Designing structured tight frames via an alternating projection method

Tight frames, also known as general Welch-bound- equality sequences, generalize orthonormal systems. Numerous applications - including communications, coding, and sparse approximation- require finite-dimensional tight frames that possess additional structural properties. This paper proposes an alternating projection method that is versatile enough to solve a huge class of inverse eigenvalue problems (IEPs), which includes the frame design problem. To apply this method, one needs only to solve a matrix nearness problem that arises naturally from the design specifications. Therefore, it is the fast and easy to develop versions of the algorithm that target new design problems. Alternating projection will often succeed even if algebraic constructions are unavailable. To demonstrate that alternating projection is an effective tool for frame design, the paper studies some important structural properties in detail. First, it addresses the most basic design problem: constructing tight frames with prescribed vector norms. Then, it discusses equiangular tight frames, which are natural dictionaries for sparse approximation. Finally, it examines tight frames whose individual vectors have low peak-to-average-power ratio (PAR), which is a valuable property for code-division multiple-access (CDMA) applications. Numerical experiments show that the proposed algorithm succeeds in each of these three cases. The appendices investigate the convergence properties of the algorithm

On receiver design for low density signature OFDM (LDS-OFDM)

Low density signature orthogonal frequency division multiplexing (LDS-OFDM) is an uplink multi-carrier multiple access scheme that uses low density signatures (LDS) for spreading the symbols in the frequency domain. In this paper, we introduce an effective receiver for the LDS-OFDM scheme. We propose a framework to analyze and design this iterative receiver using extrinsic information transfer (EXIT) charts. Furthermore, a turbo multi-user detector/decoder (MUDD) is proposed for the LDS-OFDM receiver. We show how the turbo MUDD is tuned using EXIT charts analysis. By tuning the turbo-style processing, the turbo MUDD can approach the performance of optimum MUDD with a smaller number of inner iterations. Using the suggested design guidelines in this paper, we show that the proposed structure brings about 2.3 dB performance improvement at a bit error rate (BER) equal to 10-5 over conventional LDS-OFDM while keeping the complexity affordable. Simulations for different scenarios also show that the LDS-OFDM outperforms similar well-known multiple access techniques such as multi-carrier code division multiple access (MC-CDMA) and group-orthogonal MC-CDMA

Asymptotically Locally Optimal Weight Vector Design for a Tighter Correlation Lower Bound of Quasi-Complementary Sequence Sets

A quasi-complementary sequence set (QCSS) refers to a set of two-dimensional matrices with low nontrivial aperiodic auto- and cross-correlation sums. For multicarrier code-division multiple-access applications, the availability of large QCSSs with low correlation sums is desirable. The generalized Levenshtein bound (GLB) is a lower bound on the maximum aperiodic correlation sum of QCSSs. The bounding expression of GLB is a fractional quadratic function of a weight vector w and is expressed in terms of three additional parameters associated with QCSS: the set size K, the number of channels M, and the sequence length N. It is known that a tighter GLB (compared to the Welch bound) is possible only if the condition M ≥ 2 and K ≥ K̅ + 1, where K̅ is a certain function of M and N, is satisfied. A challenging research problem is to determine if there exists a weight vector that gives rise to a tighter GLB for all (not just some) K ≥ K̅ + 1 and M ≥ 2, especially for large N, i.e., the condition is asymptotically both necessary and sufficient. To achieve this, we analytically optimize the GLB which is (in general) nonconvex as the numerator term is an indefinite quadratic function of the weight vector. Our key idea is to apply the frequency domain decomposition of the circulant matrix (in the numerator term) to convert the nonconvex problem into a convex one. Following this optimization approach, we derive a new weight vector meeting the aforementioned objective and prove that it is a local minimizer of the GLB under certain conditions

The effect of quantized ETF, grouping, and power allocation on non-orthogonal multiple accesses for wireless communication networks

Nonorthogonal multiple access (NOMA) is a significant technology in radio resource sharing and it has been recognized as a favorable method in fifth-generation (5G) wireless networks to meet the requirements of system capacity, service latency, and user connectivity. Many schemes for NOMA have been proposed in the last few years. such as transmitter linear spreading-based NOMA as a code domain, as well as a linear minimum mean square error (LMMSE), parallel interference cancellation (PIC), and serial interference cancellation (SIC) with power allocation and grouping as a power domain at the receiver side for uplink NOMA. This work aims to evaluate the performance of multiple types of linear spreading-based NOMA schemes. Simulations are achieved for the error-rate performance evaluation of these NOMA schemes, received signal after detection, and received signal and effect of every user on the other. Evaluating the performance of these technologies with comparison is also achieved through using grouping and power allocation. Simulations are achieved for the sum rate and spectral efficiency. For the future, 5G NOMA development, an equiangular tight frame (ETF) is suggested for improving performance and suggests grouping with 64qam-quantized Grassmannian for improving performance favorite about grouping with Generalized welch-bound equality (GWBE