Practices:channel modeling for modemn communication systems 265 -0.7 . 01 0 (reference model)model,for diferent vales of 9.3.4 Numerical Results and Analysis((10.3.4)) Based on the derived STF CFs for wideband and narrowband MIMO channels in Chapter 10.3.2,the degenerate CFs arenumcricaowanabKedndeai darowoeddetcTmn5t。0 the corresponding reference models.All the results pre sented in this section are obtained using the following basic parameters:fe=5 GHz,fD=463 Hz,D=2000 m,BT=/6,BR=/3,and y=7/12 Correlation Properties of Wideband MIMO Channel Models A2=4 and (R2.i TU channel mod el with comp the number of th 10MHz is used in FIGURE 10.2,while the parameter of Lnorm gue3λ applied in FIGURE 10.3 nc vary according to the nent t uencys tha eved that the the cr lecrea of angle spre of the e impact of the
Practices: channel modeling for modern communication systems 265 Fig. 9.2 The frequency CFs |ρl,oq;l,oq (χ)| (reference model) and |ρ˜l,oq;l,oq (χ)| (simulation model, N = 45) for different values of the parameter k. 9.3.4 Numerical Results and Analysis ((10.3.4)) Based on the derived STF CFs for wideband and narrowband MIMO channels in Chapter 10.3.2, the degenerate CFs are numerically analyzed in detail. In addition, verification of the proposed wideband and narrowband deterministic SoS simulation models is carried out by comparing the correlation properties of the simulation models with those of the corresponding reference models. All the results presented in this section are obtained using the following basic parameters: fc=5 GHz, fD=463 Hz, D=2000 m, βT=π/6, βR=π/3, and γ=7π/12. • Correlation Properties of Wideband MIMO Channel Models Without loss of any generality, we constrain our investigation on the correlation properties of the second tap (l = 2) with Λ2=4 and {R2,i} 3 i=0={50, 100, 400, 750} m based on (9.11). The discrete COST 207 TU channel model with {τ ′ l } 5 l=0={0, 0.2, 0.5, 1.6, 2.3, 5} µs will be applied. For simplicity, we assume that kl,i,r=k for all effective clusters in the tap. FIGURES 10.2 and 10.3 show the resulting frequency CF and space-frequency (SF) CF with δT = 0, respectively. As a good trade off between the complexity and performance of the wideband simulation model, the number of effective scatterers N = 45 and the parameter of Lp-norm p = 2 are used in both figures. Moreover, the parameter of Lp-norm χmax = 10 MHz is used in FIGURE 10.2, while the parameter of Lp-norm δ max R = 3λ is applied in FIGURE 10.3. From FIGURE 10.2, it is clear that the trend of frequency CFs decreases with the increase of the frequency separation χ. FIGURE 10.2 also illustrates that the frequency correlations vary according to the environment parameter k that controls the angle spread of the AoA. It can be observed that the frequency correlations increase with the increase of k (i.e., with the decrease of angle spread of AoA). FIGURE 10.3 shows that the trend of SF CFs decreases with the increase of the space separation δR. FIGURE 10.3 also depicts the impact of the environment parameter k on the SF correlations. It is obvious that the SF correlations increase with the increase of k. From FIGURE 10.3, we can also observe the impact of frequency separation on spatial
266 Practices:channel modeling for modern communication systems k= 25 k=100 0.5 25 correlations.It is clear that the frequency separation decreases the spatial correlation.Therefore,we can conclude that hngoncyCrgragfhonslethegtetedtoehyheacespatalcorehaionaedueohespatia ocodd MTMO-OPDMor theh 二 Correlation Properties of Narrowband MIMO Channel Models stigate the MIMO ch are obtained by using3 and eparation and spa aration and scatterer 105 h)illustates the frequenc C of the reference modeland the one of the simulation em ed deterministic simulation model can fit the
266 Practices: channel modeling for modern communication systems 0 0.5 1 1.5 2 2.5 3 0 0.5 1 Antenna element spacing (δ R /λ) Space−frequency CF 0 0.5 1 1.5 2 2.5 3 0 0.5 1 Antenna element spacing (δ R /λ) Space−frequency CF 0 0.5 1 1.5 2 2.5 3 0 0.5 1 Antenna element spacing (δ R /λ) Space−frequency CF Ref. model, χ=0 (numerical integration) Ref. model, χ=0 (closed−form) Simulation model (N=45), χ=0 Ref. model, χ=1MHz Ref. model, χ=0 (numerical integration) Ref. model, χ=0 (closed−form) Simulation model (N=45), χ=0 Ref. model, χ=1MHz Ref. model, χ=0 (numerical integration) Ref. model, χ=0 (closed−form) Simulation model (N=45), χ=0 Ref. model, χ=1MHz k=0 k=10 k=100 Fig. 9.3 The SF CFs |ρl,oq;l,o′q′ | (reference model) and |ρ˜l,oq;l,o′q′ | (simulation model, N = 45) for different values of the parameter k. correlations. It is clear that the frequency separation decreases the spatial correlation. Therefore, we can conclude that in such a case, the resulting correlation is jointly contributed to by the actual spatial correlation (i.e., due to the spatial distance/geometry of arrays only) and inherent frequency correlation. Note that this resulting correlation is important for the appropriate design of STF coded MIMO-OFDM systems ? and is also useful for the sensible utilisation of the SF diversity ?. In addition, we depict in both FIGURES 10.2 and 10.3 the CFs of the reference model with both the closed-form expression and the numerical integration method, and the simulation model. Clearly, all these results match very well, demonstrating the validity of our derivation and excellent performance of our simulation model. • Correlation Properties of Narrowband MIMO Channel Models In this subsection, we will investigate the correlation properties for narrowband MIMO channels based on (9.16) and evaluate the performance of the proposed narrowband simulation model. All the results presented in this subsection are obtained by using k = 3 and µ = π. FIGURES 10.4 (a) and (b) illustrate the SF CFs against the frequency separation and space separation at the BS and MS, respectively. Comparing them, we find that the impact of the normalized antenna spacing at the MS is greater than the one at the BS. This is because that the angular spread Θ at the BS is generally small for macro-cell scenarios. FIGURES 10.4 (a) and (b) also show that the trend of relevant CFs decreases with the increase of the frequency separation χ and space separation δT and δR. A plot of the time CF of the reference model is shown in FIGURE 10.5 (a). This figure also depicts the resulting time CF of the simulation model designed with the Lp-norm using p = 2 and τmax = 0.08 s, and the number of effective scatterers N = 30. FIGURE 10.5 (b) illustrates the frequency CF of the reference model and the one of the simulation model, when applying the Lp-norm with p = 2 and χmax = 8 MHz, and the number of effective scatterers N = 30. FIGURES 10.6 (a) and (b) depict the space CF of the reference model and the one of the simulation model with N = 30, respectively. The discrete AoAs φ˜′′R n have been obtained by using the Lp-norm with p = 2, δ max T = 30λ, and δ max R = 3λ. FIGURES 10.5 and 10.6 clearly demonstrate that the proposed deterministic simulation model can fit the underlying reference model very well in terms of time, frequency, and space correlation properties
Practices:channel modeling for modemn communication systems 267 2.5 25 0万152 22 75 (H 100 (wave length (MH 100 8 (wave length) -ACF (ref.model) 一-ACF (sim..md,h3 0 2 6 with N=30
Practices: channel modeling for modern communication systems 267 0 0.75 1.5 2.25 3 10 7.5 5 2.5 0 0 0.5 1 G R F /O (wave length) (MHz) Cross-correlation function 0 7.5 15 22.5 30 10 7.5 5 2.5 0 0 0.5 1 G T F /O (wave length) (MHz) Cross-correlation function Space-frequency CF Space-frequency CF (a) (b) Fig. 9.4 (a) The SF CF |ρoq;o′q′ (χ)| versus the frequency separation χ and the normalised antenna spacing at the MS δR with δT = 0; (b) the SF CF |ρoq;o′q′ (χ)| versus the frequency separation χ and the normalised antenna spacing at the BS δT with δR = 0. 0 0.02 0.04 0.06 0.08 0.1 0 0.2 0.4 0.6 0.8 1 Time separation, W (s) Correlation functions ACF (ref. model) ACF (sim. model, N=30) 0 2 4 6 8 10 0 0.2 0.4 0.6 0.8 1 Frequency separation, F (MHz) Correlation functions ACF (ref. model) ACF (sim. model, N=30) Time CF Frequency CF (a) (b) Fig. 9.5 (a) The time CF |ρoq;oq(τ )| of the reference model and the time CF |ρ˜oq;oq(τ )| of the corresponding simulation model with N = 30; (b) the frequency CF |ρoq;oq(χ)| of the reference model and the time CF |ρ˜oq;oq(χ)| of the corresponding simulation model with N = 30
268 Practices:channel modeling for modern communication systems 05 15 15 225 30 (wave length) .(wave length) (a) (b) 9.3.5 Summary(10.3.5) gn103.wetanemaneaeo时oeadhedod6aeeoha3Mm has been we have d the proposed d M M0 channels be reduced and the inherent freque properties betv the reference models and simul ation mo ls has valid ted the of the proposed determi inisti mla0od.heeoposedsnngbaedLmaerereceodandrdetenncmaiolomde55 such as frequency-hopping MIMO and MIMO-OFDM channels. 9.4 Scattering theoretical channel models for vehicle-to-vehicle systems((10.4)) This section will focus on the development of more real scattering theoretical channel models for MIMO V2V channels under the condition of non-isotropic scattering environments 9.4.1 Narrowband MIMO vehicle-to-vehicle channels:modeling and statistical properties investigation ((10.4.1)) The reference model applied in Chaprer 5(ie..the two-ring RSGBSM)is over-simple and capturesom arios,and has the ab most important statistics that sigificantly distinguish V2y channels from F2M channels.more detailed investigation
268 Practices: channel modeling for modern communication systems 0 7.5 15 22.5 30 3 2.25 1.5 0.75 0 0 0.5 1 G T /O (wave length) G R /O (wave length) Cross-correlation function 0 7.5 15 22.5 30 3 2.25 1.5 0.75 0 0 0.5 1 G T /O (wave length) G R /O (wave length) Cross-correlation function Space CF Space CF (a) (b) Fig. 9.6 (a) The space CF |ρoq;o′q′ | of the reference model and (b) the space CF |ρ˜oq;o′q′ | of the corresponding simulation model with N = 30. 9.3.5 Summary ((10.3.5)) In Chapter 10.3, we have extended the narrowband one-ring MIMO model to a new wideband multi-ring based MIMO RS-GBSM. According to the TDL structure of our model, the closed-formed expression of the STF CF for each tap has been derived. We have demonstrated that the traditional narrowband one-ring model is actually a special case of the proposed wideband model. Therefore, the derived generic STF CF for wideband MIMO channels can be reduced to the STF CF with a compact closed-from expression for narrowband MIMO channels by removing the frequencyselectivity. From the proposed wideband multi-ring based MIMO reference model and the traditional narrowband one-ring MIMO reference model, corresponding wideband and narrowband deterministic SoS simulation models have been proposed. Numerical results have revealed the impact of the environment parameter k on frequency correlations and the inherent frequency correlations within spatial correlations. Finally, the excellent agreement of correlation properties between the reference models and simulation models has validated the utility of the proposed deterministic simulation models. The proposed multi-ring based MIMO reference model and deterministic simulation models are very useful for the theoretical analysis and practical simulation, respectively, of frequency-correlated MIMO channels, such as frequency-hopping MIMO and MIMO-OFDM channels. 9.4 Scattering theoretical channel models for vehicle-to-vehicle systems ((10.4)) This section will focus on the development of more real scattering theoretical channel models for MIMO V2V channels under the condition of non-isotropic scattering environments. 9.4.1 Narrowband MIMO vehicle-to-vehicle channels: modeling and statistical properties investigation ((10.4.1)) The reference model applied in Chapter 5 (i.e., the two-ring RS-GBSM) is over-simple and thus cannot capture some important features of V2V channels. Therefore, as reviewed in Chapter 5, several important RS-GBSMs for narrowband MIMO V2V channels have been provided in ?????. However, none of the previously reported RS-GBSMs is sufficiently general to characterise a wide variety of V2V scenarios, especially for pico-cell scenarios, and has the ability to take the impact of the VTD on channel statistics into account. Although the Doppler PSD, envelope LCR, and AFD are the most important statistics that significantly distinguish V2V channels from F2M channels, more detailed investigations of these statistics in non-isotropic scattering environments are surprisingly lacking in the open literature. Moreover, frequency correlations of sub-channels with different carrier frequencies in V2V communications have not been studied so far, although OFDM has already been suggested for use in IEEE 802.11p. Motivated by the above gaps, in this chapter we propose a new narrowband RS-GBSM that addresses all the aforementioned shortcomings of the existing RS-GBSMs. Based on the proposed model, some important channel
Practices:channel modeling for modern communication systems 269 1)A generic RS-GBSM for narrowband non-isotropic scattering MIMO V2V Ricean fading channels will be first RS-GBSN g 5)From the proposed model.s derive analysis shows that the SD PSD of a singlbounce two-ring model for non-isotropic scattering c mo。eamg which in nd LCRs neglected but important isue observations and conclusions can be co dered as the guidance for adjusting important parametersof ourmod ent data in are compared Excellent agreement between them demonstrates the utility of the proposed model. An Adaptive Model for Non-Isotropic Scattering MIMO Mobile-to-Mobile Ricean Fading Channels Let us not and sing r MIMo V2y mult with rtr andM发eneomaetnoalaniena2eiCens.BohhexandRaeequpedaowewaionarenn FIGURE 10.7 ich is the com bination of a singl and doub 2were used here.The two-rng model defines of effective scatterers. xand the otheraroun there are Neffe the lying of radius R 2)effective scatterer is denoted by For the eTx and Rx located t the foci. The he antenna elen cnt spa the 'Ix and Rx are designated by r and or,respectively.It is normal umed tha t sr r and ing fr d the py is den gnated by Note that denotes the AoA of a Los path. of size MRx Mr.The received Mr)Tx and the gth( he carrier frequencyfe d components,and an be e h)=h()+h(+h( (9.33)
Practices: channel modeling for modern communication systems 269 statistics, such as the STF CF, SDF PSD, envelope LCR, and AFD, are derived. The content of Chapter 10.4.2 are summarised as follows. 1) A generic RS-GBSM for narrowband non-isotropic scattering MIMO V2V Ricean fading channels will be introduced. The proposed model can be adapted to a wide variety of scenarios, e.g., macro-, micro-, and pico-cell scenarios, by adjusting some model parameters. 2) By distinguishing between the moving cars and the stationary roadside environment in micro- and pico-cell scenarios, the developed model is the first RS-GBSM to consider the impact of the VTD on V2V channel characteristics. 3) This chapter will present a new general method to derive the exact relationship between the AoA and AoD for any known shapes of the scattering region, e.g., one-ring, two-ring, or ellipse, in a wide variety of scenarios. 4) This chapter will point out that the widely used CF definition in ???? is incorrect and is actually the complex conjugate of the correct CF definition as given in Stochastic Processes ?. 5) From the proposed model, this chapter will derive the STF CF and the corresponding SDF PSD, which are sufficiently general and can be reduced to many existing CFs and PSDs, respectively, e.g., those in ????. In addition, our analysis shows that the SD PSD of a single-bounce two-ring model for non-isotropic scattering MIMO V2V fading channels derived in ? is incorrect. 6) Considering the simplified version (SISO) of our proposed MIMO model, this chapter will derive the envelope LCR and AFD, which include many existing LCRs and AFDs as special cases, e.g., those in ????. Our analysis shows several flaws in the derivation and investigation of the LCR and AFD in ? and ?, revealing some easily neglected but important issues. 7) Based on the derived STF CF, SDF PSD, envelope LCR, and AFD, this chapter will study in more detail these channel statistics in terms of some important parameters and thus obtain some interesting observations. These observations and conclusions can be considered as the guidance for adjusting important parameters of our model properly and setting up more purposeful V2V channel measurement campaigns in the future. Finally, the some obtained theoretical results (e.g., Doppler PSDs, LCR, and AFD) and measurement data in ? are compared. Excellent agreement between them demonstrates the utility of the proposed model. • An Adaptive Model for Non-Isotropic Scattering MIMO Mobile-to-Mobile Ricean Fading Channels Let us now consider a narrowband single-user MIMO V2V multicarrier communication system with MT transmit and MR receive omnidirectional antenna elements. Both the Tx and Rx are equipped with low elevation antennas. FIGURE 10.7 illustrates the geometry of the proposed RS-GBSM, which is the combination of a single- and doublebounce two-ring model, a single-bounce ellipse model, and the LoS component. As an example, uniform linear antenna arrays with MT = MR = 2 were used here. The two-ring model defines two rings of effective scatterers, one around the Tx and the other around the Rx. Suppose there are N1 effective scatterers around the Tx lying on a ring of radius RT and the n1th (n1 = 1, ..., N1) effective scatterer is denoted by s (n1) . Similarly, assume there are N2 effective scatterers around the Rx lying on a ring of radius RR and the n2th (n2 = 1, ..., N2) effective scatterer is denoted by s (n2) . For the ellipse model, N3 effective scatterers lie on an ellipse with the Tx and Rx located at the foci. The semi-major axis of the ellipse and the n3th (n3 = 1, ..., N3) effective scatterer are denoted by a and s (n3) , respectively. The distance between the Tx and Rx is D = 2f with f denoting the half length of the distance between the two focal points of the ellipse. The antenna element spacings at the Tx and Rx are designated by δT and δR, respectively. It is normally assumed that the radii RT and RR, and the difference between the semi-major axis a and the parameter f, are all much greater than the antenna element spacings δT and δR, i.e., min{RT , RR, a − f} ≫ max{δT , δR}. The multi-element antenna tilt angles are denoted by βT and βR. The Tx and Rx move with speeds υT and υR in directions determined by the angles of motion γT and γR, respectively. The AoA of the wave traveling from an effective scatterer s (ni) (i ∈ {1, 2, 3}) toward the Rx is denoted by φ (ni) R . The AoD of the wave that impinges on the effective scatterer s (ni) is designated by φ (ni) T . Note that φ LoS Rq denotes the AoA of a LoS path. The MIMO fading channel can be described by a matrix H (t) = [hoq (t)]MR×MT of size MR × MT . The received complex fading envelope between the oth (o = 1, ..., MT ) Tx and the qth (q = 1, ..., MR) Rx at the carrier frequency fc is a superposition of the LoS, single-, and double-bounced components, and can be expressed as hoq (t) = h LoS oq (t) + h SB oq (t) + h DB oq (t) (9.33)