Effect of scattering environment on estimation quality in V2I and V2V communications
© Uchiteleva and Primak; licensee Springer. 2014
Received: 30 January 2014
Accepted: 16 June 2014
Published: 11 August 2014
In this paper, we use a set of modulated discrete prolate spheroidal sequences (MDPSS) to represent a band-limited channel in the scenario with scattering from one or more clusters which can be used in both vehicle-to-infrastructure (V2I) or vehicle-to-vehicle (V2V) communication cases. Then we evaluate the performance of 2×1 space-time transmit diversity (STTD) system with Alamouti coding and imperfect channel estimation at the receiver. We consider examples of different scattering environments which represent vehicular communication in urban areas, derive expressions for autocorrelation function of channel gains and verify it by simulation. Scattering effect on estimation quality of the system is examined in terms of minimum mean square error (MMSE) and bit error rate (BER).
High-quality channel state information (CSI) is essential for reliable performance of any practical communication system. The most popular approach is estimation via training sequences (pilots) which are periodically inserted into the data stream [1–3]. The receiver extracts pilot sequences and, relying on the knowledge of channel statistics, performs the estimation. For simulation purposes, Rayleigh fading channels with Jake’s spectrum  and real-valued auto-covariance function are usually assumed, for example in works [1–3, 5, 6]. This is the worst case scenario, since there is no preferable angle of arrival (AoA). Therefore, it leads to unnecessarily large amount of pilots needed for reliable estimation, which is inefficient. Moreover, practical channels usually exhibit non-symmetric spectrum and complex-valued auto-covariance functions. This work is focused on the estimation in a realistic urban environment. Hence, our goal is to account for a complex scenario, which describes scattering from one or more narrow clusters near the mobile, what results in the presence of diffusive components in received signal coming from particular AoA, and to provide qualitative analysis of estimation in different real-life scattering scenarios. Measurements show, that realistic spectrum could be represented as a sum of sub channels with a narrow and rectangular spectra [7, 8]. Therefore, we can assume that the signal spectrum can be approximated as a group of distinct rectangles (corresponding to different clusters) and not as a classical Jake’s bathtub shape. Such representation allows us to perform more practical analysis of communication link and obtain more sensible results of estimation quality.
Channel basis expansion models (BEM) recently gained attention due to simplicity of their implementation . For example, some models describing Jake’s spectrum include complex-exponential BEM  or polynomial BEM . Discrete Karhunen-Loeve BEM is optimal in mean square error (MSE) sense [11, 12]. In this expansion, optimal set of basis functions depends on the spectrum shape. It was shown in [11, 13] that for a rectangular-shaped spectrum, a set of discrete prolate spheroidal sequences (DPSS) is optimal. Moreover, with the assumption that the spectrum can be approximated as an aggregate of rectangles, DPSS would provide a universal basis expansion. The channel model we use is described by a four-dimensional tensor of MDPSS representing channel response . By modulation of the bandwidth of a set of DPSS, we achieve different scattering scenarios with parameters defined by theoretical models or/and measurements .
V2V communication is accompanied by the movement of both receive and transmit sides with low elevation antennas and scatterers, which are assumed to be located on perimeters of multiple co-focal ellipses (with the receiver and the transmitter at ellipses’ foci). MDPSS channel model is a regular-shaped geometry-based stochastic model (RS-GBSM), which is very flexible in definition of the geometry and location of different clusters in Moderate Spatial Scale (MSS) or Small Spatial Scale (SSS) scenarios . Furthermore, this model is suitable for application in both V2I and V2V scenarios, as it gives us the control over definition of the motion of both communication sides. Thereafter, we evaluate how scattering from narrow clusters affects estimation quality of the mobile. These results could be further used in analysis and optimization of IP-level protocols, such as PMIPv6 .
Multiple-input single-output (MISO) is a very common scenario in the downlink of a cellular system. Therefore, in our work, we focused on a simple yet elegant coding technique, the Alamouti scheme , which is used in some third/fourth generation wireless mobile standards. Pilot-assisted channel estimation is used with Wiener filter as a pilot filter . In IEEE 802.11p, V2x communication standard single-input single-output (SISO) systems are postulated, but multiple-input multiple-output (MIMO) systems and their variations could be employed to improve the reliability of communications.
The remainder of our paper is organized as follows: in Section 2, the MDPSS-based channel model is reviewed and simulation results for one and two cluster case are presented. The 2×1 MISO communication system with Alamouti coding and channel estimation is described in Section 3. In Section 4, two different cases of environment were tested and the performance of the system was evaluated via MMSE and BER. Moreover, an example of simulation of the channel at a real intersection was shown, followed by analysis of communication link. The conclusion is in Section 5.
2 Channel model
2.1 Geometry and channel response
2.2 Simulation examples
Example of simulation parameters for the channel with one scattering cluster
Number of antennas on the receiving side
Number of antennas on the transmitting side
Speed of the receiver
Speed of the transmitter
Required channel half-bandwidth
d r , d t
Receive/transmit antenna spacing normalized to
Power weights for clusters
Azimuthal angle at which center of the cluster
is seen to the receiver
Azimuthal angle at which center of the
cluster is seen to the transmitter
α r ,α t
The angle between broadside vector and
Δ ϕ r
Angular spread seen from receiving side
Δ ϕ t
Angular spread seen from transmitting side
0.3 μ s
A mean delay associated with the cluster
0.1 μ s
Corresponding delay spread
Sampling frequency in delay domain
Rate of sampling in Doppler domain
Length of the impulse response (num of samples)
Number of samples (in Doppler domain)
Number of equally spaced samples for process
representation at bandwidth [ −W, W]
The transmission rate, bits per second
Two-cluster environment parameters
0.3 μ s
0.8 μ s
3 Transmission system
At first symbol time, x1 =u1, x2 =u2 are transmitted
At second symbol time, , are transmitted
It is also assumed that the channel remains constant over two symbol times: h1 =h1 =h1, h2 =h2 =h2 (the quasi-static channel assumption is valid when data rates are relatively high).
is the average data signal-to-noise ratio (SNR) or E b /N0, when is the amplitude of the signal.
Index m runs on frame slots with interval 2(N b +1)T s . It is worth mentioning that since we deal with Gaussian distributed channel gains, Wiener filter is an optimal estimation filter.
4 Simulation results of system performance in different scenarios
Assuming that the exact geometry description of clusters and obstacles is available through different accessible applications like Google Maps Ⓒ for 3D street view or through different global navigation and positioning satellite systems like GPS, GLONASS or QZSS, it is possible to model the geometry of any site of interest. Further, we present different scenarios of V2I and V2V cases.
4.1 V2I communication scenario
4.2 V2V communications scenario
4.3 Simulation of a real intersection in V2I case
Parameters of clusters in scenario on Wonderland Road and Oxford Street intersection
ϕ r (°)
Δ ϕ r (°)
ϕ t (°)
Δ ϕ t (°)
τ (μ s)
Δ τ (μ s)
In a similar way, the communication in any type of terrain, containing multiple obstacles, can be analyzed. Of course, extension to more complicated scenarios describing bigger number of clusters with non-symmetrical allocation is straightforward. Also, another various kinds of modulation and transmission schemes could be evaluated to improve the overall performance of the system.
In this paper, MDPSS-based channel model was adopted for representing a practical environment containing one or more clusters whose geometry is known and predefined. It mimics realistic channels with non-symmetric spectra and complex-valued auto-covariance function, what allowed us to obtain more reasonable results. STTD communication system with Alamouti coding and pilot-based channel estimation was described in detail and applied to two different realistic scenarios: one of them depicts V2I communication with a mobile moving under a big cluster located on the way of the mobile, like a road sign. The other one sketched V2V case with two similar clusters located on one side of the road and two communicating mobiles passing by. The analysis of estimation quality were performed for each scenario. In both cases, an increase in estimation MMSE was detected in the vicinity of clusters resulting in the degradation of system performance in terms of BER. The effect of performance downgrading is larger in cases of longer frames between pilot signals, as a straightforward result from quickly decaying auto-covariance function of channel gains in occurrence of clusters in the environment. In the first scenario, the increase in MMSE and BER was higher than in the second scenario, although with shorter duration. Finally, an example of implementation of aforementioned channel model in simulation of communication at a real-life intersection was presented and discussed. It is worth mentioning that due to flexibility of the MDPSS simulator, the description of a vast variety of different scenarios is available, allowing one to easily test any kind of environment with different positioning of clusters in both V2V and V2I cases.
The authors are supported by NSERC Canada.
- Cavers JK: An analysis of pilot symbol assisted modulation for rayleigh fading channels. IEEE Trans. Veh. Tech 1991, 40: 686-693. 10.1109/25.108378View ArticleGoogle Scholar
- Almustafa K, Primak S, Willink T, Baddour K: On Achievable Data Rates and Optimal Power Allocation in Fading Channels with Imperfect Channel State Information. In IEEE 4th International Symposium on Wireless Communication Systems. Trondheim, Norway; 17–19 Oct. 2007.Google Scholar
- Jootar J, Zeidler JR, Proakis JG: Performance of Alamouti space-time code in time-varying channels with noisy channel estimates. In IEEE Wireless Communications and Networking Conference. New Orleans, LA, USA; 13–17 March 2005.Google Scholar
- Tse D, Viswanath P: Fundamentals of Wireless Communication. Cambridge University Press, New York; 2005.View ArticleMATHGoogle Scholar
- Zhu H, Xia B, Tan Z: Performance analysis of Alamouti transmit diversity with QAM in imperfect channel estimation. IEEE J. Selected Areas Commun 2011, 29: 1242-1248.View ArticleGoogle Scholar
- Tang Z, Cannizzaro RC, Leus G, Banelli P: Pilot-assisted time-varying channel estimation for OFDM systems. IEEE Trans. Sygnal Process 2007, 55: 2226-2238.MathSciNetView ArticleGoogle Scholar
- Andersen J, Blaustaein N: Multipath Phenomena in Cellular Networks. Artech House, Norwood; 2002.Google Scholar
- Blaunstein N, Toeltsch M, Laurila J, Bonek E, Katz D, Vainikainen P, Tsouri N, Kalliola K, Laitinen H: Signal power distribution in the Azimuth, elevation and time delay domains in urban environments for various elevations of base station antenna. IEEE Trans. Antenn. Propag 2006, 54: 2902-2916. 10.1109/TAP.2006.882150MathSciNetView ArticleGoogle Scholar
- Tsatsanis MK, Giannakis GB: Modeling and equalization of rapidly fading channels. Int. J. Adapt. Control Signal Process 1996, 10: 159-176. 10.1002/(SICI)1099-1115(199603)10:2/3<159::AID-ACS346>3.0.CO;2-MView ArticleMATHGoogle Scholar
- Borah DK, Hart BD: Frequecy-selective fading channel estimation with a polynomial time-varying channel model. IEEE Trans. Commn 1999, 47: 862-873. 10.1109/26.771343View ArticleGoogle Scholar
- van Trees H: Detection, Estimation and Modulation Theory: Part 1. Wiley, New York; 2001.View ArticleMATHGoogle Scholar
- Visintin M: Karhunen-Loeve expansion of fast Rayleigh fading process. IEEE Electron. Lett 1996, 32: 1712-1713. 10.1049/el:19961128View ArticleGoogle Scholar
- Zemen T, Mecklenbrauker C: Time-variant channel estimation using discrete prolate spheroidal sequences. IEEE Trans. Signal Process 2005, 53: 3597-3607.MathSciNetView ArticleGoogle Scholar
- Haghighi SJ, Primak S, Kontorovich V, Sejdic E: Wireless communications and multitaper analysis: applications to channel modeling and estimation. In Mobile and Wireless Communications Physical Layer Development and Implementation. InTech Publishing,, Rijeka; 2010.Google Scholar
- Wang C-X, Cheng X: Vehicle-to-vehicle channel modeling and measurements: recent advances and future challenges. IEEE Commun. Mag 2009, 47: 96-103.View ArticleGoogle Scholar
- Lee J-H, Ernst T, Chilamkurti N: Performance analysis of PMIPv6-based network mobility for intelligent transportation systems. IEEE Trans. Veh. Tech 2012, 61: 74-85.View ArticleGoogle Scholar
- Haykin S: Adaptive Filter Theory. Prentice Hall, Upper Saddle River; 2001.MATHGoogle Scholar
- Bernardo L, Roma A, Czink N, Paier A, Zemen T: Cluster-based scatterer identification and characterization in vehicular channels. In 11th European Wireless Conference - Sustainable Wireless Technologies (European Wireless). Vienna, Austria; 27–29 April 2011:1-6.Google Scholar
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.