Performance Analysis of Wideband SOS-based Channel Simulators by ajizai

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									  Performance Analysis of Wideband SOS-based Channel

Simulators with Respect to the Bit Error Probability of BPSK
      OFDM Systems with Perfect and Imperfect CSI

                                   Yuanyuan Ma


                       Faculty of Engineering and Science
                               University of Agder
                   P. O. Box 509, NO-4898 Grimstad, Norway
                           E-mail: yuanyuan.ma@uia.no
             Homepage: http://ikt.hia.no/mobilecommunications/




           OptiMO & M2M Joint Meeting, 14 August 2009, UiA, Norway
                                            1/18
Contents




   I.   Aims of WP1.1

  II.   Promised Output and Achieved Output

 III.   Overview of Research Topics

 IV.    Methods

  V.    Future Plan




                      OptiMO & M2M Joint Meeting, 14 August 2009, UiA, Norway
                                                       2/18
I. Aims of WP1.1


                                      Wireless MIMO Channels
Problem:     Channel changes fast due to the mobility and the environment.
             • Available channel capacity
             • Choice of the transmission schemes used in heterogeneous MIMO networks

Motivation: It is important to develop realistic and accurate MIMO channel models for the
             purpose of simulate, design, and evaluate wireless communication systems.

Aims:        • Develop MIMO channel models for different typical propagation environments.
             • Develop reference and simulation models for frequency-selective MIMO mobile
               fading channels.


                   Performance Analysis of Developed Channel Simulators
Aim:       • Analyze OFDM and STBC-OFDM system performance using the developed
             channel simulators.




                    OptiMO & M2M Joint Meeting, 14 August 2009, UiA, Norway
                                                     3/18
II. Promised Output and Achieved Output

Promised output: 2 journal papers and 6 conference papers.
Achieved output:
5 accepted conference papers:
• Y. Ma and M. Patzold, Performance Analysis of Wideband SOS-Based Channel Simulators with Respect to the Bit
                ¨
  Error Probability of BPSK-OFDM Systems with Perfect and Imperfect CSI, in Proc. WPMC 2009, Sendai, Japan,
  Sept. 2009, accepted for publication.

• Y. Ma and M. Patzold, Performance Analysis of Wideband Sum-of-Cisoids-Based Channel Simulators with Respect to
                  ¨
  the Bit Error Probability of DPSK-OFDM Systems, in Proc. VTC 2009-Spring, Barcelona, Spain, April 2009.

• Y. Ma and M. Patzold, A Wideband One-Ring MIMO Channel Model Under Non-Isotropic Scattering Conditions,
                  ¨
  in Proc. VTC 2008-Spring, Singapore, May 2008, pp. 424–429.

• Y. Ma and M. Patzold, Wideband Two-Ring MIMO Channel Models for Mobile-to-Mobile Communications,
                   ¨
  in Proc. WPMC 2007, Jaipur, India, Dec. 2007, pp. 380–384.

• Y. Ma and M. Patzold, Performance Comparison of Space-Time Coded MIMO-OFDM Systems Using Different Wide-
                ¨
  band MIMO Channel Models, in Proc. ISWCS 2007, Trondheim, Norway, Oct. 2007, pp. 762–766.


2 submitted conference papers:
• Y. Ma and M. Patzold, Performance Analysis of STBC-OFDM Systems in Temporally and Spatially Correlated Fading
                ¨
  Channels, in Proc. WCSP 2009, Nanjing, China, Nov. 2009.

• C. E. D. Sterian, Y. Ma, M. Patzold, Huaqiang He and Ion Banica, Super-Orthogonal Space-Time Trellis Codes with
                               ¨                            ˇ   ˇ
  Differential Phase Modulation for Noncoherent Mobile Communication Systems, in Proc. WCSP 2009, Nanjing, China,
  Nov. 2009.

                      OptiMO & M2M Joint Meeting, 14 August 2009, UiA, Norway
                                                       4/18
III. Overview of Research Topics


Mobile-to-Mobile MIMO Channel Modeling

• Develop a narrowband two-ring single-bounce scattering MIMO channel model.

Wideband MIMO Channel Modeling
• Extend the two-ring single-bounce scattering channel model to frequency-selectivity.

• Extend the two-ring double-bounce scattering channel model to frequency-selectivity.

• Derive the wideband one-ring MIMO channel model for non-isotropic scattering environments.

Performance Analysis of Wideband MIMO Communication Systems
• Performance of wideband sum-of-sinusoids channel simulators w.r.t the BEP of OFDM systems

• Performance of wideband sum-of-cisoids channel simulators w.r.t the BEP of OFDM systems

• Performance of STBC-OFDM systems in temporally and spatially correlated fading channels

Differential Super-Orthogonal Space-Time Trellis Codes



                  OptiMO & M2M Joint Meeting, 14 August 2009, UiA, Norway
                                                   5/18
IV. Methods–Introduction


Background:
 • Rice’s sum-of-sinusoids (SOS) method has emerged as one of the key approaches for de-
   signing channel simulators for mobile fading channels
 • Accurate and efficient SOS channel simulators have been commonly used in practical system
   simulations due to their low realization expenditure.

Motivations:

 • Fundamental statistical properties of SOS channel simulators have been studied.
 • So far, the performance of the SOS channel simulator w.r.t. bit error probability (BEP) of a
   transmission system has been studied only for narrowband fading channels.

Aim:

    Analyze the performance a wideband SOS channel simulator w.r.t. the BEP of a BPSK
    OFDM system assuming both perfect and imperfect channel state information (CSI).



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IV. Methods– Frequency-Selective Channel Models

                          The Frequency-Selective Reference Channel Model

 • A wide-sense stationary uncorrelated scattering model is employed for modeling frequency-
   selective mobile fading channels.
 • The time-variant transfer function:
                      L
                                           ′ ′
       H(f ′ , t) =         aℓµℓ(t)e−j2πf τℓ ,
                      ℓ=1

                                                                                     2
   where µℓ(t) denotes a complex random Gaussian process, each having the variance 2σ0 = 1.
                                                                            ′
 • The probability density function (PDF) pζ (r) of the envelope ζ(t) = |H(f0, t)| can be described
   by the Rayleigh distribution.

                The Frequency-Selective Sum-of-Sinusoids Channel Simulator

 • The time-variant transfer function:
                      L
                                           ′ ′
       ˜    ′
       H(f , t) =           aℓµℓ(t)e−j2πf τℓ
                              ˜
                      ℓ=1

   where µℓ(t) = µ1,ℓ(t) + j µ2,ℓ(t) represents a deterministic Gaussian process.
         ˜       ˜           ˜


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IV. Methods– Frequency-Selective Channel Models

 • The complex processes µi,ℓ(t) can be represented by a sum of Ni,ℓ sinusoids as
                         ˜
                     Ni,ℓ

       µi,ℓ(t) =
       ˜                    ci,n,ℓ cos(2πfi,n,ℓ + θi,n,ℓ ),   i = 1, 2,
                     n=1

   where ci,n,ℓ , fi,n,ℓ , and θi,n,ℓ represent the Doppler coefficient, the Doppler frequency, and the
   Doppler phase of the ℓ th path, respectively.

 • Parameter computation methods:
   1) Generalized method of exact Doppler spread (GMEDS1):

                         2                                     π       1
       ci,n,ℓ = σ0           ,           fi,n,ℓ = fmax sin          (n− )+αi,ℓ ,
                        Ni,ℓ                                  2Ni,ℓ    2

  where αi,ℓ = (−1)i−1πℓ/(4Ni,ℓL) is the angle of rotation.

   2) Monte Carlo method (MCM):

                             2                                  π
       ci,n,ℓ = σ0               ,        fi,n,ℓ = fmax sin       ui,n,ℓ ,    where ui,n,ℓ ∼ (0, 1]
                            Ni,ℓ                                2

 • For both methods, we choose N1,ℓ = N2,ℓ = N for ℓ = 1, 2, . . . , L. The Doppler phases are
   considered as outcomes of a random generator with a uniform distribution over (0, 2π].
                             OptiMO & M2M Joint Meeting, 14 August 2009, UiA, Norway
                                                              8/18
IV. Methods– Frequency-Selective Channel Models

                           The Frequency-Selective SOS channel Simulator
                                  ˜       ˜ ′
 • The PDF pζ (r) of the envelope ζ(t) =| H(f0, t) |:
           ˜
                          π ∞ L

       pζ (r) = 4πr
       ˜                             [h1,ℓ(y, θ) · h′1,ℓ(y, θ) · h2,ℓ(y, θ) · h′2,ℓ(y, θ)] · J0(2πry) y dy dθ,
                      0    0   ℓ=1

   where the terms hi,ℓ(y, θ) and h′i,ℓ(y, θ) (i = 1, 2) depends on the Doppler coefficient ci,n,ℓ .

                                        0.7
                                                                                 pζ (r) (Theory)
                                        0.6
                                                                                 ˜
                                                                                 pζ (r) (Theory)
                                        0.5                                      ˜
                                                                                 pζ (r) (Simulation)
                                        0.4
                               pζ (r)




                                        0.3
                                        0.2
                                        0.1
                                         0
                                          0     0.5     1      1.5      2      2.5     3      3.5      4
                                                                        r
 • It has been proved that pζ (r) → pζ (r) for Ni,ℓ → ∞.
                           ˜
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                                                       9/18
IV. Methods– Performance Analysis of SOS channel simulators

                         The BEP of BPSK OFDM Systems with Perfect CSI
 • BEP: average the conditional BEP over the fading channel statistics
             ∞
      ˜
      Pb =       pζ (r)Pb|r (r)dr,
                 ˜
             0
                    1
   where Pb|ζ (r) = erfc r γ b is the conditional BEP of the BPSK modulation scheme
                    2
   and γ b is the average signal-to-noise ratio per bit.
 • The actual BEP: the BEP of a transmission system composed of a transmitter, a receiver and
   a SOS channel simulator
                   π ∞          2 2                  L
      ˜     1            1 − π2γy           π2y2
      Pb =                 ·e    b · M1 1 (      )         [h1,ℓ(y, θ) · h′1,ℓ(y, θ)][h2,ℓ(y, θ) · h′2,ℓ(y, θ)] dy dθ,
           2π            y            2,2    γb
                 0 0                                 ℓ=1

   where Mλ,µ (x) is the Whittaker function.
 • The reference BEP: the BEP of a transmission system composed of a transmitter, a receiver
   and a reference channel model
   Since the envelope pζ (r) is Rayleigh distributed, we have
             1               γb
      Pb =        1−                  .
             2             1 + γb

                       OptiMO & M2M Joint Meeting, 14 August 2009, UiA, Norway
                                                       10/18
IV. Methods– Performance Analysis of SOS Channel Simulators

                                                              Simulation Results
                                                0
                                               10
                                                                              Pb (Theory)
                                                                              ˜
                                                                              Pb (Theory), GMEDS1
                                                                              ˜




                       Bit error probability
                                                −1
                                               10                             Pb (Simulation), GMEDS1
                                                                              ˜
                                                                              Pb (Theory), MCM
                                                                              ˜
                                                                              Pb (Simulation), MCM
                                                −2
                                               10



                                                −3
                                               10
                                                        N =6
                                                −4
                                               10
                                                    0     5       10     15        20       25       30
                                                                       γ b (dB)


 • The wideband SOS channel simulators designed with the GMEDS1 and the MCM are equiv-
   alent w.r.t. the BEP.
                    ˜
 • The actual BEP Pb is determined by the Doppler coefficients ci,n,ℓ , while it is independent of
   the Doppler frequencies fi,n,ℓ .
                           ˜
 • It has been proved that Pb → Pb holds as N → ∞.

                   OptiMO & M2M Joint Meeting, 14 August 2009, UiA, Norway
                                                   11/18
IV. Methods– Performance Analysis of SOS Channel Simulators

                                                             Relative Error

                         ˜
 • The deviation between Pb and Pb cannot be ignored if the number of sinusoides is small.
 • Relative error of the BEP:
                ˜
               Pb − Pb
      εBEP =
                  Pb
 • The absolute value of the relative error |εBEP | is less than 4.1% if N ≥ 3.

                                                    0

                                                   −1
                         Relative error εBEP (%)




                                                   −2
                                                                                    N =6
                                                   −3
                                                                                   N =4
                                                   −4
                                                                                   N =3
                                                   −5

                                                   −6
                                                                                    N =2
                                                   −7
                                                     0   5    10     15       20   25      30
                                                                   γ b (dB)
                    OptiMO & M2M Joint Meeting, 14 August 2009, UiA, Norway
                                                    12/18
IV. Methods– Performance Analysis of SOS Channel Simulators

                       The BEP of BPSK OFDM Systems with Imperfect CSI

 • A pilot symbol is inserted before every block of P OFDM symbols.

 • If the m th symbol is a pilot symbol, according to the least-square estimation algorithm, the
   estimated CSI is determined by
       ˆ
       Hkm = Hkm + Vkm,               k = 1, 2, . . . , K.

   which is also used for the symbol decisions for the next P OFDM symbol interval.

 • The BEP of (m + p) th OFDM symbol is given by [Ref]
                            
              1             ρ1
       Pp =     1 −                       ,     p = 1, 2, . . . , P,
                                           
              2           1+   1
                                    + ρ2
                               ¯
                               γb


   where ρ1 and ρ2 represent the real and imaginary parts of the correlation coefficient of the
                 ˆ
   estimated CSI Hkm and the real CSI Hk(m+p) at the (m + p) th symbol slot.

    [Ref] M. Chang and Y. T. Su, Performance analysis of equalized OFDM systems in Rayleigh fading. IEEE Trans.
          Commun., 1(4):721–732, Oct. 2002.


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IV. Methods– Performance Analysis of SOS Channel Simulators

 • The reference BEP:
                                         P
                                                                
              P                      HH       r       (p·Ts )
                    1        1   p=1
       Pb =           P   = 1 − 2σ2P (1+                     ,
                                                             
                    P p      2                          1   )
              p=1                             0        γb

   where rHH (p · Ts ) denotes the value of the temporal autocorrelation function (ACF) rHH (τ ) of
   the reference channel model at τ = p · Ts and Ts is the OFDM symbol duration.
 • The actual BEP:
                   P
                                                 
                     rHH (p · Ts ) 
                      ˜
       ˜   1    p=1
       Pb ≈ 1 −              1 .
                                  
           2        2
                  2σ0 P (1 + γ ) 
                                          b


   For the wideband SOS channel simulator, the temporal ACF can be expressed as
                     L
       rHH (τ ) =
       ˜                  a2rµℓµℓ (τ ),
                           ℓ˜
                    ℓ=1

                            2        Ni,ℓ 2
   where rµℓ µℓ (τ ) =
           ˜                i=1      n=1 (ci,n,ℓ /2) cos(2πfi,n,ℓ τ )   describes the temporal ACF of the determin-
   istic process µℓ(t).
                    ˜

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IV. Methods– Performance Analysis of SOS Channel Simulators

                                                    Relative Error

 • The temporal ACF rHH (p·Ts) can be approximated by the following relation
                    ˜
                                                L
                               (p·Ts)2
      rHH (p·Ts) ≈ rHH (p·Ts)−
      ˜                                               a2△βℓ,
                                                       ℓ
                                  2
                                                ℓ=1

   where △βℓ denotes the model error of the SOS channel simulator, which is determined by
   the values of the Doppler coefficients cn,ℓ and the Doppler frequencies fn,ℓ .
                        ˜
 • Thus, the actual BEP Pb can be expressed in closed-form as
      ˜
      Pb = Pb + △Pb

   where
              P              2 L
                    p · Ts
                                    a2△βℓ
                                     ℓ
              p=1     2       ℓ=1                               △Pb
      △Pb =           2         1           ,         (εBEP =       ),
                    2σ0 P (1 + γ )                               Pb
                                   b

   represents the deviation of the BEP.
 • Using the deviation of the BEP △Pb or the relative error εBEP as a criterion, we can evaluate
   the performance of the GMEDS1 and the MCM.

                    OptiMO & M2M Joint Meeting, 14 August 2009, UiA, Norway
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IV. Methods– Performance Analysis of SOS Channel Simulators

                                                                  Simulation results
                         0                                                                               0
                        10                                                                              10
                                                             Pb (Theory)                                                                             Pb (Theory)
                                                             ˜
                                                             Pb (Theory)                                                                              ˜
                                                                                                                                                     Pb (Theory)




                                                                                Bit error probability
Bit error probability




                         −1
                        10                                   ˜
                                                             Pb (Simulation)
                                                                                                         −1
                                                                                                        10                                      ·    ˜
                                                                                                                                                     Pb (Simulation)

                                                 fmax = 500 Hz, P = 5
                         −2                                                                              −2      fmax = 500 Hz, P = 10
                        10                                                                              10
                                                                                                                          fmax = 500 Hz, P = 5
                         −3
                        10
                                                                                                         −3
                                                                                                        10                         fmax = 100 Hz, P = 10
                                                 fmax = 100 Hz, P = 5                                            N =6
                                 N =6                                                                                                       fmax = 100 Hz, P = 5
                         −4                                                                              −4
                        10                                                                              10
                             0     5    10     15       20        25       30                                0        5       10       15           20     25          30
                                             γ b (dB)                                                                                γ b (dB)


           • It is shown that increasing fmax or the value of P leads to BEP performance degradations.
           • If the GMEDS1 is applied to design the SOS channel simulator, the model error △βℓ = 0.
                                                                                                    ˜
           • If the SOS channel simulator is designed by the MCM, the single realization of the BEP Pb,
             deviates from the reference BEP Pb in a random manner.




                                         OptiMO & M2M Joint Meeting, 14 August 2009, UiA, Norway
                                                                         16/18
IV. Methods– Conclusion


 • The performance of the frequency-selective SOS channel simulator has been analyzed w.r.t.
   the BEP of BPSK OFDM systems.

 • Analytical expressions for the BEP have been derived for these systems in the presence of
   perfect and imperfect CSI.

 • It has been proved that the actual BEP evaluated in the presence of a SOS channel simulator
   converges to the reference BEP, when the number of sinusoids tends to infinity.

 • By employing the relative error of the BEP as an appropriate criterion, the deterministic pa-
   rameter design method (GMEDS1) and the stochastic one (MCM) have been compared.

 • Under the assumption of perfect CSI, the SOS channel simulators designed by the GMEDS1
   and the MCM are equivalent w.r.t. the BEP performance.

 • In the presence of imperfect CSI, the GMEDS1 outperform the MCM.




                   OptiMO & M2M Joint Meeting, 14 August 2009, UiA, Norway
                                                   17/18
V. Future Plan

                                      List of Open Problems

 • Develop dynamic spatially correlated MIMO channel models.
 • Develop MIMO reference channel models for different typical propagation environments.
 • Develop efficient channel simulators by using the concept of deterministic channel modeling.
 • Develop reference and simulation models for wideband MIMO mobile fading channels.
 • Study the MIMO-OFDM system performance using the developed channel models.
 • Develop multiuser MIMO channel models.

                      Plan for Solving the Remaining Open Problems

 • Develop channel models for indoor propagation environments (2009.07.15-2009.12).
   ⇒ Analyze the statistical properties of the indoor channel models.
   ⇒ Extend the indoor channel models to frequency-selectivity.
   ⇒ Compare the system performance using indoor and outdoor channel models.

 • Develop channel models for keyhole MIMO fading channels (2010.01-2010.04).
 • Develop multiuser MIMO channel models.

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