It has been shown that the multiple-input-multiple-output (MIMO) systems employing multiple transmit and receive antennas can offer a significant increase in capacity and mitigate the detrimental effects of the channel fading in wireless communication sys-tems. However, in the uplink of a cellular system, the size of mobile handsets makes it impractical to be quipped with geographically separated multiple antennas for ensuring independent fading on the transmit side. Addressing this problem, the strategy built upon the relay channel model, where the source broadcasts a message to several intermediate relays and subsequently these relay nodes forward the message they received to the des-tination, is considered as one of the promising methods to exploit spatial diversity using a collection of distributed antennas from different users in the network. This form of di-versity is referred to as the cooperative didi-versity [6, 13], in the sense that the relay nodes cooperating with the source node creates a virtual antenna array, or virtual MIMO system, to facilitate the ultimate transmission between the source and the destination.
In conventional MIMO systems, the design of space-time codes have been well inves-tigated and shown to be a very efficient approach to invoking the diversity. An important attribute of the space-time codes is that, for achieving full diversity, the transmitter
actu-ally needs to conducts encoding across antennas. That means we need to transmit quite different signals over independent channels. However, for a virtual MIMO system created by relay nodes, it is more difficult to have the relay cooperate. For a practical concern, it is usually assumed that the relay nodes cannot have instantaneous message exchanges between each other. Still, they may cooperate to a level in a way that we pre-assign dif-ferent coding rule to each relay by a controlling center so that they can form a distributed space-time code cooperatively as suggested in [5, 12]. Such considerations let us exploit the cooperative diversity easier at the cost of lower scalability. We will follow that spirit of partial cooperation in this thesis. On the other hand, there is another interesting mech-anism using randomized space-time codes [9]. Randomization allows all relay to encode with a common randomization rule but transmit different and independent signals. Hence, it has good scalability with other problems such as instantaneous power control on each individual relay. A more general consideration on the randomized space-time codes can also be found in [2].
For frequency non-selective flat fading channels, distributed space-time codes have been proposed to effectively exploit the spatial and temporal diversity offered by the vir-tual antenna array in the cooperative relaying network [5, 7]. On the other hand, when in the frequency-selective channel environment, the presence of multipath channel fad-ing offers another dimension of diversity, i.e. the frequency diversity, that the system can further exploit. Combined with the technique of orthogonal frequency-division multiplex-ing (OFDM) modulation, the design of distributed space-frequency codes with coherent decoding is considered in [8], where the authors employ the decode-and-forward (DAF) protocol and assume that all relays decode correctly. A more realistic scheme which takes into account the condition that all the relays do not always decode reliably is proposed and analyzed in [12], where the authors assume that each relay knows whether or not it has decoded reliably, i.e., an assumption of perfect censoring in each relay. This assumption is reasonable since the censoring method, such as using the cyclic redundancy check, can
be quite accurate. However, for the purpose of diversity achieving, we need the error rate of the system vanishing rapidly as the signal-to-noise ratio (SNR) goes to infinity. The main focus is on the high SNR regime and arbitrarily small error rate. In such case, a fixed error probability of censoring could be a decisive factor and should be treated cau-tiously. To the best of our knowledge, only on work [14] considers the practical scenario that some relays may fail in censoring and forward incorrect signals to the destination.
Specifically, in [14], the approach to mitigating the effect of error propagation needs the relay nodes know the instantaneous channel gains.
In the aforementioned work, perfect channel state information (CSI) is assumed to en-able coherent detection at the end receiver [2,5,7–9,12,14]. However, performing channel estimation can be costly and very challenging in multiple-hop wireless links and/or in fast-fading environments. Therefore, noncoherent communications not requiring the CSI is of particular interests. An early work [3] of noncoherent communications on MIMO space-time systems suggests the use of unitary modulation, or the unitary space-space-time code. Such unitary constellation is then generally used in noncoherent MIMO systems. The existence and construction of the unitary space-time codes have been investigated in [15], which presents a very elegant geometric thought for the maximum-likelihood (ML) decoding with unitary modulation and a good interpretation of the diversity as the dimension of the column space of the codeword matrix. On the other hand, the analysis and design for non-coherent space-frequency coded MIMO systems has also been considered in [1], where the authors prove that the maximum achievable diversity gain is given by the product of the number of transmit antennas, the number of receive antennas, and the channel order, which is the same as the diversity gain that can be provided in coherent communications.
For cooperative networks, noncoherent communications have also been studied over fre-quency flat fading channel. For example, noncoherent decoding in amplify-and-forward (AF) relaying scheme is explored in [17].