Coherent reception under ANC is challenging due to requiring oscillator synchronization for all nodes, a problem further exacerbated by Doppler shift. This work develops a noncoherent M-ary frequency-shift keyed (FSK) demodulator implementing ANC. The demodulator produces soft outputs suitable for use with capacity-approaching channel codes and supports information feedback from the channel decoder. A unique aspect of the formulation is the presence of an infinite summation in the received symbol probability density function. Detection and channel decoding succeed when the truncated summation contains a sufficient number of terms. Bit error rate performance is investigated by Monte Carlo simulation, considering modulation orders two, four and eight, channel coded and uncoded operation, and with and without information feedback from decoder to demodulator. The channel code considered for simulation is the LDPC code defined by the DVB-S2 standard. To our knowledge this work is the first to develop a noncoherent soft-output demodulator for ANC.

This work considers optimizing LDPC codes in the physical-layer network coded two-way relay channel using noncoherent FSK modulation. The error-rate performance of channel decoding at the relay node during the multiple-access phase was improved through EXIT-based optimization of Tanner graph variable node degree distributions. Codes drawn from the DVB-S2 and WiMAX standards were used as a basis for design and performance comparison. The computational complexity characteristics of the standard codes were preserved in the optimized codes by maintaining the extended irregular repeat-accumulate (eIRA). The relay receiver performance was optimized considering two modulation orders M = {4; 8} using iterative decoding in which the decoder and demodulator refine channel estimates by exchanging information. The code optimization procedure yielded unique optimized codes for each case of modulation order and available channel state information. Performance of the standard and optimized codes were measured using Monte Carlo simulation in the flat Rayleigh fading channel, and error rate improvements up to 1:2 dB are demonstrated depending on system parameters.

Digital network coding improves the throughput of the two-way relay channel by allowing multiple sources to transmit simultaneously to the relay. This work considers the development of a relay receiver applying a specific modulation and channel coding technique - turbo-coded noncoherent orthogonal FSK in the two-way relay channel operated with digital network coding. The relay receiver supports any modulation order which is a power of two, and iterative channel decoding with information feedback from decoder to demodulator, using bit interleaved coded modulation with iterative decoding (BICM-ID). The performance of the receiver is investigated in fading channels through error-rate simulations and capacity analysis, and results show an energy efficiency improvement of 0.5-0.9 dB over similar systems which do not utilize BICM-ID.

Physical-layer network coding is a protocol capable of increasing throughput over conventional relaying in the two- way relay channel, but is sensitive to phase and frequency offsets among transmitted signals. Modulation techniques which require no phase synchronization such as noncoherent FSK can compensate for phase offset, however, the relay receiver must still compensate for frequency offset. In this work, a soft- output noncoherent detector for the relay is derived, under the assumption that the source oscillators generating FSK tones lack frequency synchronization. The derived detector is shown through simulation to improve error rate performance over a conventional detector which does not model offset, for offset values on the order of a few hundredths of a fraction of FSK tone spacing.

A channel-coded physical-layer network coding strategy is refined for practical operation. The system uses frequency-shift keying (FSK) modulation and operates noncoherently, providing advantages over coherent operation: there are no requirements for perfect power control, phase synchronism, or estimates of carrier-phase offset. In contrast with analog network coding, which relays received analog signals plus noise, the system relays digital network codewords, obtained by digital demodulation and channel decoding at the relay. The emphasis of this paper is on the relay receiver formulation. Closed-form expressions are derived that provide bitwise log-likelihood ratios, which may be passed through a standard error-correction decoder. The role of fading-amplitude estimates is investigated, and an effective fading-amplitude estimator is developed. Simulation results are presented for a Rayleigh block-fading channel, and the influence of block length is explored. An example realization of the proposed system demonstrates a 32.4% throughput improvement compared to a similar system that performs network coding at the link layer. By properly selecting the rates of the channel codes, this benefit may be achieved without requiring an increase in transmit power.