We propose a technique to calculate the diversity gain for a vector channel when the noises have any nonsingular distribution and the fading coefficients have arbitrary distribution. This technique uses the serial expansion of the outage probability of the instantaneous normalized receive SNR to obtain the diversity gain. The approach is simpler than using the pairwise symbol error rate to analyze the diversity gain.

In this technical report, we provide diversity analysis for two transmission schemes in (J;Ja;Ra;N) multi-access relay networks (MARNs), where J users, each equipped with Ja antennas, communicate to one N-antenna receiver through Ra single-antenna relays. Both transmission schemes allow all users' symbols to be transmitted concurrently through the source-relay and relay-receiver links. Therefore, both schemes have the potential of high transmission rate in multi-user relay networks. In the first scheme, called DSTC joint-user ML decoding, the relays perform distributed space-time coding (DSTC) to improve the reliability of the system, and the receiver jointly decodes all users' symbols using the ML decoding. Through rigorous analysis, this scheme achieves a symbol rate of 1/2 symbols/user/channel use, in conjunction to a diversity gain of Ra*min(Ja;N), which is the maximum diversity achievable in this network. But the decoding complexity of this scheme is exponential in the number of users. To reduce the decoding complexity, we consider a second scheme, DSTC-ICRec, in which the relay operations are the same, but the receiver first conducts interference cancellation (IC) to decouple multi-user signals, then decodes each user's symbols independently. We show analytically that in (2; 1; 2; N) and (2; 2;2;N) MARNs, DSTC-ICRec achieves a diversity of 1 and min(2;N-1), respectively, at a symbol rate of 1/2 symbols/user/channel use. Since the maximum achievable diversity gains in these two networks are 2 and 2*min(2;N), respectively, DSTC-ICRec has a lower diversity gain, compared to DSTC joint-user ML decoding, but its decoding complexity is much lower due to the IC.

We study multi-user transmission and detection schemes for a multi-access relay network (MARN) with linear constraints at all nodes. In a (J, Ja, Ra, M) MARN, J sources, each equipped with Ja antennas, communicate to one M-antenna destination through one Ra-antenna relay. A new protocol called IC-Relay-TDMA is proposed which takes two phases. During the first phase, symbols of different sources are transmitted concurrently to the relay. At the relay, interference cancellation (IC) techniques, previously proposed for systems with direct transmission, are applied to decouple the information of different sources without decoding. During the second phase, symbols of different sources are forwarded to the destination in a time division multi-access (TDMA) fashion. At the destination, the maximum-likelihood (ML) decoding is performed source-by-source. The protocol of IC-Relay-TDMA requires the number of relay antennas no less than the number of sources, i.e., Ra >= J. Through outage analysis, the achievable diversity gain of the proposed scheme is shown to be min{Ja(Ra â^È^Ò J + 1), RaM}. When M â^ɤ Ja (1 â^È^Ò (Jâ^È^Ò1) / Ra), the proposed scheme achieves the maximum interference-free (int-free) diversity gain RaM. Since concurrent transmission is allowed during the first phase, compared to full TDMA transmission, the proposed scheme achieves the same diversity, but with a higher symbol rate.