Amplitude phase shift keying (APSK) modulation signals are of low peak average power ratio and are generated to fight against the potentially non-linear high power amplifier in satellite communication. The benchmark maximum log-likelihood maximum a posteriori probability (max-log-MAP) detector requires to compute the distance squared between the received signal and each APSK constellation point for the extrinsic bit log-likelihood ratio (LLR) information. To overcome this major challenge of high detection complexity, we propose in this paper to partition and order all the APSK constellation points into rings of ordered phase shift keying (PSK) constellation points. We also propose to apply and tailor the iterative search strategies, originally used to detect multiple input multiple output (MIMO) quadrature amplitude modulation (QAM) signals, to search over the ordered irregular PSK constellation points. Compared with previously reported APSK detectors, our proposed detector achieves exactly the max-log-MAP detection, requires very low computational complexity, and is able to detect APSK signals modulated from the APSK constellation with arbitrary number of constellation points, arbitrary phase offsets, and arbitrary ring radii.

We study soft-input soft-output (SISO) maximum logarithmic maximum a posteriori (max-log-MAP) detection of coded generalized spatial modulation (GenSM) signals for the iterative detection and decoding receiver. Due to the property of GenSM, extrinsic bit log-likelihood ratio associated with each bit of the transmit antenna combination index and transmit symbol vector needs to be computed. By extending our sorting assisted successive sphere decoding algorithm (SA-SSDA) for the hard-output detection of GenSM signals, we study two-stage detection schemes here to conduct multiple single tree search sphere decoding algorithms (STS-SDAs) for the second stage computation, where the order of the multiple STS-SDAs is determined in the first stage computation. Unlike previous two-stage detectors, our emphasis is on studying the ordering metrics for determining the order of STS-SDAs and is on giving suggestions about the scenarios to use adequate ordering metrics for the purpose of complexity reduction. Accordingly, incorporating the tricks used by the SA-SSDA and STS-SDA, we arrive at a fast SA-SSTS-SDA for exactly max-log-MAP detection of GenSM signals. Our proposed detector is feasible for hardware implementation and may motivate future research on the SISO detection of coded GenSM signals.

Soft-input soft-output (SISO) detector for the iterative detection and decoding of coded spatial modulation (SM) signals needs to compute the extrinsic bit log-likelihood ratio (LLR) associated with each detected bit. The maximum logarithmic maximum a posteriori (max-log-MAP) detector is known to perform closely to the optimal logarithmic maximum a posteriori (log-MAP) detector with much lower computational complexity. In this paper, we first apply several mathematical tricks to derive a new and low-complexity algorithm for the max-log-MAP detector. The proposed algorithm features a new tree pruning technique to visit few lattice points and a smart list administration technique to retain a max-log-MAP detector. By following the proposed algorithm, we then design a hardware architecture for SISO detection of coded SM signals over the scenario of 64-QAM symbols, 8 transmit antennas, and 4 receive antennas. Under the TSMC 40 nm CMOS technology, the VLSI implementation results reveal that our architecture requires 46.4K gates and leads to detection throughput 450 Mbps, while operating at clock frequency 400 MHz and consuming power 46 mW. Being the first hardware architecture for SISO detection of coded SM signals, our proposed low-cost max-log-MAP detector is very attractive.

In the generalized spatial modulation (GenSM) multiple input multiple output (MIMO) system, each block of data bits is mapped to a set of spatially multiplexed (SMX) symbols and an index of transmit antenna combination (TAC) of active antennas. The difficulty for the GenSM MIMO receiver is to detect the SMX symbols and TAC index simultaneously. Recently, we applied the conventional sphere decoding algorithm (SDA) successively to achieve the exact maximum likelihood detection (MLD) of GenSM MIMO signals. The SDA scheme suffers from variable computational complexity and leads to hardware detectors with variable throughput rate. Instead, fixed-complexity tree search algorithms, e.g., reduced fixed sphere decoding (rFSD), with nearly MLD performance are employed to facilitate hardware implementation. Here, we propose to apply the rFSD successively and design a hardware architecture for detecting GenSM MIMO signals under the scenario of 5 transmit antennas, 2 transmit radio frequency chains, 4 receive antennas, and 64-QAM SMX symbols. The VLSI implementation results under the TSMC 90nm CMOS technology reveal that our architecture requires 276.7K gates and provides detection throughput 1.613 Gbps, while operating at 322.6 MHz. Compared with other related architectures, our architecture provides higher detection throughput rate and is of better hardware efficiency.

The Layered Orthogonal Lattice Detector (LORD), developed by Siti, et al., is a famous soft- output detector for the MIMO system. It proposes to compute bit log-likelihood ratios (LLRs) in parallel for bits in each layer of the transmitted MIMO signals and therefore can achieve high throughput rate. However, one of its disadvantages is the high complexity for high-order modulated symbols. Combining the Schnorr-Euchner enumeration and bit flipping scheme, we propose to enumerate the lattices at the top layer in a new way. Our proposed detector can avoid the bit vacancy problem and is demonstrated to outperform the fixed-complexity soft-output detector. We also report the hardware implementation results for our proposed detector, showing that our detector is practically feasible.

Based on the minimum mean squared error (MMSE) trace criterion, selection of the precoding matrix indicator (PMI) from the downlink codebook of the LTE system is considered in this paper. Due to the codebook of 16 member precoding matrices and up to 1200 sub-carriers in this MIMO-OFDM system, the PMI selection needs to compute matrix inversion of up to 19,200 matrices. To satisfy this required workload, LDLH decomposition is applied at the algorithmic level, and, pipeline matrix multiplication and backward substitution modules are used at the architectural level. The VLSI implementation results of our architecture under the TSMC 90 nm CMOS technology reveals that our architecture requires 124.6K gates at operating frequency 120 MHz. Thus, our designed architecture can finish the 19,200 matrix inversions in about 1.60 ms and meets the requirement of 2 ms period of periodic channel state report.

The compressed beamforming weights feedback is used in the precoded MIMO-OFDM system, e.g., IEEE 802.11n/ac WLAN, to reduce the amount of feedback information. The precoded sub-system at the receiver of this system needs to perform singular value decomposition (SVD) on the estimated channel matrices at all sub-carriers. The computed angles of the right singular vectors are to be feedback to the transmitter. Also the computed singular values and left singular vectors are to be used for designing the optimal detector. Under the exemplary scenario of four antennas at the access point and two antennas at the station, our designed architectures for the precoding sub-system can provide SVD throughput rates 16.8 and 50.4 M matrices/sec for the uplink and downlink transmissions, respectively.

The Alamouti space-time block coding (STBC) multiple input multiple output (MIMO) system with spatial division multiplexing (SDM) is different from the pure SDM MIMO system in transmitting groups of Alamouti STBC symbols. Because of the Alamouti STBC, the zero-forcing with successive interference cancellation (ZF-SIC) detector for this MIMO system also detects one group of Alamouti STBC symbols in its one iteration. Previous analytical studies on this MIMO system were concentrated on the scenario of only four transmit antennas and did not take full advantage of the group-wise properties of the equivalent channel matrix due to Alamouti STBC. To deliver indepth analysis of this MIMO system with arbitrary number of transmit antennas, the ZF-SIC detection of the groups of Alamouti STBC symbols over the independent identically distributed Rayleigh fading channel is analyzed. Exact average block error probability of detecting all groups of Alamotui STBC symbols and its high signal-to-noise ratio (SNR) approximation are computed. Also, exact average group error probability of detecting each group of Alamotui STBC symbols and its high SNR approximation are computed. These analytical results are shown to agree with the simulation results.

In this paper, the block-wise lattice representation of the real-valued system model for the layered space time block code (layered STBC) system is introduced to reduce the computational complexity of the detection. Due to the orthogonality of the Alamouti STBC, the equivalent real-valued channel matrix of the signal model also has the orthogonal property. We take the orthogonal property into account thoroughly and propose two fast block-wise matrix computation schemes for the MIMO detection, including the block-wise Householder QRD and block-wise sorted QRD. We also show that the matrices obtained form the QRD of the equivalent channel matrix preserve the real-valued Alamouti coded patterns. The results of the proposed schemes are then utilized in the block-wise tree search detection, where the parallel procedure is performed to detect signals in the same block independently. Compared with the single-wise signal processing, the block-wise signal processing can save about 75% of the computational complexity at the preprocessing phase of the tree-search detectors.

Codebooks with constant modulus entries are being considered for the limited feedback beamforming multiple‐input–multiple‐output (MIMO) system to improve the power amplifier efficiency at the transmitter. Assume that one such codebook is known to both the transmitter and receiver. The receiver must determine a target codeword from this codebook and send its index back to the transmitter. A receiver can be implemented with low cost if fast codeword selection algorithm is executed. In this study, the authors utilise the properties possessed by three such codebooks and propose a novel tree search algorithm for fast codeword selection. Compared with two previously reported codeword selection algorithms, our algorithm is of fixed complexity and does find the target codeword. Furthermore, our algorithm for codeword selection is similar to the tree search for MIMO detection. These two similar tree search algorithms for both codeword selection and MIMO detection can be implemented by the same hardware architecture. A baseband receiver with small chip area for the dual‐mode (the spatial multiplexing and beamforming transmission modes) MIMO system is possible.

Two real MIMO models, the new lattice representation and the conventional real model, have been proposed in literature as equivalent models to the same complex MIMO model. To learn which one shares more information with the complex model, we show in this paper that the matrices produced by singular value decomposition and QR-decomposition of the complex and new real channel matrices for the complex and new real models, respectively, are fully related. Also, the new real zero-forcing successive interference cancellation (ZF-SIC) detector is shown to find the same solution as the complex ZF-SIC detector. Comparisons of the two real ZF-SIC detectors based on the two real models are therefore equivalent to the comparisons of the complex and conventional real ZF-SIC detectors. Plenty comparisons of the two real ZF-SIC detectors over the Rayleigh fading channel are reported, including the average joint error probability at finite signal-to-noise ratio (SNR), outage probability at different layers, average error probability at high SNR, and the scenario with optimal transmit power allocation. These comparisons provide much understanding about the complex and two real models as well as their associated detectors.

We study the symbol error rate (SER) analysis for the zero-forcing detection with successive interference cancellation (ZF-SIC) in the spatial division multiplexing space time block coded (SDM-STBC) MIMO system. Independent identically Rayleigh fading MIMO channel is considered. Relying on the results obtained from matrix variate distribution, we evaluate the SER for the ZF and ZF-SIC detection in the SDM-STBC system. These analytical SER curves are shown to agree with the SER curves from Monte Carlo simulations. We also evaluate numerically the finite-SNR diversity gain for the ZF and ZF-SIC detection in the SDM-STBC MIMO system. The finite-SNR diversity gain for either ZF or ZF-SIC detection grows as SNR increases, and, is upper-limited by 2nr- nt+ 2, where nrand ntdenote the numbers of antennas at the receiver and transmitter sides, respectively.

Forney-style factor graphs are used for modeling space-frequency-coded MIMO OFDM systems over frequency-selective fading channels. We analyze the Gaussian message passing mechanism for the Alamouti scheme and linear transformation of the factor graph. A new decision rule is derived in terms of the mean vector and covariance matrix of modulation symbols. We employ the K-best algorithm with reduced complexity to justify the effectiveness of our receiver.

We study the implementation algorithm for the MMSE-SIC detection with optimal detection order in a VBLAST system. We develop the LDLHdecomposition based algorithm with backward substitution (LDBABS), which is shown to require as many multiplications as two other most efficient algorithms. We then propose a modified LDBABS algorithm that utilizes the scheme of incomplete LDLHdecomposition together with the initial ordering information. The modified LDBABS algorithm is shown to require averagely fewer multiplications than any other implementation algorithm under the independent identically distributed Rayleigh fading channel. It is known that the real-valued MMSE-SIC detector with optimal detection order outperforms its complex-valued counterpart by approximately 1 dB. We finally propose a fast algorithm for the real-valued MMSE-SIC detector with optimal detection order. The number of real-valued multiplications required by this fast algorithm is approximately 1.57 times that required by the complex-valued LDBABS algorithm.

Detection of transmitted symbols in a V-BLAST system using the minimum mean squared error criterion with successive interference cancellation (MMSE-SIC) can provide satisfactory bit error rate performance at the cost of moderate computational complexity. The fast recursive algorithm (FRA), developed by Benesty et al., is one of the well-known implementation algorithms for the MMSE-SIC detector. We modify the FRA to compute an ordered set of nulling vectors from the estimated channel information. Our modified FRA can be used with the transformation based successive interference cancellation procedure to process a V-BLAST frame that contains the preamble and payload. To our knowledge, such implementation of the MMSE-SIC detector requires the lowest complexity to process a frame of preamble and payload.

Adaptive reduced-rank (RR) multistage matrix Wiener filtering (MMWF) techniques, based on the minimum mean-square error (MMSE) criterion, are proposed for time-hopping (TH) pulse-position modulation (PPM) ultra-wideband (UWB) systems. These RR-MMWF-based algorithms employ an adaptive fuzzy-inference determined filter stage. As a consequence, the proposed schemes achieve a substantial saving in complexity without compromising system performance and dynamic convergence/tracking capability. Additionally, the fuzzy-logic-controlled matrix conjugate gradient (M-CG) algorithm is developed for a robust and reduced-rank implementation of the MMWF. Simulations are conducted to illustrate the convergence/tracking superiority and to provide a comparative evaluation of the proposed algorithms with the MMWF-based schemes using other adaptive stage-selecting criteria.

We analyze the principal component combining with differential detection (PCC-DD) with weight estimation for the demodulation of DPSK signals in diversity systems. The estimated weight vector is considered to be the principal component of the exponentially weighted sample correlation matrix of the signals at diversity channel outputs. We arrive at closed form expressions for the approximate bit error rate (BER) for the scenario where channel gains are fixed, and the approximate average BER for the scenario where channel gains are independent identically Rayleigh distributed. The analysis provides accurate BER approximation, and is justified by the results from computer simulations. We also arrive at a rule of thumb about the value of the forgetting factor of the exponentially weighted sample correlation matrix should be selected for PCC-DD to yield good performance under time varying Rayleigh fading channels

The V-BLAST system is being considered as an important technique for the future wireless communications. For practical consideration, efficient and stable implementation of the V-BLAST system is extremely desirable. Based on Hassibi's original squared root algorithm for MMSE detection, we propose new algorithms that are both numerically stable and computationally efficient. Our proposed algorithm with initial detection order requires only averagely about (29/10)M3multiplications when the number of transmit and receive antennas are equal to M. This number of complexity is the smallest among the algorithms that we know so far.

We analyze the principal component combining with differential detection (PCC-DD) with weight estimation for the demodulation of DPSK signals in diversity systems. The estimated weight vector is considered to be the principal component of the exponentially weighted sample correlation matrix of the signals at diversity channel outputs. We arrive at closed form expressions for the approximate bit error rate (BER) for the scenario where channel gains are fixed, and the approximate average BER for the scenario where channel gains are independent identically Rayleigh distributed. The analysis provides accurate BER approximation, and is justified by the results from computer simulations.

We propose a principal component combining with differential detection (PCC-DD) for the demodulation of DPSK signals over a slow fading DSSS system. Our PCC-DD does not need the pilot signal and can blindly estimate the channel information. When the symbol period is much larger than the channel delay spread, our PCC-DD is as optimal as the maximal ratio combining with differential detection (MRC-DD) in generating combining output with maximal SNR. Our analysis for the scenario when the symbol period is comparable to the channel delay spread also agrees with the results from simulations. Adaptive implementation of our PCC-DD is demonstrated to be of low computational complexity.

In this paper, we study blind channel estimation in code division multiple access systems from array signal processing perspective. As there are three direction-of-arrival estimation methods in array signal processing, we formulate three corresponding blind channel estimation methods in a framework, although some of which have already been reported. From our analysis and simulations, the constrained and subspace methods for blind channel estimation outperforms the conventional method. The conventional method is computationally more efficient, and is suitable for the scenario where only few users exist and where good power control is taken care of.

We propose a new blind multiuser detector for frequency-selective multipath channels. Our new linearly constrained minimum variance (LCMV) RAKE receiver is an enhancement to the previously published decorrelating RAKE (D-RAKE) receiver. Compared with the D-RAKE receiver, our LCMV-RAKE receiver processes full information of the desired user and is shown by simulations to provide lower bit-error rates. In some scenarios, our LCMV-RAKE receiver outperforms the minimum output energy detector by M.K. Tsatsanis and Z. Xu (see IEEE Trans. Sig. Processing, vol.46, p.3014-22, 1998). Adaptive implementation of our LCMV-RAKE receiver is demonstrated to be feasible.

Using the Gaussian approximation, we calculate the approximate bit error probabilities (BEPs) or three multiusers. The accuracy of approximate BEPs for successive interference canceller (SIC), decorrelating decision feedback detector (DDFD), and orthogonal decision feedback detector (ODFD) depends on two factors. The first factor is whether the desired component at the input to the threshold is correlated with undesired component. The second factor is whether the approximate variance of the Gaussian undesired component contains non-zero covariance terms. The Gaussian approximation leads to good approximate BEPs for DDFD, to fair approximate BEPs for ODFD, but to poor approximate BEPs for SIC. The accuracy of these approximate BEPs is also justified by the results from Monte Carlo simulations.

Our proposed orthogonal decision feedback detector (ODFD) contains an orthogonal feedforward filter and allows decision feedback. While the decorrelating decision feedback detector (DDFD) is motivated by the Cholesky factorization of the correlation matrix of signature sequences, our ODFD is motivated by the QR-factorization of the same correlation matrix. In the absence of additive noise, ODFD is robust to multiple access interference. We observe from simulations that ODFD outperforms the decorrelating detector, due to the decision feedback, but is out performed by the DDFD. While the flop counts and bit error rate analysis tends to exaggerate for Cholesky factorization based methods such as the DDFD, the QR approach such as the ODFD is comparable in efficiency if memory traffic and vectorization overheads are considered.