Performance of MUTP-aided MIMO systems over correlated frequency-selective wireless communication channels: a multi-cell perspective
- Prabagarane Nagaradjane^{1}Email author,
- Sabarish Karthik Vivek Sarathy^{2},
- Prasaanth Muralidharan^{4} and
- Yuvika Ashwina Rajan^{3}
DOI: 10.1186/1687-1499-2012-194
© Nagaradjane et al; licensee Springer. 2012
Received: 6 April 2011
Accepted: 11 June 2012
Published: 11 June 2012
Abstract
In this article, we investigate the performance of multiuser transmitter preprocessing (MUTP)-aided multiple-input multiple-output (MIMO) systems in a multi-cell multiuser setting where co-channel interference (CCI) is the major channel impairment, for both uplink (UL) and downlink (DL) transmissions. CCI can considerably reduce data rates resulting in outages in cellular systems, particularly at the cell edges in DL transmission. The MUTP considered in this article is based on singular value decomposition (SVD), which exploits the channel state information (CSI) of all the users at the base stations (BSs) with the aid of BS cooperation, and only the individual users' CSI at the mobile stations (MSs) for both UL and DL transmissions. In particular, in this article, we study the effects of three types of delay spread distributions coupled with different interferer configurations over correlated and uncorrelated frequency-selective channels. Our simulation study shows that SVD-aided MUTP perfectly eliminates CCI with lesser detection complexity under perfect CSI. Also, we provide performance comparisons of SVD-aided MUTP with various precoding techniques widely addressed in literature, and the results show that it provides better achievable symbol error rate (SER) by mitigating multi-stream interference (MSI) and CCI. Further, simulation results demonstrate that compared to equal CCI, the presence of a dominant interferer can lead to more degradation in the system performance in terms of achievable SER while, further degradation results when noise is dominant. Furthermore, this study confirms that imperfect CSI as well as imperfect power control can lead to degradation in the system performance.
Keywords
multiple-input multiple-output (MIMO) preprocessing post-processing multiuser transmitter preprocessing (MUTP) singular value decomposition (SVD) co-channel interference (CCI) multiuser interference (MUI) multi-stream interference (MSI)1. Introduction
Information theoretic results have shown that significant increase in the capacity of wireless communication systems can be achieved with the aid of multiple antennas at both the transmitters and receivers. The capacity of these multiple antenna systems, also called as multiple-input multiple-output (MIMO) systems, has been shown to grow linearly with small increase in the number of transmit and receive antennas in rich scattering environments, and at sufficiently high signal-to-noise (SNR) ratios [1]. MIMO systems can provide high data rates through spatial multiplexing (invoking Vertical Bell Laboratories layered space-time architecture (VBLAST) type processing) or considerable diversity using transmit diversity (by exploiting space-time block code type processing) [2]. Much of the research focus has been in the design of single user MIMO systems [3, 4], where only multi-stream interference (MSI) is the major channel impairment. In single-cell multiuser MIMO systems, in addition to MSI, multiuser interference (MUI) becomes the dominating channel impairment. In the case of multiuser multi-cell MIMO systems, owing to frequency reuse, co-channel interference (CCI) from other cells becomes the domineering channel impairment. Further, next generation cellular standards like the 3GPP (Third generation partnership project) Long Term Evolution Advanced (LTE-A) aim at exploiting universal frequency reuse in order to maximize the area spectral efficiency. However, this could result in high levels of CCI as simultaneous transmission takes place on the same frequency band in the adjacent cells. In this context, the users may synchronously receive their own signals from the serving base station (BS) as well as signals from adjacent co-channel BSs. The signals from the adjacent BSs, namely CCI, can greatly reduce the achievable data rates leading to outages in cellular systems mainly at the cell edges [5–8]. This CCI is asynchronous and is a critical issue that requires serious attention. Hence, disregarding CCI would result in significant degradation in the system performance in terms of achievable symbol error rate (SER). To deal with this interference, multiuser detection (MUD) can be invoked both at the mobile station (MS) and BS [9], but its complexity increases excessively, thus making it impractical for implementation even at the BS, where complexity is acceptable. An alternate way to combat interference is to exploit multiuser transmitter preprocessing (MUTP) at the BS as well as at the MS [3, 4, 10].
Recently, MUTP that mitigates MUI and CCI has received considerable attention as it facilitates the implementation of less complex and more power efficient MSs. MUTP has been proposed to keep the receiver design simple by moving the required signal processing to the transmitter [10], i.e., signal processing at the BS in the case of DL transmission and at the MS in the case of UL transmission [4]. A comprehensive treatment on transmitter preprocessing, such as transmitter MUD, multiuser transmission (MUT), etc., has been addressed in [10]. As a design choice, in [11] maximum ratio UL transmission scheme was analyzed, by considering the dominant right-hand side (RHS) and left-hand side (LHS) singular eigenvectors for the preprocessing and postprocessing vectors, respectively, to increase the achievable diversity gain. In [3], the multiuser transmission schemes invoke the block diagonalization (BD) method. In some proposed schemes [12, 13], it has been demonstrated that dirty paper (DP) precoding could approach the achievable system capacity in various joint transmissions for DL. Furthermore, singular value decomposition (SVD)-assisted space time block coding (STBC) for point-to-point transmission has found many applications [14], while in [4], SVD based MUTP is investigated for flat fading channels. Of late, BS cooperation aided multi-cell multiuser systems have received widespread attention [5–7, 12]. The study of [15] presents a detailed survey on multi-cell MIMO cooperation aided wireless networks in the context of inter-cell interference mitigation. The main difference between MUTP aided single cell transmission and multi-cell transmission is that, in the former case BS cooperation is not needed to remove MUI, while in the latter full BS cooperation is required to completely eliminate CCI. The first work in the context of full BS cooperation was investigated by Hanly as stated in [15], for uplink transmission for a MIMO multiple access channel. In this publication, it was shown that the BSs cooperate to decode each user's symbols. Also, Hanly has shown that, by exploiting interference with the aid of global receivers, interference can be completely eliminated and thus all received signals carry useful information for the global decoder [15]. Further in [15], it is addressed that Hanly et al. have shown that BS cooperation eliminates CCI by invoking optimal power control. In other words, a network of interfering cells has the same per-cell capacity (in numbers of users) as a single, isolated cell. In [16] it is shown in the context of multi-cell MIMO systems, that significant performance gain can be achieved by grouping adjacent cells and by solving the optimal beamforming and power splitting problem jointly. It is demonstrated in [8] that in addition to pairing the adjacent BSs [16], a remarkable improvement in data rates can be achieved if the BSs are synchronized. In [17], BS cooperation approach is proposed to enhance the downlink sum capacity (throughput) with single-input single-output (SISO) systems employed in each cell, by implementing the DP coding (DPC). Also, these cooperative BS-assisted systems have been demonstrated to provide substantial gain in the form of system performance for a multi-cell MIMO system [12]. In [4, 18], the performance of MUTP-aided multiuser MIMO systems has primarily been investigated in the context of single cell for DL and UL transmissions in flat-fading channels, respectively.
For cellular systems, two performance metrics namely average cell throughput and user throughput at the cell edges are vital. Improving these measures becomes indispensable in the context of next generation cellular networks. Average cell throughput can be improved by employing relatively simple methods (increasing transmission power), but improving the throughput of the users at cell edges is quite challenging. Furthermore, users at the cell edges experience strong CCI and any increase in the transmission power to improve average cell throughput further creates CCI for cell edge users. Besides this, frequency-selectivity of the channels will severely degrade the system performance resulting in an irreducible bit error rate, thus imposing a limit on the achievable data rates. Thus, improving cell edge throughput becomes imperative in such frequency-selective CCI environments, and that is why interference mitigation techniques have received wide spread attention among research communities in the context of next generation cellular standards.
Hence, in this correspondence, we will be investigating the performance of MUTP-aided MIMO systems in terms of achievable SER in such CCI limited environments with multi-cell cooperation (also called BS cooperation). Specifically, in this contribution we present the performance of joint VBLAST/STBC aided DL and STBC processing aided UL MIMO systems with MUTP in the context of multi-cell multiuser setting with BS cooperation over correlated and uncorrelated frequency-selective fading for three different delay spread distributions pertaining to LTE standard [19] and flat fading channels.
The rest of the article is organized as follows: Section 2 describes the system model of VBLAST/STBC-aided MIMO system with MUTP for DL and STBC-aided MIMO system with MUTP for UL communications. Section 3 elucidates the performance results of our analysis and in Section 4 conclusions are drawn.
Notations: The following notations are adopted for remaining of the article. All boldface capital letters represent a matrix while a lowercase boldface letter denotes a vector. (.)^{ H }denotes Hermitian transpose while (.)* refers to the complex conjugate. Additionally, (·;·) is used to denote row wise concatenation. (.)^{+} refers to the Moore-Penrose matrix (pseudo-inverse), while ε{·} gives the expectation of the argument. Trace{.} represents the trace of the argument, Q(.) specifies quantization and ∥.∥ denotes the norm operation.
2. System configuration
2.1 Downlink transmission
In DL transmission, we assume that the BS supports joint VBLAST/STBC processing architecture with MUTP based on SVD technique. The joint VBLAST/STBC technique can be described as follows:
Path delays and relative power levels
Path number (l) | LTE channel models | |||||
---|---|---|---|---|---|---|
Extended Pedestrian | Extended Vehicular | Typical Urban | ||||
Delay | Power | Delay | Power | Delay | Power | |
$({\mathbf{\tau}}_{\mathbf{l}})$ (ns) | $p({\mathbf{\tau}}_{\mathbf{l}})$ (dB) | $({\mathbf{\tau}}_{\mathbf{l}})$ (ns) | $p({\mathbf{\tau}}_{\mathbf{l}})$ (dB) | $({\mathbf{\tau}}_{\mathbf{l}})$ (ns) | $p({\mathbf{\tau}}_{\mathbf{l}})$ (dB) | |
1 | 0 | 0 | 0 | 0 | 0 | -1 |
2 | 30 | -1 | 30 | -1.5 | 50 | -1 |
3 | 70 | -2 | 150 | -1.4 | 120 | -1 |
4 | 90 | -3 | 310 | -3.6 | 200 | 0 |
5 | 110 | -8 | 370 | -0.6 | 230 | 0 |
6 | 190 | -17.2 | 710 | -9.1 | 500 | 0 |
7 | 410 | -20.8 | 1090 | -7 | 1600 | -3 |
8 | 1730 | -12 | 2300 | -5 | ||
9 | 2510 | -16.9 | 5000 | -7 |
where ${h}_{ji}^{l}$ is a complex zero-mean Gaussian random process with variance $p({\tau}_{l})$ and ${h}_{ji}^{l}$ is uncorrelated with other paths and channels. $L$ is the total number of paths between the $i\text{th}$ transmit and the $j\text{th}$ receive antenna.
where
where ${\mathit{N}}_{k}$ represents the $\left({N}_{\text{r}}\times 2\right)$ noise matrix having zero mean and covariance matrix ${\sigma}^{2}{\mathit{I}}_{{N}_{\text{r}}}$.
where
${U}_{k}=\left({N}_{\text{r}}\times {N}_{\text{r}}\right)$ unitary matrix,
${V}_{k}=\left(M{N}_{\text{t}}\times M{N}_{\text{t}}\right)$ unitary matrix,
${\mathit{\Lambda}}_{k}=({N}_{\text{r}}\times M{N}_{\text{t}})$ diagonal matrix containing the non-zero eigenvalues of ${H}_{k}{H}_{k}^{H}$,
${V}_{ks}=\left(M{N}_{\text{t}}\times {N}_{\text{r}}\right)$ matrix, constituting the eigenvectors corresponding to the non-zero eigenvalues of ${H}_{k}^{H}{H}_{k}$,
${V}_{kn}=\left[\right(M{N}_{\text{t}}\times \left(M{N}_{\text{t}}-{N}_{\text{r}}\right)]$ matrix, constituting the eigenvectors corresponding to the zero eigenvalues of ${H}_{k}^{H}{H}_{k}$.
Thus the postprocessing matrix $G$ mitigates MSI.
${\widehat{d}}_{{k}_{i}}$, denotes the $i\text{th}$ estimated symbol of the $k\text{th}$ user,
Symbols are then detected by $Q\left({\widehat{\mathit{d}}}_{k}\right)$.
2.2 Uplink transmission
where
where ${F}_{k}={V}_{k},\phantom{\rule{2.77695pt}{0ex}}\phantom{\rule{2.77695pt}{0ex}}k=1,2,\dots ,K$ formulates the preprocessing matrix [18] for the $k\text{th}$ user. The $\left({N}_{\text{t}}\times {N}_{\text{t}}\right)$ component diagonal matrix ${\mathit{\gamma}}_{k}$ constitute the power control co-efficients employed for normalizing the transmission power associated with the $k\text{th}$ MS.
where
${U}_{k}=\left({N}_{\text{r}}\times {N}_{\text{r}}\right)$ unitary matrix,
${V}_{k}=\left({N}_{\text{t}}\times {N}_{\text{t}}\right)$ unitary matrix,
${\mathit{\Lambda}}_{k}=\left({N}_{\text{r}}\times {N}_{\text{t}}\right)$ diagonal matrix containing the ${N}_{\text{t}}$ non-zero eigenvalues of ${H}_{k}{H}_{k}^{H}$,
${U}_{ks}=\left({N}_{\text{r}}\times {N}_{\text{t}}\right)$ matrix, denoting the eigenvectors corresponding to the non-zero eigenvalues of ${H}_{k}{H}_{k}^{H}$,
${U}_{kn}=\left[{N}_{\text{r}}\times \left({N}_{\text{r}}-{N}_{\text{t}}\right)\right]$ matrix, denoting the eigenvectors corresponding to the zero eigenvalues of ${H}_{k}{H}_{k}^{H}$.
The normalization in (28) is based on the assumption $\epsilon \left\{{\mathit{D}}_{k}{{\mathit{D}}_{k}}^{\mathit{H}}\right\}={\mathit{I}}_{{N}_{\text{t}}}$.
3. Performance results
Simulation parameters
Number of antennas at each BS (DL, UL) | (4, 16) |
---|---|
Number of antennas at each MS (DL, UL) | (4, 2) |
Number of co-channel users | 6 |
Channel model | LTE |
Scenarios | Pedestrian Typical Urban Vehicular |
Modulation technique | 64 QAM |
Doppler frequency (Hz) (PED/TU/VEH) | 5/70/300 |
Speed (km/h) (PED/TU/VEH) | 2.7/40.8/162 |
Channel bandwidth (MHz) | 20 |
Correlation (ρ) | 0.7 |
Carrier frequency (GHz) | 2 |
Inter-site distance (m) | 2500 |
Path loss exponent | 3.76 |
Shadowing standard deviation (dB) | 8 |
Power control | Open loop |
4. Conclusion
In this article, we have investigated the performance of multi-cell MIMO system with joint VBLAST/STBC processing for DL transmission and STBC processing for UL transmission aided by transmitter preprocessing. We have drawn comparisons between systems with and without TP and, also with other widely known precoding techniques. It is discerned from the analysis that the system with TP can significantly enhance the achievable SER performance thus allowing support for more users, and resulting in higher capacity than conventional system employing a linear ZF detector. Also, this study has confirmed that the presence of dominant interferers can degrade the system performance. Nevertheless, the performance gain in interference-limited environments is better than in the noise-limited scenario due to the presence of dominant noise in the latter case. Moreover, it is inferred that ICSI can considerably degrade the system performance due to eigenvalue perturbation. In the context of multi-cell MIMO systems, it is further observed that SVD-aided MUTP outperforms other precoding techniques by mitigating MSI and CCI. Throughout this article, we have made an idealistic assumption of perfect synchronization among the BSs. Our future study will focus on the assessment of the system performance under imperfect synchronization between BSs and network latency.
Declarations
Authors’ Affiliations
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