On the diversity and complexity of Zero Forcing receivers for MIMO Zero Padded systems

Zero padded systems with linear receivers are shown to be robust and amenable to fast implementations in single antenna scenarios. In this paper, properties of such systems are investigated when multiple antennas are present at both ends of the communication link. In particular, their diversity and complexity are evaluated for precoded transmissions. The linear receivers are shown to exploit multipath and receive diversities, even in the absence of any coding at the transmitter. Use of additional redundancy to improve performance is considered and the effect of transmission rate on diversity order is analyzed. Low complexity implementations of Zero Forcing receivers are devised to further enhance their applicability.

An Adaptive Conditional Zero-Forcing Decoder With Full-Diversity, Least Complexity and Essentially-ML Performance for STBCs

A low complexity, essentially-ML decoding technique for the Golden code and the three antenna Perfect code was introduced by Sirianunpiboon, Howard and Calderbank. Though no theoretical analysis of the decoder was given, the simulations showed that this decoding technique has almost maximum-likelihood (ML) performance. Inspired by this technique, in this paper we introduce two new low complexity decoders for Space-Time Block Codes (STBCs)-the Adaptive Conditional Zero-Forcing (ACZF) decoder and the ACZF decoder with successive interference cancellation (ACZF-SIC), which include as a special case the decoding technique of Sirianunpiboon et al. We show that both ACZF and ACZF-SIC decoders are capable of achieving full-diversity, and we give a set of sufficient conditions for an STBC to give full-diversity with these decoders. We then show that the Golden code, the three and four antenna Perfect codes, the three antenna Threaded Algebraic Space-Time code and the four antenna rate 2 code of Srinath and Rajan are all full-diversity ACZF/ACZF-SIC decodable with complexity strictly less than that of their ML decoders. Simulations show that the proposed decoding method performs identical to ML decoding for all these five codes. These STBCs along with the proposed decoding algorithm have the least decoding complexity and best error performance among all known codes for transmit antennas. We further provide a lower bound on the complexity of full-diversity ACZF/ACZF-SIC decoding. All the five codes listed above achieve this lower bound and hence are optimal in terms of minimizing the ACZF/ACZF-SIC decoding complexity. Both ACZF and ACZF-SIC decoders are amenable to sphere decoding implementation.

Delay optimized zero-forcing channel shortening algorithm for wireless communication

In Orthogonal Frequency Division Multiplexing and Discrete Multitone transceivers, a guard interval called Cyclic Prefix (CP) is inserted to avoid inter-symbol interference. The length of the CP is usually greater than the impulse response of the channel resulting in a loss of useful data carriers. In order to avoid long CP, a time domain equalizer is used to shorten the channel. In this paper, we propose a method to include a delay in the zero-forcing equalizer and obtain an optimal value of the delay, based on the location of zeros of the channel. The performance of the algorithms is studied using numerical simulations.

Two-Stage Transmitter Precoding Based on Data-Driven Code Hopping and Partial Zero Forcing Beamforming for MC-DCMA Communications

This paper proposes a hybrid transmission technique based on adaptive code-to-user allocation and linear precoding for the downlink of phase shift keying (PSK) based multi-carrier code division multiple access (MC-CDMA) systems. The proposed scheme is based on the separation of the instantaneous multiple access interference (MAI) into constructive and destructive components taking into account the dependency on both the channel variation and the instantaneous symbol values of the active users. The first stage of the proposed technique is to adaptively distribute the available spreading sequences to the users on a symbol-by-symbol basis in the form of codehopping with the objective to steer the users' instantaneous crosscorrelations to yield a favourable constructive to destructive MAI ratio. The second stage is to employ a partial transmitter based zero forcing (ZF) scheme specifically designed for the exploitation of constructive MAI. The partial ZF processing decorrelates destructive interferers, while users that interfere constructively remain correlated. This results in a signal to interference-plus-noise ratio (SINR) enhancement without the need for additional power-per-user investment. It will be shown in the results section that significant bit error rate (BER) performance benefits can be achieved with this technique.

Performance comparison of the optimal and the zero-forcing beamforming algorithms under practical conditions

The optimal and the zero-forcing beamformers are two commonly used algorithms in the subspace-based blind beamforming technology. The optimal beamformer is regarded as the algorithm with the best output SINR. The zero-forcing algorithm emphasizes the co-channel interference cancellation. This paper compares the performance of these two algorithms under some practical conditions: the effect of the finite data length and the existence of the angle estimation error. The investigation reveals that the zero-forcing algorithm can be more robust in the practical environment than the optimal algorithm.

Spatial Modulation Aided Zero-Padded Single Carrier Transmission for Dispersive Channels

In this paper, we consider spatial modulation (SM) operating in a frequency-selective single-carrier (SC) communication scenario and propose zero-padding instead of the cyclic-prefix considered in the existing literature. We show that the zero-padded single-carrier (ZP-SC) SM system offers full multipath diversity under maximum-likelihood (ML) detection, unlike the cyclic-prefix based SM system. Furthermore, we show that the order of ML detection complexity in our proposed ZP-SC SM system is independent of the frame length and depends only on the number of multipath links between the transmitter and the receiver. Thus, we show that the zero-padding applied in the SC SM system has two advantages over the cyclic prefix: 1) achieves full multipath diversity, and 2) imposes a relatively low ML detection complexity. Furthermore, we extend the partial interference cancellation receiver (PIC-R) proposed by Guo and Xia for the detection of space-time block codes (STBCs) in order to convert the ZP-SC system into a set of narrowband subsystems experiencing flat-fading. We show that full rank STBC transmissions over these subsystems achieves full transmit, receive as well as multipath diversity for the PIC-R. Furthermore, we show that the ZP-SC SM system achieves receive and multipath diversity for the PIC-R at a detection complexity order which is the same as that of the SM system in flat-fading scenario. Our simulation results demonstrate that the symbol error ratio performance of the proposed linear receiver for the ZP-SC SM system is significantly better than that of the SM in cyclic prefix based orthogonal frequency division multiplexing as well as of the SM in the cyclic-prefixed and zero-padded single carrier systems relying on zero-forcing/minimum mean-squared error equalizer based receivers.

Novel channel tracking and equalization methods in MU-MIMO-OFDM systems

The methodology undertaken, the channel model and the system model created for developing a novel adaptive equalization method and a novel channel tracking method for uplink of MU-MIMO-OFDM systems is presented in this paper. The results show that the channel tracking method works with 97% accuracy, while the training-based initial channel estimation method shows poor performance in estimating the actual channel comparatively.

Precoder Designs for MIMO Broadcast Channels with Imperfect CSI

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Interference Alignment Algorithms for the K User Constant MIMO Interference Channel

This paper considers the degrees of freedom (DOF) for a K user multiple-input multiple-output (MIMO) M x N interference channel using interference alignment (IA). A new performance metric for evaluating the efficacy of IA algorithms is proposed, which measures the extent to which the desired signal dimensionality is preserved after zero-forcing the interference at the receiver. Inspired by the metric, two algorithms are proposed for designing the linear precoders and receive filters for IA in the constant MIMO interference channel with a finite number of symbol extensions. The first algorithm uses an eigenbeamforming method to align sub-streams of the interference to reduce the dimensionality of the interference at all the receivers. The second algorithm is iterative, and is based on minimizing the interference leakage power while preserving the dimensionality of the desired signal space at the intended receivers. The improved performance of the algorithms is illustrated by comparing them with existing algorithms for IA using Monte Carlo simulations.

Collocated and Distributed STBCs with Partial Interference Cancellation Decoding, Part I: Full-Diversity Criterion

Low complexity decoders called Partial Interference Cancellation (PIC) and PIC with Successive Interference Cancellation (PIC-SIC), which include the Zero Forcing (ZF) and ZF-SIC receivers as special cases, were given by Guo and Xia along with sufficient conditions for a Space-Time Block Code (STBC) to achieve full diversity with PIC/PIC-SIC decoding for point-to-point MIMO channels. In Part-I of this two part series of papers, we give new conditions for an STBC to achieve full diversity with PIC and PIC-SIC decoders, which are equivalent to Guo and Xia's conditions, but are much easier to check. We then show that PIC and PIC-SIC decoders are capable of achieving the full cooperative diversity available in wireless relay networks and give sufficient conditions for a Distributed Space-Time Block Code (DSTBC) to achieve full diversity with PIC and PIC-SIC decoders. In Part-II, we construct new low complexity full-diversity PIC/PIC-SIC decodable STBCs and DSTBCs that achieve higher rates than the known full-diversity low complexity ML decodable STBCs and DSTBCs.

On the generalized degrees of freedom of the K-user symmetric MIMO Gaussian interference channel

This work derives inner and outer bounds on the generalized degrees of freedom (GDOF) of the K-user symmetric MIMO Gaussian interference channel. For the inner bound, an achievable GDOF is derived by employing a combination of treating interference as noise, zero-forcing at the receivers, interference alignment (IA), and extending the Han-Kobayashi (HK) scheme to K users, depending on the number of antennas and the INR/SNR level. An outer bound on the GDOF is derived, using a combination of the notion of cooperation and providing side information to the receivers. Several interesting conclusions are drawn from the bounds. For example, in terms of the achievable GDOF in the weak interference regime, when the number of transmit antennas (M) is equal to the number of receive antennas (N), treating interference as noise performs the same as the HK scheme and is GDOF optimal. For K >; N/M+1, a combination of the HK and IA schemes performs the best among the schemes considered. However, for N/M <; K ≤ N/M+1, the HK scheme is found to be GDOF optimal.