Space-Time Coded Spatial Modulated Physical Layer Network Coding for Two-Way Relaying

Using the spatial modulation approach, where only one transmit antenna is active at a time, we propose two transmission schemes for two-way relay channel using physical layer network coding with space time coding using Coordinate Interleaved Orthogonal Designs (CIOD's). It is shown that using two uncorrelated transmit antennas at the nodes, but using only one RF transmit chain and space-time coding across these antennas can give a better performance without using any extra resources and without increasing the hardware implementation cost and complexity. In the first transmission scheme, two antennas are used only at the relay, Adaptive Network Coding (ANC) is employed at the relay and the relay transmits a CIOD Space Time Block Code (STBC). This gives a better performance compared to an existing ANC scheme for two-way relay channel which uses one antenna each at all the three nodes. It is shown that for this scheme at high SNR the average end-to-end symbol error probability (SEP) is upper bounded by twice the SEP of a point-to-point fading channel. In the second transmission scheme, two transmit antennas are used at all the three nodes, CIOD STBC's are transmitted in multiple access and broadcast phases. This scheme provides a diversity order of two for the average end-to-end SEP with an increased decoding complexity of $\mathcal{O}(M^3)$ for an arbitrary signal set and $\mathcal{O}(M^2\sqrt{M})$ for square QAM signal set.Comment: 9 pages, 7 figure

Distributed space-time block codes for two-hop wireless relay networks

Recently, the idea of space-time coding has been applied to wireless relay networks wherein a set of geographically separated relay nodes cooperate to process the received signal from the source and forward them to the destination such that the signal received at the destination appears like a Space-Time Block Code (STBC). Such STBCs (referred to as Distributed Space-Time Block Codes (DSTBCs)) when appropriately designed are known to offer spatial diversity. It is known that different classes of DSTBCs can be designed primarily depending on (i) whether the Amplify and Forward (AF) protocol or the Decode and Forward (DF) protocol is employed at the relays and (ii) whether the relay nodes are synchronized or not. In this paper, we present a survey on the problems and results associated with the design of DSTBCs for the following classes of two-hop wireless relay networks: (i) synchronous relay networks with AF protocols, (ii) asynchronous relay networks with AF protocols (iii) synchronous relay networks with DF protocols and (iv) asynchronous relay Fig. 1. Co-located MIMO channel model networks with DF protocols

Exploiting diversity in wireless channels with bit-interleaved coded modulation and iterative decoding (BICM-ID)

This dissertation studies a state-of-the-art bandwidth-efficient coded modulation technique, known as bit interleaved coded modulation with iterative decoding (BICM-ID), together with various diversity techniques to dramatically improve the performance of digital communication systems over wireless channels. For BICM-ID over a single-antenna frequency non-selective fading channel, the problem of mapping over multiple symbols, i.e., multi-dimensional (multi-D) mapping, with 8-PSK constellation is investigated. An explicit algorithm to construct a good multi-D mapping of 8-PSK to improve the asymptotic performance of BICM-ID systems is introduced. By comparing the performance of the proposed mapping with an unachievable lower bound, it is conjectured that the proposed mapping is the global optimal mapping. The superiority of the proposed mapping over the best conventional (1-dimensional complex) mapping and the multi-D mapping found previously by computer search is thoroughly demonstrated. In addition to the mapping issue in single-antenna BICM-ID systems, the use of signal space diversity (SSD), also known as linear constellation precoding (LCP), is considered in BICM-ID over frequency non-selective fading channels. The performance analysis of BICM-ID and complex N-dimensional signal space diversity is carried out to study its performance limitation, the choice of the rotation matrix and the design of a low-complexity receiver. Based on the design criterion obtained from a tight error bound, the optimality of the rotation matrix is established. It is shown that using the class of optimal rotation matrices, the performance of BICM-ID systems over a frequency non-selective Rayleigh fading channel approaches that of the BICM-ID systems over an additive white Gaussian noise (AWGN) channel when the dimension of the signal constellation increases. Furthermore, by exploiting the sigma mapping for any M-ary quadrature amplitude modulation (QAM) constellation, a very simple sub-optimal, yet effective iterative receiver structure suitable for signal constellations with large dimensions is proposed. Simulation results in various cases and conditions indicate that the proposed receiver can achieve the analytical performance bounds with low complexity. The application of BICM-ID with SSD is then extended to the case of cascaded Rayleigh fading, which is more suitable to model mobile-to-mobile communication channels. By deriving the error bound on the asymptotic performance, it is first illustrated that for a small modulation constellation, a cascaded Rayleigh fading causes a much more severe performance degradation than a conventional Rayleigh fading. However, BICM-ID employing SSD with a sufficiently large constellation can close the performance gap between the Rayleigh and cascaded Rayleigh fading channels, and their performance can closely approach that over an AWGN channel. In the next step, the use of SSD in BICM-ID over frequency selective Rayleigh fading channels employing a multi-carrier modulation technique known as orthogonal frequency division multiplexing (OFDM) is studied. Under the assumption of correlated fading over subcarriers, a tight bound on the asymptotic error performance for the general case of applying SSD over all N subcarriers is derived and used to establish the best achievable asymptotic performance by SSD. It is then shown that precoding over subgroups of at least L subcarriers per group, where L is the number of channel taps, is sufficient to obtain this best asymptotic error performance, while significantly reducing the receiver complexity. The optimal joint subcarrier grouping and rotation matrix design is subsequently determined by solving the Vandermonde linear system. Illustrative examples show a good agreement between various analytical and simulation results. Further, by combining the ideas of multi-D mapping and subcarrier grouping, a novel power and bandwidth-efficient bit-interleaved coded modulation with OFDM and iterative decoding (BI-COFDM-ID) in which multi-D mapping is performed over a group of subcarriers for broadband transmission in a frequency selective fading environment is proposed. A tight bound on the asymptotic error performance is developed, which shows that subcarrier mapping and grouping have independent impacts on the overall error performance, and hence they can be independently optimized. Specifically, it is demonstrated that the optimal subcarrier mapping is similar to the optimal multi-D mapping for BICM-ID in frequency non-selective Rayleigh fading environment, whereas the optimal subcarrier grouping is the same with that of OFDM with SSD. Furthermore, analytical and simulation results show that the proposed system with the combined optimal subcarrier mapping and grouping can achieve the full channel diversity without using SSD and provide significant coding gains as compared to the previously studied BI-COFDM-ID with the same power, bandwidth and receiver complexity. Finally, the investigation is extended to the application of BICM-ID over a multiple-input multiple-output (MIMO) system equipped with multiple antennas at both the transmitter and the receiver to exploit both time and spatial diversities, where neither the transmitter nor the receiver knows the channel fading coefficients. The concentration is on the class of unitary constellation, due to its advantages in terms of both information-theoretic capacity and error probability. The tight error bound with respect to the asymptotic performance is also derived for any given unitary constellation and mapping rule. Design criteria regarding the choice of unitary constellation and mapping are then established. Furthermore, by using the unitary constellation obtained from orthogonal design with quadrature phase-shift keying (QPSK or 4-PSK) and 8-PSK, two different mapping rules are proposed. The first mapping rule gives the most suitable mapping for systems that do not implement iterative processing, which is similar to a Gray mapping in coherent channels. The second mapping rule yields the best mapping for systems with iterative decoding. Analytical and simulation results show that with the proposed mappings of the unitary constellations obtained from orthogonal designs, the asymptotic error performance of the iterative systems can closely approach a lower bound which is applicable to any unitary constellation and mapping

Generalized Silver Codes

For an $n_t$ transmit, $n_r$ receive antenna system ($n_t \times n_r$ system), a {\it{full-rate}} space time block code (STBC) transmits $n_{min} = min(n_t,n_r)$ complex symbols per channel use. The well known Golden code is an example of a full-rate, full-diversity STBC for 2 transmit antennas. Its ML-decoding complexity is of the order of $M^{2.5}$ for square $M$-QAM. The Silver code for 2 transmit antennas has all the desirable properties of the Golden code except its coding gain, but offers lower ML-decoding complexity of the order of $M^2$. Importantly, the slight loss in coding gain is negligible compared to the advantage it offers in terms of lowering the ML-decoding complexity. For higher number of transmit antennas, the best known codes are the Perfect codes, which are full-rate, full-diversity, information lossless codes (for $n_r \geq n_t$) but have a high ML-decoding complexity of the order of $M^{n_tn_{min}}$ (for $n_r < n_t$, the punctured Perfect codes are considered). In this paper, a scheme to obtain full-rate STBCs for $2^a$ transmit antennas and any $n_r$ with reduced ML-decoding complexity of the order of $M^{n_t(n_{min}-(3/4))-0.5}$, is presented. The codes constructed are also information lossless for $n_r \geq n_t$, like the Perfect codes and allow higher mutual information than the comparable punctured Perfect codes for $n_r < n_t$. These codes are referred to as the {\it generalized Silver codes}, since they enjoy the same desirable properties as the comparable Perfect codes (except possibly the coding gain) with lower ML-decoding complexity, analogous to the Silver-Golden codes for 2 transmit antennas. Simulation results of the symbol error rates for 4 and 8 transmit antennas show that the generalized Silver codes match the punctured Perfect codes in error performance while offering lower ML-decoding complexity.Comment: Accepted for publication in the IEEE Transactions on Information Theory. This revised version has 30 pages, 7 figures and Section III has been completely revise