Polynomial matrix decomposition techniques for frequency selective MIMO channels

For a narrowband, instantaneous mixing multi-input, multi-output (MIMO) communications system, the channel is represented as a scalar matrix. In this scenario, singular value decomposition (SVD) provides a number of independent spatial subchannels which can be used to enhance data rates or to increase diversity. Alternatively, a QR decomposition can be used to reduce the MIMO channel equalization problem to a set of single channel equalization problems. In the case of a frequency selective MIMO system, the multipath channel is represented as a polynomial matrix. Thus conventional matrix decomposition techniques can no longer be applied. The traditional solution to this broadband problem is to reduce it to narrowband form by using a discrete Fourier transform (DFT) to split the broadband channel into N narrow uniformly spaced frequency bands and applying scalar decomposition techniques within each band. This describes an orthogonal frequency division multiplexing (OFDM) based system. However, a novel algorithm has been developed for calculating the eigenvalue decomposition of a para-Hermitian polynomial matrix, known as the sequential best rotation (SBR2) algorithm. SBR2 and its QR based derivatives allow a true polynomial singular value and QR decomposition to be formulated. The application of these algorithms within frequency selective MIMO systems results in a fundamentally new approach to exploiting spatial diversity. Polynomial matrix decomposition and OFDM based solutions are compared for a wide variety of broadband MIMO communication systems. SVD is used to create a robust, high gain communications channel for ultra low signal-to-noise ratio (SNR) environments. Due to the frequency selective nature of the channels produced by polynomial matrix decomposition, additional processing is required at the receiver resulting in two distinct equalization techniques based around turbo and Viterbi equalization. The proposed approach is found to provide identical performance to that of an existing OFDM scheme while supporting a wider range of access schemes. This work is then extended to QR decomposition based communications systems, where the proposed polynomial approach is found to not only provide superior bit-error-rate (BER) performance but significantly reduce the complexity of transmitter design. Finally both techniques are combined to create a nulti-user MIMO system that provides superior BER performance over an OFDM based scheme. Throughout the work the robustness of the proposed scheme to channel state information (CSI) error is considered, resulting in a rigorous demonstration of the capabilities of the polynomial approach

Waveforms and channel coding for 5G

Abstract. The fifth generation (5G) communication systems are required to perform significantly better than the existing fourth generation (4G) systems in data rate, capacity, coverage, latency, energy consumption and cost. Hence, 5G needs to achieve considerable enhancements in the areas of bandwidth, spectral, energy, and signaling efficiencies and cost per bit. The new radio access technology (RAT) of 5G physical layer needs to utilize an efficient waveform to meet the demands of 5G. Orthogonal frequency division multiplexing (OFDM) is considered as a baseline for up to 30 GHz. However, a major drawback of OFDM systems is their large peak to average power ratio (PAPR). Here in this thesis, a simple selective-mapping (SLM) technique using scrambling is proposed to reduce the PAPR of OFDM signals. This technique selects symbol sequences with high PAPR and scrambles them until a PAPR sequence below a specific threshold is generated. The computational complexity of the proposed scheme is considerably lower than that of the traditional SLM. Also, performance of the system is investigated through simulations and more than 4.5 dB PAPR reduction is achieved. In addition, performance of single carrier waveforms is analyzed in multiple-input multiple-output (MIMO) systems as an alternative to OFDM. Performance of a single carrier massive MIMO system is presented for both uplink and downlink with single user and multiple user cases and the effect of pre-coding on the PAPR is studied. A variety of channel configurations were investigated such as correlated channels, practical channels and the channels with errors in channel estimate. Furthermore, the candidate coding schemes are investigated for the new RAT in the 5G standard corresponding the activities in the third generation partnership project (3GPP). The schemes are evaluated in terms of block error rate (BLER), bit error rate (BER), computational complexity, and flexibility. These parameters comprise a suitable set to assess the performance of different services and applications. Turbo, low density parity check (LDPC), and polar codes are considered as the candidate schemes. These are investigated in terms of obtaining suitable rates, block lengths by proper design for a fair comparison. The simulations have been carried out in order to obtain BLER / BER performance for various code rates and block lengths, in additive white Gaussian noise (AWGN) channel. Although polar codes perform well at short block lengths, LDPC has a relatively good performance at all the block lengths and code rates. In addition, complexity of the LDPC codes is relatively low. Furthermore, BLER/BER performances of the coding schemes in Rayleigh fading channels are investigated and found that the fading channel performance follows a similar trend as the performance in the AWGN channel

Evaluation of Overlay/underlay Waveform via SD-SMSE Framework for Enhancing Spectrum Efficiency

Recent studies have suggested that spectrum congestion is mainly due to the inefficient use of spectrum rather than its unavailability. Dynamic Spectrum Access (DSA) and Cognitive Radio (CR) are two terminologies which are used in the context of improved spectrum efficiency and usage. The DSA concept has been around for quite some time while the advent of CR has created a paradigm shift in wireless communications and instigated a change in FCC policy towards spectrum regulations. DSA can be broadly categorized as using a 1) Dynamic Exclusive Use Model, 2) Spectrum Commons or Open sharing model or 3) Hierarchical Access model. The hierarchical access model envisions primary licensed bands, to be opened up for secondary users, while inducing a minimum acceptable interference to primary users. Spectrum overlay and spectrum underlay technologies fall within the hierarchical model, and allow primary and secondary users to coexist while improving spectrum efficiency. Spectrum overlay in conjunction with the present CR model considers only the unused (white) spectral regions while in spectrum underlay the underused (gray) spectral regions are utilized. The underlay approach is similar to ultra wide band (UWB) and spread spectrum (SS) techniques utilize much wider spectrum and operate below the noise floor of primary users. Software defined radio (SDR) is considered a key CR enabling technology. Spectrally modulated, Spectrally encoded (SMSE) multi-carrier signals such as Orthogonal Frequency Domain Multiplexing (OFDM) and Multi-carrier Code Division Multiple Access (MCCDMA) are hailed as candidate CR waveforms. The SMSE structure supports and is well-suited for SDR based CR applications. This work began by developing a general soft decision (SD) CR framework, based on a previously developed SMSE framework that combines benefits of both the overlay and underlay techniques to improve spectrum efficiency and maximizing the channel capacity. The resultant SD-SMSE framework provides a user with considerable flexibility to choose overlay, underlay or hybrid overlay/underlay waveform depending on the scenario, situation or need. Overlay/Underlay SD-SMSE framework flexibility is demonstrated by applying it to a family of SMSE modulated signals such as OFDM, MCCDMA, Carrier Interferometry (CI) MCCDMA and Transform Domain Communication System (TDCS). Based on simulation results, a performance analysis of Overlay, Underlay and hybrid Overlay/Underlay waveforms are presented. Finally, the benefits of combining overlay/underlay techniques to improve spectrum efficiency and maximize channel capacity are addressed