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This study investigates the optimal tracking performance of multiple-input multiple-output linear time-invariant systems over a noisy channel in the feedback path. The communication channel is also subject to data dropouts, which was modelled as a binary stochastic process. The problem under consideration amounts to determining the minimal error in tracking a Brownian motion random process, which emulates a step reference signal in the deterministic setting. With the unity feedback and two-parameter control structure, a lower bound and an exact expression of optimal tracking performance are obtained respectively. It is shown how the noise may degenerate the tracking performance and how the data dropouts effect may intertwine with unstable poles and non-minimum phase zeros, including the location and direction, which are intrinsic characteristics of the plant. Finally, computer simulations are provided to illustrate the analytical results obtained.

A simple and efficient search method based on the coset concept is proposed to construct (3, L) quasi-cyclic low-density parity-check (QC-LDPC) codes without small cycles. Compared with the random search method, the chance to find large-girth codes is remarkably increased for the new method. Compared with Tanner's construction, the proposed method is much more flexible in the selection of row weight L. Some new codes are constructed with the shortest lengths compared with those constructed by the existing well-known methods. Simulation results show that the novel codes with moderate length perform well in the additive white Gaussian noise channel.

In this study, we analyse the error performance of decode and forward (DF) and amplify and forward (AF) multi-way relay networks (MWRNs). The authors consider a MWRN with pair-wise data exchange protocol using binary phase shift keying (BPSK) modulation in both additive white Gaussian noise (AWGN) and Rayleigh fading channels. The authors quantify the possible error events in an L-user DF or AF MWRN and derive accurate asymptotic bounds on the probability for the general case that a user incorrectly decodes the messages of exactly k (k ∈ [1, L − 1]) users. They show that at high signal-to-noise ratio (SNR), the higher order error events (k ≥ 3) are less probable in AF MWRN, but all error events are equally probable in a DF MWRN. They derive the average BER of a user in a DF or AF MWRN in both AWGN and Rayleigh fading channels under high SNR conditions. Simulation results validate the correctness of the derived expressions. The authors results show that at medium to high SNR, DF MWRN provides better error performance than AF MWRN in AWGN channels even with a large number of users (e.g. L = 100). Whereas, AF MWRN outperforms DF MWRN in Rayleigh fading channels even for much smaller number of users (e.g. L > 10).

Synchronised On/Off keying (S‐OOK) is a pulse modulation format where timing synchronisation pulses are embedded with each bit in the data stream resulting in a 1.5 pulse/bit format, but allowing for synchronisation and demodulation with a single block. In this reported work, the error ratio for S‐OOK symbols received in a non‐fading AWGN channel is analysed and a mathematical model aware of the physical parameters of a CMOS integrated prototype is introduced. Using this model, the S‐OOK RX sensitivity is shown to be close to that of a high‐threshold OOK RX for similar error‐ratios but assuming perfect synchronisation.

A K $K$ ‐user cyclic shift‐aided serial concatenated code (SCC) is proposed over a Gaussian multiple access channel (MAC). In this code, a cyclic shift‐aided SCC, which integrates a regular repeat‐accumulate code with rate‐1/q $1/q$and cyclic shift spreading (CSS), is employed for each user. Here, CSS consists of a length‐L $L$bit spreading, a same chip‐level interleaver and a user‐specific cyclic shifter. This change avoids repeated complex interleaver generation operation and the main objective is to replace the random interleaver. At the receiver, iterative decoding is considered. For the design and optimization of the proposed code, a fixed point analysis (FPA) is developed to obtain the optimal q∗ $q^*$and L∗ $L^*$that achieves the maximum sum rate. Then, an analytic expression of collision probability is derived as a function of q $q$and L $L$ . Finally, the advantage is analysed by comparing the generation time of interleaver. Moreover, FPA provides lower computation complexity in optimizing system parameters than the traditional EXIT chart method. Numerical results show that the design and optimization of the proposed code is more accurate, and support distinguishing between the users. The proposed code not only outperforms the traditional IDMA scheme in the bit error rate performance, but also provides much lower generation time of interleaver, especially for multiuser scenarios. A K‐user cyclic shift‐aided serial concatenated code (SCC) is proposed over a Gaussian multiple access channel. In this code, a cyclic shift‐aided SCC, which integrates a regular repeat‐accumulate code with rate‐1/q $1/q$and cyclic shift spreading (CSS), is employed for each user. This change avoids complex interleaving operation and the main objective is to replace the random interleaver.

A ‐user cyclic shift‐aided serial concatenated code (SCC) is proposed over a Gaussian multiple access channel (MAC). In this code, a cyclic shift‐aided SCC, which integrates a regular repeat‐accumulate code with rate‐ and cyclic shift spreading (CSS), is employed for each user. Here, CSS consists of a length‐ bit spreading, a same chip‐level interleaver and a user‐specific cyclic shifter. This change avoids repeated complex interleaver generation operation and the main objective is to replace the random interleaver. At the receiver, iterative decoding is considered. For the design and optimization of the proposed code, a fixed point analysis (FPA) is developed to obtain the optimal and that achieves the maximum sum rate. Then, an analytic expression of collision probability is derived as a function of and . Finally, the advantage is analysed by comparing the generation time of interleaver. Moreover, FPA provides lower computation complexity in optimizing system parameters than the traditional EXIT chart method. Numerical results show that the design and optimization of the proposed code is more accurate, and support distinguishing between the users. The proposed code not only outperforms the traditional IDMA scheme in the bit error rate performance, but also provides much lower generation time of interleaver, especially for multiuser scenarios.

The multiple-input multiple-output singular value decomposition (MIMO SVD) modulation is an efficient way of sending data through a multi-antenna communications link in which the transmitter has knowledge of the channel state. Despite its importance, no simple formula for its symbol error rate (SER) has been found, and hence no intuitive characterisation of the quality of this technique for data transmission is available at the present. In this study, the authors present a method for approximating the statistics of each eigenchannel of MIMO SVD using the Nakagami-m fading model. Using the proposed method, it is seen that the SER of the entire MIMO SVD link can be approximated by the average of the SER of Nakagami-m channels. The expression found is simple and yet accurate. This leads to characterise the eigenchannels of N × N MIMO channels with N larger than 14, showing that the smallest eigenchannel distributes as a Rayleigh channel, the next four eigenchannels closely distributes as Nakagami-m channels with m = 4, 9, 25 and 36, and the N − 5 remaining eigenchannels have statistics similar to an additive white Gaussian noise (AWGN) channel within 1 dB signal-to-noise ratio. It is also shown that 75% of the total mean power gain of the MIMO SVD channel goes to the top third of all the eigenchannels.

In this study, a method is presented to construct column weight 3 (CW3) low-density parity-check (LDPC) codes using three-partite graphs. Let Gb be a bipartite graph and Ng be the set of all minimum length cycles in Gb. Using Gb and Ng, a three-partite graph denoted G(Gb, Ng), or simply Gt, is formed. Let T be the set of length 3 cycles in Gt and Ta be the set of three element subsets of vertices in Gt such that each of these subsets form a subgraph with no edges in Gt and has precisely one element in each section of Gt. Furthermore, let H be the binary matrix in which the set of rows represent the set of vertices of Gt, the columns represent the elements of V:= T ∪ Ta, and hij = 1 if and only if the ith vertex of Gt belongs to the jth three element set in V. Then H is a CW3 binary matrix. Using the Tanner graph representing H, a recursive construction for CW3 LDPC codes is provided. Applying a simple restriction on T and Ta, codes free of length 4 cycles are generated. Euclidean and finite geometry codes are used as the base codes for generating new CW3 LDPC codes. Results are presented which show that these new codes perform well in an additive white Gaussian noise (AWGN) channel with the iterative sum-product decoding algorithm.

A column‐weight k $k$LDPC code with the parity‐check matrix H $H$is called decomposable if there exists a permutation π $\\pi$on the rows of H $H$ , such that π(H) ${\\pi }(H)$can be decomposed into k $k$column‐weight one matrix. In this paper, some variations of edge coloring of graphs are used to construct some column‐weight three decomposable LDPC codes with girths at least six and eight. Applying the presented method on several known classes of bipartite graphs, some classes of column‐weight three decomposable LDPC codes are derived having flexibility in length and rate. Interestingly, the constructed parity‐check matrices based on the proper edge coloring of graphs can be considered as the base matrix of some high rate column‐weight three quasi‐cyclic (QC) LDPC codes with maximum‐achievable girth 20. The paper also leads to a simple characterization of elementary trapping sets of the decomposable codes based on the chromatic index of the corresponding normal graphs. This characterization corresponds to a simple search algorithm finds all possible existing elementary trapping sets in a girth‐6 or girth‐8 column‐weight 3 LDPC code which are layered super set of a short cycle in the Tanner graph of the code. Simulation results indicate that the QC‐LDPC codes with large girths lifted from the constructed base matrices have good performances over AWGN channel. In this paper, some variations of edge coloring of graphs are used to construct some column‐weight‐three decomposable LDPC codes with girths at least six and eight. Applying the presented method on several known classes of bipartite graphs, some classes of column‐weight‐three decomposable LDPC codes are derived having flexibility in length and rate. Interestingly, the constructed parity‐check matrices based on the proper edge coloring of graphs can be considered as the base matrix of some high rate column‐weight‐three quasi‐cyclic (QC) LDPC codes with maximum‐achievable girth 20. The paper also leads to a simple characterization of elementary trapping sets of the decomposable codes based on the chromatic index of the corresponding normal graphs.

Backscatter communications, which originated from World War II, have been widely applied in the logistics domain, and recently attract emerging interest from both academic and industrial circles. Here, the backscatter communication systems equipped with retrodirective arrays that can re‐transmit the impinging signals back toward the direction of incidence are studied so as to reduce the power loss of the signals. Specifically, the authors consider the tag is equipped with retrodirective arrays to improve reliability and enhance communication range. The probability density function of channel coefficients is then derived. Next, a channel estimator based on Bayesian theory is proposed to acquire the modulus values of channel parameters and calculate its Bayesian Cramer–Rao Lower Bound. Finally, simulation results are provided to corroborate these theoretical studies. Here, the authors consider the tag is equipped with retrodirective arrays to improve reliability and enhance communication range. The probability density function of channel coefficients is then derived. Next, a channel estimator based on Bayesian theory is proposed to acquire the modulus values of channel parameters and calculate its Bayesian Cramer–Rao Lower Bound.