Compute-Forward Multiple Access (CFMA) is a multiple access transmission scheme based on Compute-and-Forward (CF), which allows the receiver to first decode linear combinations of the transmitted signals and then solve for individual messages. This paper extends the CFMA scheme to a two-user Gaussian multiple-input multiple-output (MIMO) multiple access channel (MAC). We propose the CFMA Serial Coding Scheme (SCS) and the CFMA Parallel Coding Scheme (PCS) with nested lattice codes. We first derive the expression of the achievable rate pair for MIMO MAC with CFMA-SCS. We prove a general condition under which CFMA-SCS can achieve the sum capacity of the channel. Furthermore, this result is specialized to single-input multiple-output (SIMO) and 2-by-2 diagonal MIMO multiple access channels, for which more explicit sum capacity-achieving conditions on power and channel matrices are derived. We then study the achievable rate of CFMA-PCS by using an equivalent SIMO model, and analyze its sum capacity-achieving conditions. Numerical results are provided for the performance of CFMA-SCS and CFMA-PCS in different channel conditions. In general, CFMA-PCS has better sum capacity achievability, although with a higher computational complexity for encoding and decoding.

Compute-forward multiple access (CFMA) is a transmission strategy which allows the receiver in a multiple access channel (MAC) to first decode linear combinations of the transmitted signals and then solve for individual messages. Compared to existing MAC strategies such as joint decoding or successive interference cancellation (SIC), CFMA was shown to achieve the MAC capacity region for fixed channels under certain signal-to-noise (SNR) conditions without time-sharing using only single-user decoders. This paper studies the CFMA scheme for a two-user Gaussian fast fading MAC with channel state information only available at the receiver (CSIR). We investigate appropriate lattice decoding schemes to decode linear combinations with any integer coefficients in the fading MAC and derive the achievable rate pairs. We give a sufficient and necessary condition under which the proposed scheme can achieve the ergodic sum capacity. Furthermore, we investigate the impact of channel statistics on the capacity achievability of the CFMA scheme. In general, the sum capacity is achievable if the channel variance is small compared to the mean value of the channel strengths. Various numerical results are presented to illustrate the theoretical findings.

Compute-forward multiple access (CFMA) is a transmission strategy which allows the receiver in a multiple access channel (MAC) to first decode linear combinations of the transmitted signals and then solve for individual messages. Compared to existing MAC strategies such as joint decoding or successive interference cancellation (SIC), CFMA was shown to achieve the MAC capacity region for fixed channels under certain signal-to-noise (SNR) conditions without time-sharing using only single-user decoders. This paper studies the CFMA scheme for a two-user Gaussian fast fading MAC with channel state information only available at the receiver (CSIR). We develop appropriate lattice decoding schemes for the fading MAC and derive the achievable rate pairs for decoding linear combinations of codewords with any integer coefficients. We give a sufficient and necessary condition under which the proposed scheme can achieve the ergodic sum capacity. Furthermore, we investigate the impact of channel statistics on the capacity achievability of the CFMA scheme. In general, the sum capacity is achievable if the channel variance is small compared to the mean value of the channel strengths. Various numerical results are presented to illustrate the theoretical findings.

Compute-forward multiple access (CFMA) is a multiple access transmission scheme based on Compute-and-Forward (CF) which allows the receiver to first decode linear combinations of the transmitted signals and then solve for individual messages. This paper extends the CFMA scheme to a two-user Gaussian multiple-input multiple-output (MIMO) multiple access channel (MAC). We first derive the expression of the achievable rate pair for MIMO MAC with CFMA. We prove a general condition under which CFMA can achieve the sum capacity of the channel. Furthermore, this result is specialized to SIMO and 2-by-2 diagonal MIMO multiple access channels, for which more explicit sum capacity-achieving conditions on power and channel matrices are derived. Numerical results are also provided for the performance of CFMA on general MIMO multiple access channels.

In this paper, we consider an underlay cognitive radio network assisted by dual-hop decode-and-forward (DF) relaying. For a general multi-user network, we adopt a max-min fairness relay selection scheme and analyse the outage probability when the channels are subject to independent and non-identical Nakagami-m fading. The relay network operates within the constraint imposed on the peak interference power tolerable by the primary receiver. We then analyse the asymptotic outage probability performance and illustrate the existence of i) the full-diversity order when the interference level at the primary user increases proportionally with the relay transmit power; and ii) an outage floor when the transmit powers of the relays are restricted by the primary receiver. We also analyse the outage probability with imperfect channel state information (CSI) and the average throughput over Rayleigh fading channels. Illustrative analytical results are accurately validated by numerical simulations.