Hybrid beamforming (HB) has been widely studied for reducing the number of costly radio frequency (RF) chains in massive multiple-input multiple-output (MIMO) systems. However, previous works on HB are limited to a single user equipment (UE) or a single group of UEs, employing the frequency-flat first-level analog beamforming (AB) that cannot be applied to multiple groups of UEs served in different frequency resources in an orthogonal frequency-division multiplexing (OFDM) system. In this paper, a novel HB algorithm with unified AB based on the spatial covariance matrix (SCM) knowledge of all UEs is proposed for a massive MIMO-OFDM system in order to support multiple groups of UEs. The proposed HB method with a much smaller number of RF chains can achieve more than 95% performance of full digital beamforming. In addition, a novel practical subspace construction (SC) algorithm based on partial channel state information is proposed to estimate the required SCM. The proposed SC method can offer more than 97% performance of the perfect SCM case. With the proposed methods, significant cost and power savings can be achieved without large loss in performance. Furthermore, the proposed methods can be applied to massive MIMO-OFDM systems in both time-division duplex and frequency-division duplex.

Massive Multiple-Input Multiple-Output (MIMO) systems, dense Small-Cells (SCs), and full duplexing are three candidates for next-generation wireless systems. The cooperation of the three techniques could offer more benefits, e.g., SC in-band wireless backhaul in massive MIMO systems. In this paper, three strategies of SC in-band wireless backhaul in massive MIMO systems are introduced and compared. Simulation results show that SC in-band wireless backhaul has the potential to improve the throughput for massive MIMO systems, and applying full-duplexing techniques at SCs could provide greater gain.

Zero-Forcing (ZF) has been considered as one of the potential practical precoding and detection method for massive MIMO systems. One of the most important advantages of massive MIMO is the capability of supporting a large number of users in the same time-frequency resource, which requires much larger dimensions of matrix inversion for ZF than conventional multi-user MIMO systems. In this case, Neumann Series (NS) has been considered for the Matrix Inversion Approximation (MIA), because of its suitability for massive MIMO systems and its advantages in hardware implementation. The performance-complexity trade-off and the hardware implementation of NS-based MIA in massive MIMO systems have been discussed. In this paper, we analyze the effects of the ratio of the number of massive MIMO antennas to the number of users on the performance of NS-based MIA. In addition, we derive the approximation error estimation formulas for different practical numbers of terms of NS-based MIA. These results could offer useful guidelines for practical massive MIMO systems.

The demand for data service is increasing dramatically and wireless systems with high throughput and the capability to serve a large number of User Equipments (UEs) are desired. The massive MIMO system is considered as one of the most promising systems for the fifth generation of mobile telecommunication technology. Compared to conventional wireless systems, the spectrum efficiency of massive MIMO can be increased by an order of magnitude as tens of UEs can be served on the same time-frequency resource by exploring spatial multiplexing. Though extensively studied, massive MIMO still faces tough practical issues, such as excessive cost for fronthaul, channel estimation, beamforming matrix calculation within the latency requirement, signal quality at the deep fading zones or cell edge, etc. This paper presents a repeater-enhanced massive MIMO system with improved channel quality and reduced fronthaul cost, where Amplify-and-Forward Repeaters (AFRs) are employed without additional baseband processing at the base station or UEs. The disadvantages of AFRs, such as extra delay, increased delay spread and compromised channel reciprocity, are discussed and the corresponding solutions are suggested. Performances of different beamforming methods are analyzed and verified by simulations.

The millimeter Wave (mmWave) is considered as a promising technology of the future fifth-generation wireless systems due to the currently underutilized multi-GHz spectrum surrounding the 60GHz carrier frequency, particularly with the recent advances in low cost sub-terahertz semiconductor circuitry. Since the mmWave suffers high attenuation during transmission, the repeater is a key technique to enable mmWave systems with seamless coverage. This paper considers the following practical design issues of Amplified-and-Forward Repeater (AFR) enhanced mmWave systems. First, the distribution of excess delay through multiple AFR hops is derived, which helps the design of cyclic-prefix length to avoid inter-symbol interference in orthogonal frequency division multiplexing systems. In addition, we show that the AFR decreases the channel coherence bandwidth and then propose a novel AFR design with a finite impulse response filter based channel equalizer to address this problem. Simulation results show that the proposed method is able to significantly increase channel coherence bandwidth and effectively reduce bit error rate.

Massive multiple-input multiple-output (MIMO) systems, dense small-cells (SCs), and full duplex are three candidate techniques for next-generation communication systems. The cooperation of next-generation techniques could offer more benefits, e.g., SC in-band wireless backhaul in massive MIMO systems. In this paper, three strategies of SC in-band wireless backhaul in massive MIMO systems are introduced and compared, i.e., complete time-division duplex (CTDD), zero-division duplex (ZDD), and ZDD with interference rejection (ZDD-IR). Simulation results demonstrate that SC in-band wireless backhaul has the potential to improve the throughput for massive MIMO systems. Specifically, among the three strategies, CTDD is the simplest one and could achieve decent throughput improvement. Depending on conditions, with the self-interference cancellation capability at SCs, ZDD could achieve better throughput than CTDD, even with residual self-interference. Moreover, ZDD-IR requires the additional interference rejection process at the BS compared to ZDD, but it could generally achieve better throughput than CTDD and ZDD.

For Multiple-Input Multiple-Output (MIMO) systems with frequency selective fading channels, Bit-Interleaved Coded Multiple Beamforming (BICMB) with Orthogonal Frequency Division Multiplexing (OFDM) can offer both spatial and multipath diversity, making it an important technique. It was proved that full diversity of BICMB-OFDM can be achieved with a condition of RcSL ≤ 1, where Rc, S, and L are the code rate, the number of parallel streams at each subcarrier, and the number of channel taps, respectively. In this paper, the precoding technique is applied to overcome the full diversity restriction with the minimum achievable decoding complexity.

For Multiple-Input Multiple-Output (MIMO) systems with frequency selective fading channels, Bit-Interleaved Coded Multiple Beamforming (BICMB) with Orthogonal Frequency Division Multiplexing (OFDM) can be employed to offer both spatial and multipath diversity, making it an important technique. Nevertheless, analyzing its diversity 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 is proved. Then, the performance degradation due to the subcarrier correlation is investigated. Finally, the subcarrier grouping technique is applied to combat the performance degradation and provide multi-user compatibility.

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 RcSL ≤ 1, where Rc, 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, Rcmay 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 RcSL ≤ 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.

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.

When the Channel State Information (CSI) is known by both the transmitter and the receiver, beamforming techniques employing Singular Value Decomposition (SVD) are commonly used in Multiple-Input Multiple-Output (MIMO) systems. Without channel coding, there is a trade-off between full diversity and full multiplexing. When channel coding is added, both of them can be achieved as long as the code rate Rcand the number of employed subchannels S satisfy the condition RcS ≤1. By adding a properly designed constellation precoder, both full diversity and full multiplexing can be achieved for both uncoded and coded systems with the trade-off of a higher decoding complexity, e.g., Fully Precoded Multiple Beamforming (FPMB) and Bit-Interleaved Coded Multiple Beamforming with Full Precoding (BICMB-FP) without the condition RcS ≤1. Recently discovered Perfect Space-Time Block Code (PSTBC) is a full-rate full-diversity space-time code, which achieves efficient shaping and high coding gain for MIMO systems. In this paper, a new technique, Bit-Interleaved Coded Multiple Beamforming with Perfect Coding (BICMB-PC), is introduced. BICMB-PC transmits PSTBCs through convolutional coded SVD systems. Similarly to BICMB-FP, BICMB-PC achieves both full diversity and full multiplexing, and its performance is almost the same as BICMB-FP. The advantage of BICMB-PC is that it can provide a much lower decoding complexity than BICMB-FP, since the real and imaginary parts of the received signal can be separated for BICMB-PC of dimensions 2 and 4, and only the part corresponding to the coded bit is required to acquire one bit metric for the Viterbi decoder.

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.

In Multiple-Input Multiple-Output (MIMO) systems, Sphere Decoding (SD) can achieve performance equivalent to full search Maximum Likelihood (ML) decoding with reduced complexity. Several researchers reported techniques that reduce the complexity of SD further. In this paper, a new technique is introduced which decreases the computational complexity of SD substantially, without sacrificing performance. The reduction is accomplished by deconstructing the decoding metric to decrease the number of computations and exploiting the structure of a lattice representation. Simulation results show that this approach achieves substantial gains for the average number of real multiplications and real additions needed to decode one transmitted vector symbol. As an example, for a 4 × 4 MIMO system, the gains in the number of multiplications are 85% with 4-QAM and 90% with 64-QAM, at low SNR.

Multiple beamforming is realized by singular value decomposition of the channel matrix which is assumed to be known to both the transmitter and the receiver. Bit-Interleaved Coded Multiple Beamforming (BICMB) can achieve full diversity as long as the code rate Rcand the number of employed subchannels S satisfy the condition RcS ≤ 1. Bit-Interleaved Coded Multiple Beamforming with Constellation Precoding (BICMB-CP), on the other hand, can achieve full diversity without the condition RcS ≤ 1. However, the decoding complexity of BICMB-CP is much higher than BICMB. In this paper, a reduced complexity decoding technique, which is based on Sphere Decoding (SD), is proposed to reduce the complexity of Maximum Likelihood (ML) decoding for BICMB-CP. The decreased complexity decoding achieves several orders of magnitude reduction, in terms of the average number of real multiplications needed to acquire one precoded bit metric, not only with respect to conventional ML decoding, but also, with respect to conventional SD.

Beamforming techniques that employ Singular Value Decomposition (SVD) are commonly used in Multi-Input Multi-Output (MIMO) wireless communication systems. In the absence of channel coding, when a single symbol is transmitted, these systems achieve the full diversity order provided by the channel; whereas when multiple symbols are simultaneously transmitted, this property is lost. When channel coding is employed, full diversity order can be achieved. For example, when Bit-Interleaved Coded Modulation (BICM) is combined with this technique, full diversity order of NM in an M x N MIMO channel transmitting S parallel streams is possible, provided a condition on S and the BICM convolutional code rate is satisfied. In this paper, we present constellation precoded multiple beamforming which can achieve the full diversity order both with BICM-coded and uncoded SVD systems. We provide an analytical proof of this property. To reduce the computational complexity of Maximum Likelihood (ML) decoding in this system, we employ Sphere Decoding (SD). We report an SD technique that reduces the computational complexity beyond commonly used approaches to SD. This technique achieves several orders of magnitude reduction in computational complexity not only with respect to conventional ML decoding but also, with respect to conventional SD.

ABSTRACT In multiple‐input multiple‐output (MIMO) systems, sphere decoding (SD) can achieve a performance equivalent to a full‐search maximum likelihood decoding, with reduced complexity. Several researchers reported techniques that reduce the complexity of SD further. In this paper, a new technique that decreases the computational complexity of SD substantially, without sacrificing performance, is introduced. The reduction is accomplished by deconstructing the decoding metric to decrease the number of computations and by exploiting the structure of a lattice representation. Furthermore, an application of SD employing a proposed smart implementation with very low computational complexity is introduced. This application calculates the soft bit metrics of a bit‐interleaved convolutional‐coded MIMO system in an efficient manner. On the basis of the reduced complexity SD, the proposed smart implementation employs the initial radius acquired by zero‐forcing decision feedback equalization, which ensures no empty spheres. Other than that, a technique of a particular data structure is also incorporated to efficiently reduce the number of executions carried out by SD. Simulation results show that these approaches achieve substantial gains in terms of the computational complexity for both uncoded and coded MIMO systems. Copyright © 2011 John Wiley & Sons, Ltd.

The Golden Code is a full-rate full-diversity space-time code, which achieves maximum coding gain for Multiple-Input Multiple-Output (MIMO) systems with two transmit and two receive antennas. Since four information symbols taken from an M-QAM constellation are selected to construct one Golden Code codeword, a maximum likelihood decoder using sphere decoding has the worst-case complexity of O(M4), when the Channel State Information (CSI) is available at the receiver. Previously, this worst-case complexity was reduced to O(M2.5) without performance degradation. When the CSI is known by the transmitter as well as the receiver, beamforming techniques that employ singular value decomposition are commonly used in MIMO systems. In the absence of channel coding, when a single symbol is transmitted, these systems achieve the full diversity order provided by the channel. Whereas this property is lost when multiple symbols are simultaneously transmitted. However, uncoded multiple beamforming can achieve the full diversity order by adding a properly designed constellation precoder. For 2 × 2 Fully Precoded Multiple Beamforming (FPMB), the general worst-case decoding complexity is O(M). In this paper, Golden Coded Multiple Beamforming (GCMB) is proposed, which transmits the Golden Code through 2 × 2 multiple beamforming. GCMB achieves the full diversity order and its performance is similar to general MIMO systems using the Golden Code and FPMB, whereas the worst-case decoding complexity of O(√(M)) is much lower. The extension of GCMB to larger dimensions is also discussed.