Bit-Interleaved Coded Multiple Beamforming Research Articles

Bit-Interleaved Coded Multiple Beamforming With Perfect Coding in Millimeter-Wave MIMO Systems

This letter investigates bit-interleaved coded multiple beamforming (BICMB) with perfect coding in millimeter-wave (mm-wave) multiple-input multiple-output (MIMO) systems to achieve the maximum diversity gain. Using perfect coding with BICMB enables us to do this. We show that by using BICMB and perfect coding, the diversity gain becomes independent of the number of transmitted data streams and the number of antennas in each remote antenna unit (RAU) at the transmitter and the receiver. The assumption is that the perfect channel state information (CSI) is known at both the transmitter and the receiver. With the assumption of the perfect CSI at the transmitter and the receiver, simulation results show that the use of BICMB with perfect coding results in the diversity gain values predicted by the analysis.

Bit-Interleaved Coded Multiple Beamforming in Millimeter-Wave Massive MIMO Systems

An analysis of the diversity gain for bit-interleaved coded multiple beamforming (BICMB) method in millimeter-wave (mm-Wave) massive multiple-input multiple-output (MIMO) systems is carried out for both the single-user and multi-user scenarios. We show that full diversity gain and full spatial multiplexing order can be achieved in both scenarios. Also, we show that the diversity gain in the multi-user scenario is independent of the number of users in the system. The assumption here is that the channel state information (CSI) is known at both sides of the transmitter and the receiver and the number of antennas in each remote antenna unit (RAU) tends to infinity. Based on these assumptions, the diversity gain for the single-user scenario is (Σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i,j</sub> β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ij</sub> /) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /Σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i,j</sub> β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ij</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ij</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> where L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ij</sub> is the number of propagation paths and β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ij</sub> is the large scale fading coefficient between the ith RAU in the transmitter and the jth RAU in the receiver. The diversity gain in the multi-user scenario for the kth user is M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /Σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">kj</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> where M represents the number of RAUs at the transmitter. Simulation results show that when the perfect CSI assumption is satisfied, the use of BICMB results in the diversity gain values predicted by the analysis.

Diversity Analysis of Bit-Interleaved Coded Multiple Beamforming with Orthogonal Frequency Division Multiplexing

For broadband wireless communication systems, Orthogonal Frequency Division Multiplexing (OFDM) has been combined with Multi-Input Multi-Output (MIMO) techniques. Bit-Interleaved Coded Multiple Beamforming (BICMB) can achieve both spatial diversity and spatial multiplexing for flat fading MIMO channels. For frequency selective fading MIMO channels, BICMB with OFDM (BICMB-OFDM) can be applied to achieve both spatial diversity and multipath diversity, making it an important technique. However, analyzing the diversity of BICMB-OFDM is a challenging problem. In this paper, the diversity analysis of BICMB-OFDM is carried out. First, the maximum achievable diversity is derived and a full diversity condition RcSL <= 1 is proved, where Rc, S, and L are the code rate, the number of parallel steams transmitted at each subcarrier, and the number of channel taps, respectively. Then, the performance degradation due to the correlation among subcarriers is investigated. Finally, the subcarrier grouping technique is employed to combat the performance degradation and provide multi-user compatibility.

Full-Diversity Precoding Design of Bit-Interleaved Coded Multiple Beamforming with Orthogonal Frequency Division Multiplexing

Multi-Input Multi-Output (MIMO) techniques have been incorporated with Orthogonal Frequency Division Multiplexing (OFDM) for broadband wireless communication systems. Bit-Interleaved Coded Multiple Beamforming (BICMB) can achieve both spatial diversity and spatial multiplexing for flat fading MIMO channels. For frequency selective fading MIMO channels, BICMB with OFDM (BICMB-OFDM) can be employed to provide both spatial diversity and multipath diversity, making it an important technique. In our previous work, the subcarrier grouping technique was applied to combat the negative effect of subcarrier correlation. It was also proved that full diversity of BICMB-OFDM with Subcarrier Grouping (BICMB-OFDM-SG) can be achieved within the condition R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> SL ≤ 1, where R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> , S, and L are the code rate, the number of parallel streams at each subcarrier, and the number of channel taps, respectively. The full diversity condition implies that if S increases, R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> may have to decrease to maintain full diversity. As a result, increasing the number of parallel streams may not improve the total transmission rate. In this paper, the precoding technique is employed to overcome the full diversity restriction issue of R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> SL ≤ 1 for BICMB-OFDM-SG. First, the diversity analysis of precoded BICMB-OFDM-SG is carried out. Then, the full-diversity precoding design is developed with the minimum achievable decoding complexity.

Multiple Beamforming with Perfect Coding

Perfect Space-Time Block Codes (PSTBCs) achieve full diversity, full rate, nonvanishing constant minimum determinant, uniform average transmitted energy per antenna, and good shaping. However, the high decoding complexity is a critical issue for practice. When the Channel State Information (CSI) is available at both the transmitter and the receiver, Singular Value Decomposition (SVD) is commonly applied for a Multiple-Input Multiple-Output (MIMO) system to enhance the throughput or the performance. In this paper, two novel techniques, Perfect Coded Multiple Beamforming (PCMB) and Bit-Interleaved Coded Multiple Beamforming with Perfect Coding (BICMB-PC), are proposed, employing both PSTBCs and SVD with and without channel coding, respectively. With CSI at the transmitter (CSIT), the decoding complexity of PCMB is substantially reduced compared to a MIMO system employing PSTBC, providing a new prospect of CSIT. Especially, because of the special property of the generation matrices, PCMB provides much lower decoding complexity than the state-of-the-art SVD-based uncoded technique in dimensions 2 and 4. Similarly, the decoding complexity of BICMB-PC is much lower than the state-of-the-art SVD-based coded technique in these two dimensions, and the complexity gain is greater than the uncoded case. Moreover, these aforementioned complexity reductions are achieved with only negligible or modest loss in performance.

Diversity Analysis of Bit-Interleaved Coded Multiple Beamforming

In this paper, diversity analysis of bit-interleaved coded multiple beamforming (BICMB) is extended to the case of general spatial interleavers, removing a condition on their previously known design criteria. We provide a method to get diversity order, simplifying the calculation of pairwise error probability (PEP). By using the Singleton bound, we also show the maximum achievable diversity for given code rate and the number of subchannels.

Bit-Interleaved Coded Multiple Beamforming with Imperfect CSIT

This paper addresses the performance of bit-interleaved coded multiple beamforming (BICMB) [1], [2] with imperfect knowledge of beamforming vectors. Most studies for limited-rate channel state information at the transmitter (CSIT) assume that the precoding matrix has an invariance property under an arbitrary unitary transform. In BICMB, this property does not hold. On the other hand, the optimum precoder and detector for BICMB are invariant under a diagonal unitary transform. In order to design a limited-rate CSIT system for BICMB, we propose a new distortion measure optimum under this invariance. Based on this new distortion measure, we introduce a new set of centroids and employ the generalized Lloyd algorithm for codebook design. We provide simulation results demonstrating the performance improvement achieved with the proposed distortion measure and the codebook design for various receivers with linear detectors.We show that although these receivers have the same performance for perfect CSIT, their performance varies under imperfect CSIT.

Bit Interleaved Coded Multiple Beamforming

In this paper, we investigate the performance of bit-interleaved coded multiple beamforming (BICMB). We provide interleaver design criteria such that BICMB achieves full spatial multiplexing of min( N, M) and full spatial diversity of NM with N transmit and M receive antennas over quasi-static Rayleigh flat fading channels. If the channel is frequency selective, then BICMB is combined with orthogonal frequency division multiplexing (OFDM) (BICMB-OFDM) in order to combat ISI caused by the frequency-selective channels. BICMB-OFDM achieves full spatial multiplexing of min(N, M), while maintaining full spatial and frequency diversity of NML for an NtimesM system over L-tap frequency-selective channels when an appropriate convolutional code is used. Both systems analyzed in this paper assume perfect channel state information both at the transmitter and the receiver. Simulation results show that, when the perfect channel state information assumption is satisfied, BICMB and BICMB-OFDM provide substantial performance or complexity gains when compared to other spatial multiplexing and diversity systems.