Integer-Forcing Linear Receivers

Abstract

Abstract-Linear receivers are often used to reduce the implementation complexity of multiple-antenna systems. In a traditional linear receiver architecture, the receive antennas are used to separate out the codewords sent by each transmit antenna, which can then be decoded individually. Although easy to implement, this approach can be highly suboptimal when the channel matrix is near singular. This paper develops a new linear receiver architecture that uses the receive antennas to create an effective channel matrix with integer-valued entries. Rather than attempting to recover transmitted codewords directly, the decoder recovers integer combinations of the codewords according to the entries of the effective channel matrix. The codewords are all generated using the same linear code which guarantees that these integer combinations are themselves codewords. Provided that the effective channel is full rank, these integer combinations can then be digitally solved for the original codewords. This paper focuses on the special case where there is no coding across transmit antennas and no channel state information at the transmitter(s), which corresponds either to a multi-user uplink scenario or to single-user V-BLAST encoding. In this setting, the proposed integer-forcing linear receiver significantly outperforms conventional linear architectures such as the zero-forcing and linear MMSE receiver. In the high SNR regime, the proposed receiver attains the optimal diversity-multiplexing tradeoff for the standard MIMO channel with no coding across transmit antennas. It is further shown that in an extended MIMO model with interference, the integer-forcing linear receiver achieves the optimal generalized degrees-of-freedom.

Low-Complexity Integer-Forcing Methods for Block Fading MIMO Multiple-Access Channels

“…Proposed Method 3 and Proposed Method 4 have similar complexity as Proposed Method 1 and 2, respectively. Finally, the complexity of optimal GM/AM-SIF by exhaustive search follows from the bound in [2] (see also [2], [9]).…”

“…Thus, if decoding is successful and V is recovered, then X can also be recovered, provided A is full-rank. 1 As a consequence, it is shown in [2], [3] that the following rate is achievable…”

“…An integer-forcing receiver [2] shares the same basic structure of a conventional linear receiver, as illustrated in Fig. 1: first, the received matrix is linearly transformed by an equal- ization matrix; then, each resulting stream is individually processed by a channel decoder.…”

“…Crucial to this noise removal step at the channel decoders is the use of a lattice code common to all transmitters [2], [3]. A lattice Λ ∈ R n is a discrete subgroup of R n , i.e., it is closed under integer linear combinations [16].…”

“…Although joint maximum likelihood (ML) receivers achieve the best performance among all methods, by searching over all possible transmitted codewords [5], their complexity is prohibitively high, increasing exponentially with the number of users. In contrast, IF receivers have a much lower complexity and can approach the ML performance in many situations [2]. Moreover, the performance of an IF receiver can be further improved in some situations by successive computation, leading to the so-called successive IF (SIF) receiver, analogously to the successive interference cancellation (SIC) technique for conventional linear receivers.…”