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The Bell Labs layered space-time (BLAST) algorithm is simple, and hence, a popular choice for a multiple-input multiple-output (MIMO) receiver. Its bit-error rate (BER) performance has been studied mainly using numerical (Monte Carlo) techniques, since exact analytical evaluation presents serious difficulties. Close examination of the problem of BL...
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... is found using (66) and the high-SNR approximation in (72) (74) and , , and . Finally, the total average BER is expressed as (75) Note that are constants at high SNR. Fig. 2 shows that the ap- proximations in (73)-(75) are indeed accurate, even for moder- ately large SNR (especially for the total average BER). Table II gives the coefficients and for the system. Note that with is independent of . In fact, it depends only on , but not and individually, e.g., is the same for all systems with . represents the ...
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Citations
... At the receiver, each of the N antennas capture the mixed transmitted signals, and V-BLAST processes the received signals in such a way that the channel matrix is transformed into a set of virtual parallel independent channels. Loyka and Gagnon [23] have provided a performance analysis of V-BLAST based on the Gram-Schmidt orthogonalization process and a statistical analysis of the postprocessing signal-to-noise ratio for an M × N system. They have derived closed-form expressions for the average BER of uncoded M × N BPSK system. ...
... with C n k denoting the binomial coefficient, and γ 0 the average SNR. For the sake of space, we refer the reader to [23] for the formal definition of the terms a i . It is worth noting that the average total BER P et is an average with respect to the order of symbol stream detection, as well. ...
This paper investigates the performance of MIMO ad hoc networks that employ transmit diversity, as delivered by the Alamouti scheme, and/or spatial multiplexing, according to the Vertical Bell Labs Layered Space-Time system (V-BLAST). Both techniques are implemented in a discrete-event network simulator by focusing on their overall effect on the resulting signal-to-interference-plus-noise ratio (SINR) at the intended receiver. Unlike previous works that have studied fully-connected scenarios or have assumed simple abstractions to represent MIMO behavior, this paper evaluates MIMO ad hoc networks that are not fully connected by taking into account the effects of multiple antennas on the clear channel assessment (CCA) mechanism of CSMA-like medium access control (MAC) protocols. In addition to presenting a performance evaluation of ad hoc networks operating according to each individual MIMO scheme, this paper proposes simple modifications to the IEEE 802.11 DCF MAC to allow the joint operation of both MIMO techniques. Hence, each pair of nodes is allowed to select the best MIMO configuration for the impending data transfer. The joint operation is based on three operation modes that are selected based on the estimated SINR at the intended receiver and its comparision with a set of threshold values. The performance of ad hoc networks operating with the joint MIMO scheme is compared with their operation using each individual MIMO scheme and the standard SISO IEEE 802.11. Performance results are presented based on MAC-level throughput per node, delay, and fairness under saturated traffic conditions.
... Proof: The proof is relegated in Appendix B. It is noteworthy that (16) represents an extension of ZF and ZF-SIC reception under Rayleigh-only fading channels [8], [48], where the corresponding SNR of each stream follows a central chi-squared PDF, such as Y i d = χ 2 N −M+i . For rank-1 Rician fading channels, the Rician-faded stream follows a non-central chi-squared PDF, conditioned on its non-centrality parameter. ...
... are in the range of [0.0064 − 0.0306]. 8 For ease of presentation, we normalize the ergodic capacity with the factor 1/ln(2) ≈ 1.442695. Furthermore, it trivially follows that the sum-capacity of the entire system is defined as ...
The performance of a multiuser communication system with single-antenna transmitting terminals and a multi-antenna base-station receiver is analytically investigated. The system operates under independent and non-identically distributed rank-$1$ Rician fading channels with imperfect channel estimation and residual hardware impairments (compensation algorithms are assumed, which mitigate the main impairments) at the transceiver. The spatial multiplexing mode of operation is considered where all the users are simultaneously transmitting their streams to the receiver. Zero-forcing is applied along with successive interference cancellation (SIC) as a means for efficient detection of the received streams. New analytical closed-form expressions are derived for some important performance metrics, namely, the outage probability and ergodic capacity of the entire system. Both the analytical expressions and simulation results show the impact of imperfect channel estimation and hardware impairments to the overall system performance in the usage scenarios of massive MIMO and mmWave communication systems.
... There is considerable related analytical work in the V-BLAST literature [3]- [7], but not of direct relevance to the P-V-BLAST system with MM. For example, most work considers ZF in the detection stage [3]- [7] and much of the work neglects ordering [3], [4]. ...
... There is considerable related analytical work in the V-BLAST literature [3]- [7], but not of direct relevance to the P-V-BLAST system with MM. For example, most work considers ZF in the detection stage [3]- [7] and much of the work neglects ordering [3], [4]. Due to the difficulties of V-BLAST analysis, most of the results are bounds [3], [5] and some make restrictions to 2 users [3], [6] to develop closed form results. Error propagation is handled to at least some extent in [4], [6]. ...
... For example, most work considers ZF in the detection stage [3]- [7] and much of the work neglects ordering [3], [4]. Due to the difficulties of V-BLAST analysis, most of the results are bounds [3], [5] and some make restrictions to 2 users [3], [6] to develop closed form results. Error propagation is handled to at least some extent in [4], [6]. In this paper, the use of MRC and a single deterministic ordering makes analytic progress more tractable. ...
In this paper, we take a proposed low-complexity Vertical Bell Laboratories Layered Space Time receiver based on maximal ratio combining and further simplify the algorithm by replacing the channel norm ordering by a power based ordering. The receiver operates in an uplink massive multiple-input-multiple-output deployment with distributed single-antenna users and a large base station (BS) array. The novel receiver is compared with other more complex detection schemes such as linear zero forcing. Moreover, an explicit closed form analysis for error probability for both co-located and distributed BSs is provided. It is shown that the error performance of the distributed scenario is well approximated by a modified version of a co-located scenario. The simulation study demonstrates the performance of the proposed scheme and confirms the accuracy of analytical results.
... To this end, the successive interference cancellation (SIC) technique is considered, which has shown very good results in conventional MIMO systems. Moreover, the unordered SIC with a fixed ordering is adopted, which appropriately balances performance and computational complexity at the receiver [12]. First, unordered SIC is utilized at the relay and then at the secondary receiver (after retransmission from the relay), in orthogonal transmission phases, where all the received streams are sequentially detected, decoded and then canceled from the remaining signal. ...
... where Q 1 is a n R × n R unitary matrix with its columns representing the orthonormal ZF nulling vectors satisfying Q 1 Q H 1 = I n R , where I n stands for the n-sized identity matrix, while R 1 = Q H 1 F 1 is an n R × m ST upper triangular matrix. In fact, QR decomposition can be computed by means of the Gram-Schmidt process, Householder transformations, or Givens rotations [12]. By virtue of ZF-SIC, the received signal is decomposed in m ST parallel streams and the corresponding signal-to-interference-plus-noise ratio (SINR) of the ith stream is expressed as ...
... where N 0 is the single-sided power spectral density of the noise. Thus, it holds that X j,i d = p j x i /N 0 , while x i r 2 ii denotes an auxiliary chi-squared random variable (RV) with 2(n j − m ST + i) degrees of freedom (DoF) [12]. 2 Similarly ...
A spectrum sharing system with primary and secondary nodes, each equipped with an arbitrary number of antennas, is investigated. Particularly, the outage performance of an underlay cognitive system is analytically studied, in the case when the end-to-end ( ) communication is established via an intermediate relay node. To better enhance the communication, successive interference cancellation (SIC) is adopted, which compensates for both the transmission power constraint and the presence of interference from primary nodes. Both the relay and secondary receiver perform unordered SIC to successively decode the multiple streams, whereas the decode-and-forward relaying protocol is used for the communication. New closed-form expressions for the outage performance of each transmitted stream are derived in terms of finite sum series of the Tricomi confluent hypergeometric function. In addition, simplified yet tight approximations for the asymptotic outage performance are obtained. Useful engineering insights are manifested, such as the diversity order of the considered system and the impact of interference from the primary nodes in conjunction with the constrained transmission power of the secondary nodes.
... Proof: The detailed proof is relegated in [5]. In the simplified scenario of fixed symbol ordering (i.e., no ordering), f pr 2 ii (.) d = X 2 2(n−i+1) [8]. Thereby, in this case, ...
In this paper, a spatial multiplexing multiple-input multiple-output (MIMO) system when hardware along with RF imperfections occur during the communication setup is analytically investigated. More specifically, the scenario of hardware impairments at the transceiver and imperfect channel state information (CSI) at the receiver is considered, when successive interference cancellation (SIC) is implemented. Two popular linear detection schemes are analyzed, namely, zero forcing SIC (ZF-SIC) and minimum mean-square error SIC (MMSE-SIC). New analytical expressions for the outage probability of each SIC stage are provided, when independent and identically distributed Rayleigh fading channels are considered. In addition, the well-known error propagation effect between consecutive SIC stages is analyzed, while closed-form expressions are derived for some special cases of interest. Finally, useful engineering insights are manifested, such as the achievable diversity order, the performance difference between ZF- and MMSE-SIC, and the impact of imperfect CSI and/or the presence of hardware impairments to the overall system performance.
... It uses nonlinear (serial cancellation) and linear combining (interference suppression) and has been studied with imperfect channel estimation [42] and with correlated channels [43]. Most of the work on traditional V-BLAST discusses ZF or MMSE combiners and rarely considers MRC [44,45]. Also, very little work has appeared on V-BLAST with MM since the prime focus of MM is simplicity whereas V-BLAST requires repeated detection and ordering. ...
... One of the most popular schemes in traditional MIMO is the V-BLAST approach, which is discussed in Section 2.8.2. Most of the work on traditional V-BLAST discusses ZF or MMSE combining and rarely considers MRC [44]. Also, very little work has appeared on V-BLAST with MM probably because of the complexity of V-BLAST with large numbers of antennas. ...
... Also, most of the work on traditional V-BLAST considers ZF or MMSE combining and rarely discusses MRC [44,45]. ...
... It uses nonlinear (serial cancellation) and linear combining (interference suppression) and has been studied with imperfect channel estimation [8] and with correlated channels [9]. Most of the work on traditional V-BLAST discusses zero forcing (ZF) or minimummean-square-error (MMSE) combining and rarely considers maximum ratio combining (MRC) [10]. On the other hand, very little work has appeared on V-BLAST with MM probably because of the complexity of V-BLAST with large numbers of antennas. ...
In an uplink massive multiple-input-multiple-output (MIMO) deployment with distributed single-antenna users and a large base-station array, we consider the performance of Vertical Bell Laboratories Layered Space Time (V-BLAST) with maximum ratio combining (MRC) and V-BLAST with zero forcing (ZF). In the performance evaluation, we include the effects of imperfect channel state information (CSI) and channel correlation since these system imperfections are of particular importance in massive MIMO. The main contribution is that the performance of MRC V-BLAST is shown to approach that of ZF V-BLAST under a range of imperfect CSI levels, different channel powers and different types of array, as long as the channel correlations are not too high.
... Very little work has appeared on V-BLAST with MM since the prime focus of MM is simplicity whereas V-BLAST requires repeated detection and ordering. Also, most of the work on traditional V-BLAST considers ZF or minimum-mean-squareerror (MMSE) combining and rarely discusses MRC [4], [5]. In this paper, we integrate MRC with V-BLAST in MM and propose a simple, low complexity receiver design. ...
In an uplink massive multiple-input-multiple-output deployment with distributed single-antenna users and a large base-station array, we consider several combinations of receivers using linear combiners (maximum ratio combining (MRC) and zero forcing (ZF)) in conjunction with Vertical Bell Laboratories Layered Space Time (V-BLAST). We show that the performance loss of MRC relative to ZF can be removed in certain situations through the use of V-BLAST. Furthermore, we develop a low complexity ordering scheme which results in a V-BLAST scheme with MRC which has much less complexity than a single ZF linear combiner. An analysis of the signal-to-interference-and-noise-ratio at each stage of the V-BLAST approach is also given to support the findings of the proposed technique.
... T HE V-BLAST approach represents a cornerstone reception strategy for multiple input-multiple output (MIMO) infrastructures because it achieves a high spectral efficiency and a substantial capacity gain [1], [2]. It utilizes successive interference cancellation (SIC) in a number of consecutive stages. ...
... Thereby, analytical research studies for the V-BLAST (or SIC) approach are very limited in the bibliography so far. More specifically, Loyka et al performed an analytical framework with respect to ASER for 2 × n MIMO systems with optimal ordering in [3] and for the generalized l × n case without optimal ordering in [2], where l and n denote the number of transmit and receive antennas, respectively. Nevertheless, these contributions assumed an error-free SIC approach and Rayleigh channel fading conditions. ...
The performance of the V-BLAST approach, which utilizes successive
interference cancellation (SIC) with optimal ordering, over independent
Nakagami-m fading channels is studied. Systems with two transmit and n receive
antennas are employed whereas the potential erroneous decision of SIC is also
considered. In particular, tight closed-form bound expressions are derived in
terms of the average symbol error rate (ASER) and the outage probability, in
case of binary and rectangular M-ary constellation alphabets. The mathematical
analysis is accompanied with selected performance evaluation and numerical
results, which demonstrate the usefulness of the proposed approach.
... where ⌊α⌋ denotes the largest integer smaller than or equal to a real number α. Using (3), (6) and (11), the conditional probability in (10) can be derived as follows: ...
The symbol error rate (SER) and bit error rate (BER) of the multiple-input–multiple-output (MIMO) system with decision-feedback detection (DFD) are analyzed over a Rayleigh fading channel. By using the concepts of “event” and “state” related to error propagation due to the decision-feedback process, we present general closed-form expressions for the SER and BER of each layer over quadrature-amplitude modulation (QAM) or phase-shift keying (PSK) for an arbitrary number of transmit and receive antennas. We also derive the asymptotic BER and SER performances of each layer. Numerical results show that our analysis matches very well with the Monte Carlo simulation. Our approach can be extended to the exact performance analysis of various wireless communication systems.
