L2 Orthogonal Space Time Code for Continuous Phase Modulation

To combine the high power efficiency of Continuous Phase Modulation (CPM) with either high spectral efficiency or enhanced performance in low Signal to Noise conditions, some authors have proposed to introduce CPM in a MIMO frame, by using Space Time Codes (STC). In this paper, we address the code design problem of Space Time Block Codes combined with CPM and introduce a new design criterion based on L2 orthogonality. This L2 orthogonality condition, with the help of simplifying assumption, leads, in the 2x2 case, to a new family of codes. These codes generalize the Wang and Xia code, which was based on pointwise orthogonality. Simulations indicate that the new codes achieve full diversity and a slightly better coding gain. Moreover, one of the codes can be interpreted as two antennas fed by two conventional CPMs using the same data but with different alphabet sets. Inspection of these alphabet sets lead also to a simple explanation of the (small) spectrum broadening of Space Time Coded CPM

Full Rate L2-Orthogonal Space-Time CPM for Three Antennas

To combine the power efficiency of Continuous Phase Modulation (CPM) with enhanced performance in fading environments, some authors have suggested to use CPM in combination with Space-Time Codes (STC). Recently, we have proposed a CPM ST-coding scheme based on L2-orthogonality for two transmitting antennas. In this paper we extend this approach to the three antennas case. We analytically derive a family of coding schemes which we call Parallel Code (PC). This code family has full rate and we prove that the proposed coding scheme achieves full diversity as confirmed by accompanying simulations. We detail an example of the proposed ST codes that can be interpreted as a conventional CPM scheme with different alphabet sets for the different transmit antennas which results in a simplified implementation. Thanks to L2-orthogonality, the decoding complexity, usually exponentially proportional to the number of transmitting antennas, is reduced to linear complexity

L2 OSTC-CPM: Theory and design

The combination of space-time coding (STC) and continuous phase modulation (CPM) is an attractive field of research because both STC and CPM bring many advantages for wireless communications. Zhang and Fitz [1] were the first to apply this idea by constructing a trellis based scheme. But for these codes the decoding effort grows exponentially with the number of transmitting antennas. This was circumvented by orthogonal codes introduced by Wang and Xia [2]. Unfortunately, based on Alamouti code [3], this design is restricted to two antennas. However, by relaxing the orthogonality condition, we prove here that it is possible to design L2-orthogonal space-time codes which achieve full rate and full diversity with low decoding effort. In part one, we generalize the two-antenna code proposed by Wang and Xia [2] from pointwise to L2-orthogonality and in part two we present the first L2-orthogonal code for CPM with three antennas. In this report, we detail these results and focus on the properties of these codes. Of special interest is the optimization of the bit error rate which depends on the initial phase of the system. Our simulation results illustrate the systemic behavior of these conditions

Separable Implementation of L2-Orthogonal STC CPM with Fast Decoding

In this paper we present an alternative separable implementation of L2-orthogonal space-time codes (STC) for continuous phase modulation (CPM). In this approach, we split the STC CPM transmitter into a single conventional CPM modulator and a correction filter bank. While the CPM modulator is common to all transmit antennas, the correction filter bank applies different correction units to each antenna. Thereby desirable code properties as orthogonality and full diversity are achievable with just a slightly larger bandwidth demand. This new representation has three main advantages. First, it allows to easily generalize the orthogonality condition to any arbitrary number of transmit antennas. Second, for a quite general set of correction functions that we detail, it can be proved that full diversity is achieved. Third, by separating the modulation and correction steps inside the receiver, a simpler receiver can be designed as a bank of data independent inverse correction filters followed by a single CPM demodulator. Therefore, in this implementation, only one correlation filter bank for the detection of all transmitted signals is necessary. The decoding effort grows only linearly with the number of transmit antennas

Capacity -based parameter optimization of bandwidth constrained CPM

Continuous phase modulation (CPM) is an attractive modulation choice for bandwidth limited systems due to its small side lobes, fast spectral decay and the ability to be noncoherently detected. Furthermore, the constant envelope property of CPM permits highly power efficient amplification. The design of bit-interleaved coded continuous phase modulation is characterized by the code rate, modulation order, modulation index, and pulse shape. This dissertation outlines a methodology for determining the optimal values of these parameters under bandwidth and receiver complexity constraints. The cost function used to drive the optimization is the information-theoretic minimum ratio of energy-per-bit to noise-spectral density found by evaluating the constrained channel capacity. The capacity can be reliably estimated using Monte Carlo integration. A search for optimal parameters is conducted over a range of coded CPM parameters, bandwidth efficiencies, and channels. Results are presented for a system employing a trellis-based coherent detector. To constrain complexity and allow any modulation index to be considered, a soft output differential phase detector has also been developed.;Building upon the capacity results, extrinsic information transfer (EXIT) charts are used to analyze a system that iterates between demodulation and decoding. Convergence thresholds are determined for the iterative system for different outer convolutional codes, alphabet sizes, modulation indices and constellation mappings. These are used to identify the code and modulation parameters with the best energy efficiency at different spectral efficiencies for the AWGN channel. Finally, bit error rate curves are presented to corroborate the capacity and EXIT chart designs

New Classes of Partial Geometries and Their Associated LDPC Codes

The use of partial geometries to construct parity-check matrices for LDPC codes has resulted in the design of successful codes with a probability of error close to the Shannon capacity at bit error rates down to $10^{-15}$. Such considerations have motivated this further investigation. A new and simple construction of a type of partial geometries with quasi-cyclic structure is given and their properties are investigated. The trapping sets of the partial geometry codes were considered previously using the geometric aspects of the underlying structure to derive information on the size of allowable trapping sets. This topic is further considered here. Finally, there is a natural relationship between partial geometries and strongly regular graphs. The eigenvalues of the adjacency matrices of such graphs are well known and it is of interest to determine if any of the Tanner graphs derived from the partial geometries are good expanders for certain parameter sets, since it can be argued that codes with good geometric and expansion properties might perform well under message-passing decoding.Comment: 34 pages with single column, 6 figure

A low complexity distributed differential scheme based on orthogonal space time block coding for decode-and-forward wireless relay networks

This work proposes a new differential cooperative diversity scheme with high data rate and low decoding complexity using the decode-and-forward protocol. The proposed model does not require either differential encoding or channel state information at the source node, relay nodes, or destination node where the data sequence is directly transmitted and the differential detection method is applied at the relay nodes and the destination node. The proposed technique enjoys a low encoding and decoding complexity at the source node, the relay nodes, and the destination node. Furthermore, the performance of the proposed strategy is analyzed by computer simulations in quasi-static Rayleigh fading channel and using the decode-and-forward protocol. The simulation results show that the proposed differential technique outperforms the corresponding reference strategies

Quasi-Orthogonal Space-Time Block Coding Using Polynomial Phase Modulation

Recently, polynomial phase modulation (PPM) was shown to be a power- and bandwidth-efficient modulation format. These two characteristics are in high demand nowadays specially in mobile applications, where devices with size, weight, and power (SWaP) constraints are common. In this paper, we propose implementing a full-diversity quasiorthogonal space-time block code (QOSTBC) using polynomial phase signals as modulation format. QOSTBCs along with PPM are used in order to improve the power efficiency of communication systems with four transmit antennas. We obtain the optimal PPM constellations that ensure full diversity and maximize the QOSTBC\u27s minimum coding gain distance. Simulation results show that by using QOSTBCs along with a properly selected PPM constellation, full diversity in flat fading channels and thus low BER at high signal-to-noise ratios (SNR) can be ensured. More importantly, it is also shown that QOSTBCs using PPM achieve a better error performance than those using conventional modulation formats