Integer-Forcing Linear Receivers

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.Comment: 40 pages, 16 figures, to appear in the IEEE Transactions on Information Theor

Generalized feedback detection for spatial multiplexing multi-antenna systems

We present a unified detection framework for spatial multiplexing multiple-input multiple-output (MIMO) systems by generalizing Heller’s classical feedback decoding algorithm for convolutional codes. The resulting generalized feedback detector (GFD) is characterized by three parameters: window size, step size and branch factor. Many existing MIMO detectors are turned out to be special cases of the GFD. Moreover, different parameter choices can provide various performance-complexity tradeoffs. The connection between MIMO detectors and tree search algorithms is also established. To reduce redundant computations in the GFD, a shared computation technique is proposed by using a tree data structure. Using a union bound based analysis of the symbol error rates, the diversity order and signal-to-noise ratio (SNR) gain are derived analytically as functions of the three parameters; for example, the diversity order of the GFD varies between 1 and N. The complexity of the GFD varies between those of the maximum-likelihood (ML) detector and the zero-forcing decision feedback detector (ZFDFD). Extensive computer simulation results are also provided

MIMO Transceivers With Decision Feedback and Bit Loading: Theory and Optimization

This paper considers MIMO transceivers with linear precoders and decision feedback equalizers (DFEs), with bit allocation at the transmitter. Zero-forcing (ZF) is assumed. Considered first is the minimization of transmitted power, for a given total bit rate and a specified set of error probabilities for the symbol streams. The precoder and DFE matrices are optimized jointly with bit allocation. It is shown that the generalized triangular decomposition (GTD) introduced by Jiang, Li, and Hager offers an optimal family of solutions. The optimal linear transceiver (which has a linear equalizer rather than a DFE) with optimal bit allocation is a member of this family. This shows formally that, under optimal bit allocation, linear and DFE transceivers achieve the same minimum power. The DFE transceiver using the geometric mean decomposition (GMD) is another member of this optimal family, and is such that optimal bit allocation yields identical bits for all symbol streams—no bit allocation is necessary—when the specified error probabilities are identical for all streams. The QR-based system used in VBLAST is yet another member of the optimal family and is particularly well-suited when limited feedback is allowed from receiver to transmitter. Two other optimization problems are then considered: a) minimization of power for specified set of bit rates and error probabilities (the QoS problem), and b) maximization of bit rate for fixed set of error probabilities and power. It is shown in both cases that the GTD yields an optimal family of solutions

Kilohertz-driven Bose-Einstein condensates in optical lattices

We analyze time-of-flight absorption images obtained with dilute Bose-Einstein con-densates released from shaken optical lattices, both theoretically and experimentally. We argue that weakly interacting, ultracold quantum gases in kilohertz-driven optical potentials constitute equilibrium systems characterized by a steady-state distri-bution of Floquet-state occupation numbers. Our experimental results consistently indicate that a driven ultracold Bose gas tends to occupy a single Floquet state, just as it occupies a single energy eigenstate when there is no forcing. When the driving amplitude is sufficiently high, the Floquet state possessing the lowest mean energy does not necessarily coincide with the Floquet state connected to the ground state of the undriven system. We observe strongly driven Bose gases to condense into the former state under such conditions, thus providing nontrivial examples of dressed matter waves.Comment: 36 pages, 3 figures, Advance Atomic Molecular Physics in pres