Pre-Compensation of Fading Channels for Uplink Time Division Duplex MC-CDMA Systems Ivan Cosovic1 , Michael Schnell1 , Andreas Springer2 German Aerospace Center (DLR), Institute of Communications and Navigation, D-82234 Wessling, Germany, Phone: +49-8153-282853, Email:
[email protected] /
[email protected] 2 Institute for Communication and Information Engineering, University of Linz, A-4040 Linz, Austria, Phone: +43-732-2468-9725, Email:
[email protected]
Over the past several years MC-CDMA emerged as the most promising candidate for the downlink in next generation of wireless mobile radio systems [1] [2]. On the other hand, considering MC-CDMA for uplink transmission introduces some additional problems due to the more complex propagation conditions. Especially, channel estimation and channel compensation are more difficult and require more complex algorithms. When applying TDD mode to MC-CDMA transmission it is possible to mainly overcome these problems [3] [4]. TDD/MC-CDMA exploits the strong correlation between upand downlink channel conditions of the slowly time-varying channels and therefore enables pre-compensation of the channel influence on the uplink signal already at the mobile station, based on the channel estimation from the downlink signal [5]. The aim of this paper is to carry out a performance comparison of different TDD/MC-CDMA channel pre-compensation techniques in the uplink. Considered pre-compensation techniques are maximum ratio combining (MRC), equal gain combining (EGC), zero-forcing (ZF) equalization, controlled equalization (CE), minimum mean-square error (MMSE) equalization and quasi-MMSE equalization. Furthermore, the power constraint condition, that maintains the transmitted power the same as in the case without pre-compensation, is introduced. Taking into account the power constraint condition the different pre-compensation techniques are analyzed in different mobile radio environments and for different lengths of the transmission frame. The paper is organized as follows: In Section II the TDD/MC-CDMA uplink transmission system is described. The power constraint condition and the considered precompensation techniques are discussed in Section III. The performance of the TDD/MC-CDMA system achieved with
II. T RANSMISSION S YSTEM The uplink transmitter of an TDD/MC-CDMA system is shown in Fig. 1. Each MC-CDMA symbol of user i, i = (i) (i) 1, . . . , K, consists of M symbols d(i) = (d1 , . . . , dM ) and is generated in the following way. After serial-to-paralel conversion (S/P) the symbols are spread with an user-specific spread(i) (i) ing sequence c(i) = (c1 , . . . , cL )T of length L, where (.)T denotes transposition. After another S/P frequency interleaving is performed. For interleaving a block interleaver is used which ensures the maximum frequency separation between the L (i) spread chips of each data symbol dm , m = 1, . . . , M .
ˆ (i ) H (i )
c d 1( i )
d
(i )
. . S/P .
x
S/P
c(i)
d M( i ) x
Fig. 1.
S/P
v1(i)
s1(i)
. . .(i )
sNc
. . .(i )
IFFT
I. I NTRODUCTION
the different pre-compensation techniques is presented in Section IV. Finally, Section V summarizes the results.
PRE-COMP.
Abstract— Time division duplex multi-carrier code-division multiple-access (TDD/MC-CDMA) exploits the strong correlation between up- and downlink channel conditions of the slowly timevarying channels. The TDD mode enables pre-compensation of the channel influence on the uplink signal already at the mobile station based on the channel estimation from the downlink signal. The aim of this paper is to carry out a performance comparison of different TDD/MC-CDMA channel pre-compensation techniques in the uplink and to evaluate the limitations of applicability of TDD/MC-CDMA due to the time variations of the channel. Furthermore, the power constraint condition, that keeps the transmitted power the same as in the case without pre-compensation, is introduced. Different pre-compensation techniques with power constraint are investigated in different mobile radio environments and for different lengths of the transmission frame.
FREQUENCY INTERLEAVER
1
vN c
. . .
P/S
CYC. EXT.
TDD/MC-CDMA uplink transmitter. (i)
(i)
The resulting Nc = M L chips s(i) = (s1 , . . . , sNc )T are pre-compensated, with an Nc × Nc diagonal channel pre-compensation matrix G(i) . The elements of the precompensation matrix G(i) are calculated from the channel state information derived from downlink channel estimation. Pilot-symbol-aided channel estimation is applied in the downlink and the channel state information can be represented as ˆ (i) with elements that represent diagonal Nc × Nc matrix H the estimated fading on the Nc subcarriers [2]. The estimated values are acquired from the previous MC-CDMA downlink frame. An MC-CDMA frame is a block of subsequent MCCDMA symbols. In the following, perfect downlink channel estimation will be assumed. The result of the pre-compensation can be represented by the vector v(i) as (i)
(i)
v(i) = G(i) s(i) = (v1 , . . . , vNc )T .
(1)
The pre-compensated sequence v(i) is modulated onto Nc subcarriers using the inverse fast Fourier transform (IFFT). After that, parallel-to-serial conversion (P/S) is performed and a guard interval, that exceeds the delay spread of the multipath
channel, is added as cyclic prefix. Several subsequent MCCDMA symbols are grouped into one MC-CDMA uplink frame. Due to the frequency-selective fading of the time-variant multipath channel, the AWGN influence, and the interference from other users the received signal for K active users at the base station after guard interval removal and fast Fourier transform (FFT) can be represented as y=
K X
H(j) G(j) s(j) + n = (y1 , . . . , yNc )T .
(2)
j=1
The Nc × Nc diagonal matrix H(j) represents the channel influence on the Nc subcarriers of user j. Since the duration of the guard interval exceeds the delay spread of the multipath channel, intersymbol interference is avoided. The vector n = (n1 , . . . , nNc )T represents the AWGN with variance σ 2 . The received signal y can alternatively be represented in a form in which the desired signal part r(i) of user i and the multiple-access interference (MAI) component i(i) are clearly visible as (3)
The interference from other users on user i is given by K X
(i)
(i)
H(j) G(j) s(j) = (i1 , . . . , iNc )T .
(4)
j=1,j6=i
Finally, the received signal is despread and decoded. A complete TDD/MC-CDMA uplink transmission system for the case M = 1 is illustrated in Fig. 2.
c1(i )
G1( i )
H 1( i )
n1
i1( i )
x
x
x
+
+
(i ) 2
d (i)
(i) 2
c
G
H
x
x
x
(i ) 2
c1( i )* x
n2
i
c2( i )*
+
+
x
(i) 2
+ ...
...
...
...
...
...
cL(i )
GL(i )
H L(i )
nL
iL(i )
cL(i )*
x
x
x
+
+
x
Fig. 2.
dˆ (i )
III. P RE -C OMPENSATION T ECHNIQUES As already indicated, channel pre-compensation can be performed with MRC, EGC, ZF equalization, CE, MMSE equalization, or quasi-MMSE equalization. The main focus of this investigation is on constrained pre-compensation, where the transmit power is the same as in the case without precompensation. In the following, the index which denotes the user i is omitted for convenience. The condition for constrained pre-compensation can be derived from
l=1
2
|Gl sl | =
Nc X
2
|sl | .
2
|Gl | =
Nc X
|Fl W |2 = Nc ,
(6)
l=1
l=1
where Fl is the compensation coefficient without power constraint and W is a normalization factor, that keeps the transmitted power constant. W can be expressed as ! 12 Nc . (7) W = PNc 2 t=1 |Ft | Different pre-compensation techniques lead to different compensation coefficients Fl , different normalization factors W , and different pre-compensation coefficients Gl , l = 1, . . . , Nc . A. Maximum Ratio Combining MRC corrects the phase shift and weights the transmitted signal with a coefficient proportional to the attenuation of the channel fading. The assigned pre-compensation coefficient is ! 12 Nc ∗ Gl = Hl PNc , (8) 2 t=1 |Ht | B. Equal Gain Combining EGC, also known as phase equalization, corrects the phase shift, but not the attenuation of the channel fading. This results in a normalization factor W = 1. The assigned precompensation coefficient is H∗ Gl = l . (9) |Hl | C. Zero-Forcing Equalization ZF equalization restores the orthogonality between users and eliminates MAI by inverting the channel fading coefficients. However, due to the power constraint condition residual fading remains which is equal for all subcarriers. Since large amounts of power are invested to pre-compensate the signal on subcarriers in deep fade, the received power on the subcarriers is very low compared to the noise level and, thus, the received signal is largely affected by AWGN. The assigned pre-compensation coefficient is ! 12 1 Nc Gl = . (10) PNc 1 Hl 2 t=1 |Ht |
TDD/MC-CDMA uplink transmission system, M = 1.
Nc X
Nc X
where the superscript ”∗” denotes complex conjugation.
y = r(i) + i(i) + n = H(i) G(i) s(i) + i(i) + n.
i(i) =
reduces to
(5)
l=1
Under the presumption that the power of the transmitted symbol is constant on all subcarriers in the frequency domain, (5)
D. Controlled Equalization CE combines EGC and ZF equalization [2]. When the channel attenuation |Hl | is below a threshold athresh , only EGC is used to prevent investing large amounts of power on weak subcarriers. Otherwise ZF equalization is performed. The assigned pre-compensation coefficient is ( 1 : |Hl | ≥ athresh Hl W Gl = (11) Hl∗ : |Hl | < athresh , |Hl | W where the normalization coefficient W is equal to ! 12 Nc W = PNc , t=1 Wt and Wt is given by Wt =
1 |Ht |2
1
: |Ht | ≥ athresh : |Ht | < athresh .
(12)
(13)
E. MMSE Equalization According to (3) the received signal part on one subcarrier l can be represented as yl = Hl Gl sl + il + nl .
(14)
Equalization according to the MMSE criterion minimizes the mean-square value of the error l between the transmitted signal part sl and the received signal part yl l = sl − yl .
(15)
Jl = E |l |2
(16)
The mean-square error
IV. S IMULATION R ESULTS In this section, the simulation results for uplink TDD/MCCDMA with channel pre-compensation in different indoor scenarios are presented. The maximal Doppler frequency is chosen in such a way that it corresponds to typical pedestrian movements in an indoor environment. A. Channel Models and TDD/MC-CDMA System Parameters
can be minimized applying ∂Jl ∂G∗
= 0.
(17)
l Gl,opt
MMSE without power constraint results in the following pre-compensation coefficients Gl,opt =
1 , Hl
(18)
which in fact is the same result as for ZF equalization without power constraint. In the case of ideal channel estimation, unconstrained MMSE is capable to pre-compensate the influence of the channel completely. However, for unconstrained MMSE the transmitted power is not limited and therefore this approach is not practical. Considering MMSE with power constraint leads to the problem to minimize the mean-square error under the power constraint condition ! Nc X 2 2 Jl = E |l | + λ |Gt | − Nc . (19) t=1
From (19) the optimal pre-compensation coefficients are Gl,opt =
Since MMSE-PS is the best known single-user equalization technique for downlink transmission, it is expected that quasiMMSE pre-compensation performs quite good. The drawback of quasi-MMSE is that the knowledge about both the number of active users K and the noise variance σ 2 is required at the mobile station.
Hl∗ , |Hl |2 + E{|sλl |2 }
(20)
where λ is the solution of Nc X
|Hl |2
l=1
(|Hl |2 + λ)
2
= Nc .
(21)
Constrained MMSE pre-compensates the channel only partly, but keeps the transmitted power constant. The drawback of constrained MMSE is, that in general λ can be determined only numerically. This introduces a large computational complexity. F. Quasi-MMSE Equalization The MMSE per subcarrier equalization (MMSE-PS) [2] used in downlink MC-CDMA transmission can be modified in order to satisfy the power constraint condition and applied to uplink transmission. This solution is termed quasi-MMSE equalization, since it does not represent the real MMSE uplink pre-compensation technique. The assigned pre-compensation coefficient is 12 ∗ Hl Nc P . Gl = Nc |Ht |2 (K − 1)|Hl |2 + σ 2 L 2 2 2 t=1 ((K−1)|Ht | +σ L)
(22)
Table I shows the main parameters of the channel models used for the simulations. The mobile radio channel models are taken from [6]. For the indoor scenario with line of sight condition (LOS) ’Model D’ is used, whereas for the indoor scenario without line of sight condition (NLOS) ’Model E’ is used. For both channels the maximum Doppler frequency is chosen to be fDmax = 26 Hz, which corresponds to a velocity of 1.5 ms (5.4 km h ) for operation in the 5.2 GHz frequency band. The coherence time of the channel can be defined as the time over which the time correlation function is above 0.5 and, thus, can be approximated by [7] (∆t)c ≈ 16πf9Dmax . TABLE I M AIN CHANNEL MODEL PROPERTIES
Line of Sight (LOS) Max. Channel Delay Max. Doppler Frequency Coherence Time of the Channel
Model D Model E yes no 1050 ns 1760 ns 26 Hz 6.89 ms
The TDD/MC-CDMA system under investigation uses a transmission bandwidth of 25 MHz and a carrier frequency of 5.2 GHz. The number of subcarriers is Nc = 256, resulting in an useful MC-CDMA symbol duration of 10.24 µs. The guard interval duration is 1.8 µs. The loss in transmission energy due to the guard interval is not taken into account, since it is the same for all simulations. Walsh-Hadamard codes of length L = 16 are used for spreading. The number of simultaneously transmitted symbols is M = 16. Table II shows the main parameters of the MC-CDMA simulation system. TABLE II MC-CDMA
SYSTEM PARAMETERS FOR SIMULATIONS
Carrier Frequency Transmission Bandwidth Number of Subcarriers Useful MC-CDMA Symbol Duration Guard Length Length of MC-CDMA Frame Spreading Codes Length of Spreading Codes Signal Constellation Channel Coding
5.2 GHz 25 MHz 256 10.24 µs 1.8 µs variable Walsh-Hadamard 16 QPSK no
B. Results Different power constrained channel pre-compensation techniques for a fully-loaded TDD/MC-CDMA system are compared in Fig. 3 for the indoor mobile radio channel ’Model E’.
0
10
0
-1
10
10
-1
Bit Error Rate
Bit Error Rate
10
-2
10
AWGN channel MRC EGC ZF CE Quasi-MMSE
-3
10
-4
10
0
5
-2
10
AWGN channel MRC EGC ZF CE Quasi-MMSE
-3
10
10
15
20
Eb/No in dB
-4
10
0
5
10
15
20
Eb/No in dB
Fig. 3. Performance of basic TDD/MC-CDMA power constrained precompensation techniques; Channel ’Model E’, spreading length L = 16, K = 16 active users, frame length Nsym = 1.
Fig. 5. Performance of basic TDD/MC-CDMA power constrained precompensation techniques; Channel ’Model D’, spreading length L = 16, K = 16 active users, frame length Nsym = 1.
0
10
-1
10 Bit Error Rate
’Model D’ is used can be found in Fig. 5. The frame length is set to Nsym = 1 MC-CDMA symbol. ’Model D’ has a dominant LOS component but a considerably shorter channel delay. This leads to a slightly better TDD/MC-CDMA performance compared to the case in which ’Model E’ is applied.
AWGN channel 1 MC-CDMA Symbol, 0.17% of (∆t)c 50 MC-CDMA Symbols, 8.74% of (∆t)c 100 MC-CDMA Symbols, 17.47% of (∆t)c 150 MC-CDMA Symbols, 26.21% of (∆t)c 200 MC-CDMA Symbols, 34.95% of (∆t).c
V. C ONCLUSIONS
-2
10
-3
10
-4
10
0
5
10
15
20
Eb/No in dB
Fig. 4. Performance of TDD/MC-CDMA with various transmission frame lengths; Channel ’Model E’, quasi-MMSE pre-compensation, spreading length L = 16, K = 16 active users.
In this case, the frame length is set to Nsym = 1 MC-CDMA symbol. As it can be seen, quasi-MMSE and CE perform very good, while other pre-compensation techniques show much larger signal degradation. For CE the threshold value is set to athresh = 0.175. This threshold value gives optimal performance for the bit error rate probability of Pb = 10−3 for the investigated system. In Fig. 4 the influence of the transmission frame length on the performance of a fully-loaded TDD/MC-CDMA system with quasi-MMSE pre-compensation for the indoor mobile radio channel ’Model E’ is shown. It can be seen, that MCCDMA frame lengths which are not larger than approximately 10% of the coherence time of the channel are acceptable and do not suffer from large signal degradation. Moreover, Fig. 4 illustrates, that the coherence time of the channel is the crucial parameter that determines the limits of TDD applicability to uplink MC-CDMA. The performance of different power constrained channel pre-compensation techniques for a fully-loaded TDD/MCCDMA system in the case when indoor mobile radio channel
Different power constrained channel pre-compensation techniques for uplink TDD/MC-CDMA systems have been analyzed and compared in different indoor mobile radio environments. It can be seen, that quasi-MMSE and CE outperform other pre-compensation techniques. Analysis of the influence of the transmission frame length on the performance has shown, that the coherence time of the channel is the most important parameter that determines TDD applicability to MCCDMA. A rule of thumb has been derived, which states that MC-CDMA transmission frame lengths which are not larger than approximately 10% of the coherence time of the considered channel are acceptable. In this case, MC-CDMA performance does not suffer from large signal degradation. R EFERENCES [1] K. Fazel and L. Papke, “On the performance of convolutionally-coded CDMA/OFDM for mobile communication system,” in Proceedings IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’93), Sept. 1993, pp. 468–472. [2] S. Kaiser, Multi-Carrier CDMA Mobile Radio Systems - Analysis and Optimization of Detection, Decoding and Channel Estimation. D¨usseldorf: VDI Verlag, Fortschritt-Berichte VDI, series 10, no. 531, 1998. [3] I. Cosovic and M. Schnell, “Time division duplex MC-CDMA for next generation mobile radio systems,” in Proceedings Telecommunications Forum (TELFOR’02), Nov. 2002, pp. 216–219. [4] S. Nobilet and J.-F. Helard, “A pre-equalization technique for uplink MC-CDMA systems using TDD and FDD modes,” in Proceedings IEEE Vehicular Technology Conference (VTC’02, Fall), Oct. 2002, pp. 346–350. [5] D. Jeong and M. Kim, “Effects of channel estimation error in MCCDMA/TDD systems,” in Proceedings IEEE Vehicular Technology Conference (VTC’00, Spring), May 2000, pp. 1773–1777. [6] J. Medbo, “Channel models for HIPERLAN/2 in different indoor scenarios,” in ETSI EP BRAN 3ERI085B, March 1998. [7] T. S. Rappaport, Wireless Communications: Principles and Practice. Upper Saddle River: Prentice-Hall, 1996.
