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 Mathematics , 2012, Abstract: In this paper, the achievable DoF of MIMO X channels for constant channel coefficients with $M_t$ antennas at transmitter $t$ and $N_r$ antennas at receiver $r$ ($t,r=1,2$) is studied. A spatial interference alignment and cancelation scheme is proposed to achieve the maximum DoF of the MIMO X channels. The scenario of $M_1\geq M_2\geq N_1\geq N_2$ is first considered and divided into 3 cases, $3N_2N_1$, otherwise it is 1/2 or 1 less than the outer-bound; in Case $C$, the achievable DoF is equal to the outer-bound $2/3(M_1+M_2)$ if $(3N_2-M_1-M_2)\mod 3=0$, and it is 1/3 or 1/6 less than the outer-bound if $(3N_2-M_1-M_2)\mod 3=1 \mathrm{or} 2$. In the scenario of $M_t\leq N_r$, the exact symmetrical results of DoF can be obtained.
 Mathematics , 2009, Abstract: In this paper, we analyze the fundamental tradeoff of diversity and multiplexing in multi-input multi-output (MIMO) channels with imperfect channel state information at the transmitter (CSIT). We show that with imperfect CSIT, a higher diversity gain as well as a more efficient diversity-multiplexing tradeoff (DMT) can be achieved. In the case of multi-input single-output (MISO)/single-input multi-output (SIMO) channels with K transmit/receive antennas, one can achieve a diversity gain of d(r)=K(1-r+K\alpha) at spatial multiplexing gain r, where \alpha is the CSIT quality defined in this paper. For general MIMO channels with M (M>1) transmit and N (N>1) receive antennas, we show that depending on the value of \alpha, different DMT can be derived and the value of \alpha has a great impact on the achievable diversity, especially at high multiplexing gains. Specifically, when \alpha is above a certain threshold, one can achieve a diversity gain of d(r)=MN(1+MN\alpha)-(M+N-1)r; otherwise, the achievable DMT is much lower and can be described as a collection of discontinuous line segments depending on M, N, r and \alpha. Our analysis reveals that imperfect CSIT significantly improves the achievable diversity gain while enjoying high spatial multiplexing gains.
 Mathematics , 2011, Abstract: Training-based transmission over Rayleigh block-fading multiple-input multiple-output (MIMO) channels is investigated. As a training method a combination of a pilot-assisted scheme and a biased signaling scheme is considered. The achievable rates of successive decoding (SD) receivers based on the linear minimum mean-squared error (LMMSE) channel estimation are analyzed in the large-system limit, by using the replica method under the assumption of replica symmetry. It is shown that negligible pilot information is best in terms of the achievable rates of the SD receivers in the large-system limit. The obtained analytical formulas of the achievable rates can improve the existing lower bound on the capacity of the MIMO channel with no channel state information (CSI), derived by Hassibi and Hochwald, for all signal-to-noise ratios (SNRs). The comparison between the obtained bound and a high SNR approximation of the channel capacity, derived by Zheng and Tse, implies that the high SNR approximation is unreliable unless quite high SNR is considered. Energy efficiency in the low SNR regime is also investigated in terms of the power per information bit required for reliable communication. The required minimum power is shown to be achieved at a positive rate for the SD receiver with no CSI, whereas it is achieved in the zero-rate limit for the case of perfect CSI available at the receiver. Moreover, numerical simulations imply that the presented large-system analysis can provide a good approximation for not so large systems. The results in this paper imply that SD schemes can provide a significant performance gain in the low-to-moderate SNR regimes, compared to conventional receivers based on one-shot channel estimation.
 Mathematics , 2015, Abstract: Transceiver hardware impairments (e.g., phase noise, in-phase/quadrature-phase (I/Q) imbalance, amplifier non-linearities, and quantization errors) have obvious degradation effects on the performance of wireless communications. While prior works have improved our knowledge on the influence of hardware impairments of single-user multiple-input multiple-output (MIMO) systems over Rayleigh fading channels, an analysis encompassing the Rician fading channel is not yet available. In this paper, we pursue a detailed analysis of regular and large-scale (LS) MIMO systems over Rician fading channels by deriving new, closed-form expressions for the achievable rate to provide several important insights for practical system design. More specifically, for regular MIMO systems with hardware impairments, there is always a finite achievable rate ceiling, which is irrespective of the transmit power and fading conditions. For LS-MIMO systems, it is interesting to find that the achievable rate loss depends on the Rician $K$-factor, which reveals that the favorable propagation in LS-MIMO systems can remove the influence of hardware impairments. However, we show that the non-ideal LS-MIMO system can still achieve high spectral efficiency due to its huge degrees of freedom.
 Computer Science , 2014, Abstract: The relationship between the transmitted signal and the noiseless received signals in correlatively changing fading channels is modeled as a nonlinear mapping over manifolds of different dimensions. Dimension counting argument claims that the dimensionality of the neighborhood in which this mapping is bijective with probability one is achievable as the degrees of freedom of the system.We call the degrees of freedom achieved by the nonlinear decoding methods the nonlinear degrees of freedom.
 Mathematics , 2014, Abstract: This paper studies the achievable degrees of freedom for multi-user MIMO two-way relay channels, where there are $K$ source nodes, each equipped with $M$ antennas, one relay node, equipped with $N$ antennas, and each source node exchanges independent messages with an arbitrary set of other source nodes via the relay. By allowing an arbitrary information exchange pattern, the considered channel model is a unified one. It includes several existing channel models as special cases: $K$-user MIMO Y channel, multi-pair MIMO two-way relay channel, generalized MIMO two-way X relay channel, and $L$-cluster MIMO multiway relay channel. Previous studies mainly considered the achievability of the DoF cut-set bound $2N$ at the antenna configuration $N < 2M$ by applying signal alignment. This work aims to investigate the achievability of the DoF cut-set bound $KM$ for the case $N\geq 2M$. To this end, we first derive tighter DoF upper bounds for three special cases of the considered channel model. Then, we propose a new transmission framework, generalized signal alignment, to approach these bounds. The notion of GSA is to form network-coded symbols by aligning every pair of signals to be exchanged in a compressed subspace at the relay. A necessary and sufficient condition to construct the relay compression matrix is given. We show that using GSA, the new DoF upper bound is achievable when i) $\frac{N}{M} \in \big(0, 2+\frac{4}{K(K-1)}\big] \cup \big[K-2, +\infty\big)$ for the $K$-user MIMO Y channel; ii) $\frac{N}{M} \in \big(0, 2+\frac{4}{K}\big] \cup \big[K-2, +\infty\big)$ for the multi-pair MIMO two-way relay channel; iii) $\frac{N}{M} \in \big(0, 2+\frac{8}{K^2}\big] \cup \big[K-2, +\infty\big)$ for the generalized MIMO two-way X relay channel. We also provide the antenna configuration regions for the general multi-user MIMO two-way relay channel to achieve the total DoF $KM$.
 Int'l J. of Communications, Network and System Sciences (IJCNS) , 2010, DOI: 10.4236/ijcns.2010.31001 Abstract: In this work, we consider a multi-antenna channel with orthogonally multiplexed non-cooperative users, and present its achievable information rate regions with and without channel knowledge at the transmitter. With an informed transmitter, we maximize the rate for each user. With an uninformed transmitter, we consider the optimal power allocation that causes the fastest convergence to zero of the fraction of channels whose mutual information is less than any given rate as the transmitter channel knowledge converges to zero. We assume a deterministic space and time dispersive multipath channel with multiple transmit and receive antennas, generating an orthogonally multiplexed Multiple-Input Multiple-Output (MIMO) broadcast system. Under limited transmit power; we consider different user specific space-time modulation formats that represent assignments of signal dimensions to transmit antennas. For the two-user orthogonally multiplexed MIMO broadcast channels, the achievable rate regions, with and without transmitter channel knowledge, evolve from a triangular region at low SNR to a rectangular region at high SNR. We also investigate the maximum sum rate for these regions and derive the associated power allocations at low and high SNR. Furthermore, we present numerical results for a two-user system that illustrate the effects of channel knowledge at the transmitter, the multi-dimensional space-time modulation format and features of the multipath channel.
 Mathematics , 2011, DOI: 10.1109/TWC.2013.041713.120773 Abstract: In this paper, we propose opportunistic interference alignment (OIA) schemes for three-transmitter multiple-input multiple-output (MIMO) interference channels (ICs). In the proposed OIA, each transmitter has its own user group and selects a single user who has the most aligned interference signals. The user dimensions provided by multiple users are exploited to align interfering signals. Contrary to conventional IA, perfect channel state information of all channel links is not required at the transmitter, and each user just feeds back one scalar value to indicate how well the interfering channels are aligned. We prove that each transmitter can achieve the same degrees of freedom (DoF) as the interference free case via user selection in our system model that the number of receive antennas is twice of the number of transmit antennas. Using the geometric interpretation, we find the required user scaling to obtain an arbitrary non-zero DoF. Two OIA schemes are proposed and compared with various user selection schemes in terms of achievable rate/DoF and complexity.
 Mathematics , 2011, Abstract: In this paper, the asymptotic performance of the lattice sequential decoder for LAttice Space-Time (LAST) coded MIMO channel is analyzed. We determine the rates achievable by lattice coding and sequential decoding applied to such a channel. The diversity-multiplexing tradeoff (DMT) under lattice sequential decoding is derived as a function of its parameter---the bias term, which is critical for controlling the amount of computations required at the decoding stage. Achieving low decoding complexity requires increasing the value of the bias term. However, this is done at the expense of losing the optimal tradeoff of the channel. In this work, we derive the tail distribution of the decoder's computational complexity in the high signal-to-noise ratio regime. Our analysis reveals that the tail distribution of such a low complexity decoder is dominated by the outage probability of the channel for the underlying coding scheme. Also, the tail exponent of the complexity distribution is shown to be equivalent to the DMT achieved by lattice coding and lattice sequential decoding schemes. We derive the asymptotic average complexity of the sequential decoder as a function of the system parameters. In particular, we show that there exists a cut-off multiplexing gain for which the average computational complexity of the decoder remains bounded.
 Mathematics , 2010, Abstract: We consider the problem of communicating over a multiple-input multiple-output (MIMO) real valued channel for which no mathematical model is specified, and achievable rates are given as a function of the channel input and output sequences known a-posteriori. This paper extends previous results regarding individual channels by presenting a rate function for the MIMO individual channel, and showing its achievability in a fixed transmission rate communication scenario.
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