Practical Performance of MIMO-OFDM-LDPC with ... - Semantic Scholar
Practical Performance of MIMO-OFDM-LDPC with Low Complexity Double Iterative Receiver Hajime Suzuki, Iain B. Collings, Mark Hedley, and Graham Daniels CSIRO ICT Centre PO Box 76, Epping NSW 1710 Australia Email: [email protected]
Abstract—This paper considers MIMO-OFDM transmission with low density parity check (LDPC) codes. We employ a low complexity minimum mean-square-error (MMSE) softinterference-cancelation (SIC) based double iterative receiver (DIR). Results are presented for a real system implementation at 5.2 GHz. We achieve zero packet errors at 90% of the measured indoor locations, when transmitting at 600 Mbit/s, with 15 bit/s/Hz spectral efficiency and 26 dB signal-to-noise ratio. We show that the proposed receiver actually outperforms a list sphere detection (LSD) based single iterative receiver (SIR) at high coding rates, in practice. Investigations reveal that the LSDSIR is adversely affected by the non-Gaussian noise present at the receiver, while at the same time the MMSE-SIC-DIR is better able to handle transmitter noise present in the practical system.
I. I NTRODUCTION Multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) [1], [2] is the most popular transmission scheme adopted in next generation wireless standards. In many cases, MIMO-OFDM is combined with low density parity check (LDPC) codes [3], [4]. MIMO-OFDMLDPC packet error probability (PEP) results were previously presented in [5] for two receiver structures, zero-forcing (ZF) [6] and list sphere detection (LSD) [7], based on simulation as well as actual measurements, using four transmitters and four receivers (denoted as 4×4) in an indoor environment. In this paper we consider the use of a low-complexity minimum mean-square-error soft-interference-cancelation (MMSE-SIC) double iterative receiver (DIR) [4], [8]. The double iteration arises since there is an outer iteration between the MIMO detection and LDPC decoding, and an inner iteration within the LDPC decoder itself. In [4], LDPC codes with rate 1/2 were used, and it was shown that a soft maximum a posteriori (MAP) MIMO detection based DIR can perform within 1 dB from the ergodic capacity of a MIMO-OFDM system. It was also shown that the MMSE-SIC-DIR has only a small performance loss compared to the MAP-DIR. In [8], the performance of MMSE-SIC-DIR was examined using a rate 1/3 LDPC code. Almost no performance loss was observed compared to the MAP based DIR. In this paper we are interested in higher rate codes, which are needed to achieve the high end spectral efficiencies defined in next generation wireless standards. The contributions of this paper are as follows: • We present results from a 4×4 MIMO-OFDM-LDPC
transmission implementation at 5.2 GHz. With the MMSE-SIC double iterative receiver we achieve zero packet errors at 90% of the measured indoor locations, when transmitting at 600 Mbit/s, with 15 bit/s/Hz spectral efficiency and 26 dB signal-to-noise ratio (SNR). By comparison, the coverage for previous ZF and LSD based single iterative receiver (SIR) systems, as reported in [5], was 73% and 84%, respectively. Notably, the improved coverage was achieved with a lower computational complexity when compared to LSD-SIR. • We present an analysis of the practical system noise, that explains the superior performance of the MMSE-SICDIR, compared with the LSD-SIR, in practice. Similar to our observation for ZF-SIR in [5], the performance of MMSE-SIC is seriously underestimated if the transmitter noise is neglected in simulations. An important point to note, is that transmitter noise was found to be present in the practical MIMO-OFDM system, and it was not sufficient from a modeling point of view to consider it as simply adding extra effective uncorrelated noise at the receiver; particularly for the MMSE-SIC-DIR receiver. Transmitter noise can occur, for example, by nonlinearity of amplifier and phase noise in OFDM transmission [9] and/or quantization and clipping by digital to analog converters (DACs) [10]. In order to clarify our argument, we use the term apparent receiver noise to refer to the noise seen by the receiver, which is the combination of the noise generated both at the transmitter and the receiver. The noise inherent only to the receiver is referred as an inherent receiver noise. This paper is organized as follows. A brief overview of the system is given in Section II. Section III presents MMSE-SIC operation in the presence of transmitter noise. Measurement and simulation results are given in Section IV, followed by the conclusions in Section V. II. S YSTEM D ESCRIPTION Fig. 1 shows the block diagram of a MIMO-OFDM-LDPCDIR system. The LDPC encoder operates with a coding rate of 1/2, 2/3, 3/4, or 5/6, with an input block size of 864, 1152, 1296, or 1440 bits, respectively, as specified in [11]. The output (coded) block size is fixed to 1728 bits for all coding rates. Each of the spatial streams is mapped into M level quadrature amplitude modulation (M -QAM) symbols using
QAM Mapping S/P
...
LDPC Encoding
Source
F-to-T
QAM Mapping
F-to-T
(a) Transmitter.
...
T-to-F
T-to-F
MMSE-SIC and Bit Value Probability Estimation
LDPC Decoding
Sink
(b) Receiver.
Fig. 1: Block diagram of MIMO-OFDM-LDPC-DIR system.
Gray-labeling. While BPSK, QPSK, 16QAM and 64QAM are used in [11], only the later two are implemented in this paper for the interest of high data rate transmission. A set of QAM symbols together with pilot symbols are transformed into time domain symbols by the inverse fast Fourier transform (IFFT). 108 data and 6 pilot symbols as specified in [11] for 40 MHz bandwidth are used in this paper. Cyclic extension is added to provide a 400 ns guard interval which was found adequate to eliminate the effects of delayed multipath components in the indoor environment tested. The time domain signals are then transmitted to the air after appropriate frequency conversion. The IFFT, cyclic extension, and frequency conversion are grouped into a frequency to time domain conversion block, F-to-T, in Fig. 1. At the receiver, a MMSE-SIC detector produces streams of bit value probability estimates. The extrinsic bit value probabilities provided by the LDPC iterative decoder (the inner iteration), are used to form soft estimates of the transmitted symbols, which are then fed back in an outer (second) iterative loop to the MMSE-SIC detector. To arrive at the specific number of iterations we used, we ran simulations for 5, 10, 20, 40, and 80 inner iterations, and 1 to 6 outer iterations, and found that the best combination was 40 inner iterations, and 4 outer iterations. The process was terminated when the parity check operation detected no errors. III. MMSE-SIC WITH T RANSMITTER N OISE As noted in the introduction, our practical measurements indicate that transmitter noise can not be ignored in practice. In this section, we derive the MMSE-SIC detector in the presence of transmitter noise. In doing so, we make the simplifying assumption that the transmitter noise, when measured at the receiver, is uncorrelated. In this case, the MMSE-SIC has the same form as in [8], but with the noise variance term replaced by the apparent noise variance, as follows. Suppose Nt transmitters, Nr receivers, Nf OFDM data sub-carriers, and Ns OFDM data symbols are used in a MIMO-OFDM system, where Nr ≥ Nt . A consistent notation, (i, j, k, l), is used to denote the parameter at the ith transmitter,
jth receiver, kth OFDM data sub-carrier, and lth OFDM symbol, where i = 1, ..., Nt , j = 1, ..., Nr , k = 1, ..., Nf , and l = 1, ..., Ns . Here we assume a frequency domain flat fading channel model provided by an adequate cyclic extension [12]. The transmitted and received symbols are x(i, k, l) and r(j, k, l), respectively. The transmitted symbols are chosen from an M -QAM constellation set, s(m), m = 1, 2, ..., M , and var[x(i, k, l)]=1. AWGN at the transmitter is nt (i, k, l) with the mean of zero and the variance of ηt (i, k) while that at the receiver is nr (j, k, l) with the mean of zero and the variance of ηr (j, k). These noises are assumed to be uncorrelated. The noise generated by the non-linearity of the amplifier at an OFDM transmitter has been found to be approximated as a Gaussian noise in [13]. The channel transfer function is h(i, j, k), where the channel is assumed to be stationary for the duration of Ns OFDM symbols. The channel is normalized so that var[h(i, j, k)] = 1. The received signal vector is expressed as r(k, l) = H(k)x(k, l) + na (k, l),
(1)
where the channel transfer matrix H(k) is an Nr × Nt matrix whose jth row and ith column element is h(i, j, k). The apparent noise na (k, l) observed at the receiver is given by na (k, l) = H(k)nt (k, l) + nr (k, l).
(2)
The average apparent receiver SNR, S¯a , can be defined as Nt , (3) S¯a = ηa where Nt X ηa (j, k) = [|h(i, j, k)|2 · ηt (i, k)] + ηr (j, k). (4) i=1
Assuming that the estimate of the channel transfer matrix is correct, then the apparent noise can be estimated by transmitting known symbols as na (k, l) = r(k, l) − H(k)x(k, l).
(5)
For the packet transmission simulation and measurement described in the following section, (5) is used to estimate the variance of the apparent receiver noise. In the following derivation, we drop the index for k and l focusing on the MIMO detection at kth OFDM sub-carrier and lth OFDM symbol. The MMSE-SIC detector first forms soft estimates of the transmitted symbols by computing the symbol mean x ¯(i) based on the available a-priori information [8] M X x ¯(i) = s(m)PC (x(i) = s(m)). (6) m=1
The a-priori symbol value probabilities PC (x(i) = s(m)) are calculated from the extrinsic bit value probabilities PC (b(i, q) = c(m, q)) as PC (x(i) = s(m)) =
Q Y
(PC (b(i, q) = c(m, q))),
q=1
(7)
where b(i, q) is the value of the qth bit of the ith transmitted symbol x(i) and c(m, q) is the value of the qth bit of the mth chosen M -QAM constellation symbol s(m). For the initial MIMO detectioin, x ¯(i) = 0, ∀i, when using M -QAM constellation set. For the subsequent iterations, the extrinsic bit value probabilities are provided by the LDPC decoder. Interference-cancelled received symbol vector r0 (i), where the interference from the other antennas for the ith transmit antenna is canceled, is given by Nt X
r0 (i) = r −
x ¯(i0 )h(i0 ) Nt X
(x(i0 ) − x ¯(i0 ))h(i0 ) + na ,
(9)
where h(i0 ) is the i0 th column vector of H. A detection estimate x ˆ(i) of the transmitted symbol on the ith antenna is obtained by applying a linear filter w(i) to r0 (i) x ˆ(i) = wH (i)r(i) = (wH (i)h(i))x(i) +
H
1 16 1/2 240 6 27,648
0
0
(10) 0
H
(w (i)h(i ))(x(i ) − x ¯(i )) + w (i)na ,
i0 =1,i0 6=i
(11) where H represents the conjugate transpose operator. The filter w(i) is given by ¡ ¢−1 h(i), (12) w(i) = ηa INr + H∆(i)HH
2 16 3/4 360 9 41,472
3 64 2/3 480 12 55,296
4 64 3/4 540 13.5 66,208
5 64 5/6 600 15 69,120
is s(m), without using the extrinsic bit value probability for the qth bit of the ith transmitted symbol, is given as PC (x(i) = s(m), q) = 0.5
i0 =1,i0 6=i
Nt X
MCS mode index QAM number Coding rate Data rate (Mbit/s/Hz) Efficiency (bit/s/Hz) Bits per packet
(8)
i0 =1,i0 6=i
= x(i)h(i) +
TABLE I: MCS and associated parameters.
Q Y
PC (b(i, q 0 ) = c(m, q 0 )).
q 0 =1,q 0 6=q
(18) The updated symbol value probability PU combining the symbol value probabilities provided by the MMSE-SIC detection and the bit value probabilities from LDPC decoding is PU (x(i) = s(m), q) PD (x(i) = s(m))PC (x(i) = s(m), q) = PM . 0 0 m0 =1 PD (x(i) = s(m ))PC (x(i) = s(m ), q)
(19)
The updated bit value probability to be fed to the next iteration of LDPC decoding is M/2
PU (b(i, q) = 0) =
X
PCD (x(i) = s0 (m, q), q)
(20)
m=1
where s0 (m, q) is a set of symbols where the value of qth bit is 0, and PU (b(i, q) = 1) can be similarly derived. where the covariance matrix ∆(i) is ¢ ¡ 2 IV. M EASUREMENT AND S IMULATION R ESULTS ∆(i) = diag σx (1), . . . , σx2 (i − 1), 1, σx2 (i + 1), . . . , σx2 (Nt ) , (13) The actual packet transmission test was performed in the and σx2 (i) is the variance of the ith antenna symbol computed CSIRO ICT Centre in Marsfield, Sydney whose details are as given in [5]. Since the performance of MIMO-OFDM channels M can differ substantially with a small shift of antenna locations X σx2 (i) = |s(m) − x ¯(i)|2 PC (x(i) = s(m)). (14) (less than a half-wavelength in a typical multipath environm=1 ment) [14], it is important to test MIMO-OFDM transmission Following [8], we approximate x ˆ(i) by the output of an schemes at a large number of different locations within a equivalent AWGN channel with x ¯(i) = µ(i)x(i) + z(i), where small local area. For this reason, we use an antenna array positioner (AP) controlled by the PC to automatically position µ(i) = wH (i)h(i), (15) the receiving antenna array in different locations. The simuand z(i) is a zero-mean complex Gaussian variable with lation results given in Fig. 2 are based on the MIMO-OFDM channels measured on a grid of 80×80 = 6400 locations with variance η(i) given by 0.05 wavelength resolution. The actual packet transmission 2 η(i) = µ(i) − µ (i). (16) and simulation results given in Fig. 3 are based on a linearly aligned 80 locations with 0.05 wavelength resolution, due Given the detection estimates x ˆ(i), the symbol value proba- to time constraint on the actual packet transmission. Five bilities PD provided from the current MMSE-SIC detection is MIMO-OFDM-LDPC packets corresponding to the different approximated by modulation and coding schemes (MCS) shown in Table I are µ ¶ 2 sent to each of 80 receiving antenna array locations. To process 1 |ˆ x(i) − µ(i)s(m)| PD (x(i) = s(m)) ≈ exp − . 80×5=400 packets takes 5,762 seconds for LSD-SIR and πη(i) η(i) (17) 4,271 seconds for MMSE-SIC-DIR, respectively, on MATLAB For the qth bit of ith transmitted symbol, we derive the symbol running on an Intel Xeon PC at 3 GHz. value probabilities from the extrinsic bit value probabilities. Fig. 2 shows PEP simulation results for LSD-SIR and The symbol value probability that the ith transmitted symbol MMSE-SIC-DIR based on the 6400 measured MIMO-OFDM
0
PEP
10
16QAM 1/2 16QAM 3/4 64QAM 2/3 64QAM 3/4 64QAM 5/6 LSD-SIR MMSE-SIC-DIR
-1
10
-2
10
10
12
14
16
18
20
22 24 26 28 30 Average inherent receiver SNR (dB)
32
34
36
38
40
Fig. 2: Simulation results on LSD-SIR and MMSE-SIC-DIR packet error probability (PEP).
channels. As is commonly assumed, the simulations were performed assuming zero noise at the transmitter. The following observations can be made: • For coding rate 1/2, 16QAM, the MMSE-SIC-DIR performs better than LSD-SIR. • For higher coding rates the LSD-SIR shows the best performance. This is expected as the higher coding rate reduces the ability of LDPC decoding to improve bit value probabilities and thus reducing the ability of MMSE-SIC detection to cancel other-antenna-interference. Fig. 3 shows that the above observations do not always hold in practice. The figure shows PEP of MMSE-SIC-DIR and LSD-SIR as a function of average apparent receiver SNR, S¯a , based on actual packet transmission (denoted as ‘meas’) and simulation. The simulation curves are generated with varying ratios of transmitter noise variance in relation to receiver noise variance; from ηt =0 to ηt =ηr . The actual packet transmission results are indicated by the markers shown at 26 dB. Note that the irregularities seen in some of the PEP curves are attributed to the smaller number of MIMO-OFDM channels used in the simulation, i.e. 80 channels, as discussed above. Clearly, there is a discrepancy between the simulated curves which assume zero transmitter noise, and the measured values. For the MMSE-SIC-DIR we see that the measured PEP is significantly lower than that predicted under the assumption that all the apparent receiver noise is actually generated at the receiver (ηt =0). This can be explained by observing that curves for non-zero transmitter noise show significantly lower PEP, indicating that the MMSE-SIC-DIR is relatively unaffected by transmitter noise (compared with the effect of inherent receiver noise). Both Fig. 3(a) and 3(b) show that the MMSE-SICDIR curve corresponding to ηt =ηr /2 roughly matches with the measured point (shown as an open square, at 26 dB). In fact, this is similar to the case of a ZF-SIR, as reported in [5]. The measured results for LSD-SIR show higher PEP than predicted, irrespective of the amount of the transmitter noise. The deviation is considered to be due to the sensitivity of LSDSIR on the non-Gaussian characteristics of actual apparent
receiver noise affecting the accuracy of bit value probability estimates, as shown in [5]. Fig. 4 shows the variation of required SNR to achieve PEP=10−2 as a function of the transmitter noise and MCS. For comparison, we also show curves for the ZF-SIR. The following observations can be made. • The LSD-SIR results show little variation of required SNR as a function of transmitter noise for all MCS. Since the current method employed to calculate bit value probabilities from the LSD does not take into account the correlation of the noise, the performance of LSD-SIR is mainly determined by the variance of apparent noise. • The ZF-SIR results show an improvement of 4.3 dB in average from ηt =0 to ηt =ηr /2, and of 6.3 dB in average from ηt =0 to ηt =ηr independent of MCS. This can be understood by the fact that the performance of ZF-SIR mainly depends on the effective noise seen by the ZF detector, which is a combination of transmitter noise plus inherent receiver noise enhanced by the channel inverse. As the noise contribution is shifted from the inherent receiver noise to the transmitter noise, the performance of ZF detector improves irrespective of the MCS. • The MMSE-SIC-DIR results show a similar improvement as ZF-SIR at higher coding rates (2/3, 3/4, and 4/5), but a smaller improvement at a low coding rate (1/2). This is attributed to the fact that the performance of MMSE-SICDIR depends both on the amount of transmitter noise, in the same way as ZF-SIR, and on the FEC coding rate which affects the performance of other-antennainterference cancelation. V. C ONCLUSIONS A low complexity MIMO-OFDM-LDPC with a MMSESIC-DIR achieving 600 Mbit/s and 15 bit/s/Hz spectral efficiency has been successfully implemented on an actual radio hardware at 5.2 GHz. Zero error transmission was achieved at 90 % of indoor locations measured, with an average receiver SNR of 26 dB. The results set a benchmark for
0
0
10
10
PEP
PEP
LSD-SIR meas MMSE-SIC-DIR meas LSD-SIR sim MMSE-SIC-DIR sim ηt=0 -1
10
ηt=ηr/4
-1
10
ηt=ηr/2 ηt=ηr
-2
10
22
-2
24 26 28 30 Average apparent receiver SNR (dB)
32
10
22
(a) PEP (64QAM, rate 3/4 coding)
24 26 28 30 Average apparent receiver SNR (dB)
32
(b) PEP (64QAM, rate 5/6 coding)
Average apparent receiver SNR (dB) required at PEP=10 -2
Fig. 3: Packet error probability (PEP) based on actual packet transmission (meas) and simulation.
40
35
64QAM 4/5 64QAM 3/4 64QAM 2/3 16QAM 3/4 16QAM 1/2 ZF-SIR LSD-SIR MMSE-SIC-DIR
30
25
20
15
10 ηt=0
ηt= ηr/2
ηt= ηr
Fig. 4: Variation of required SNR to achieve PEP=10−2 as a function of transmitter noise.
the further improvement of a high spectral efficiency wireless communication with a reduced computational complexity. R EFERENCES [1] G. L. St¨uber, J. R. Barry, S. W. McLaughlin, Y. G. Li, M. A. Ingram, and T. G. Pratt, “Broadband MIMO-OFDM wireless communications,” Proceedings of the IEEE, vol. 92, no. 2, pp. 271–294, February 2004. [2] H. B¨olcskei, “MIMO-OFDM wireless systems: Basics, perspectives, and challenges,” IEEE Wireless Communications, vol. 13, no. 4, pp. 31–37, August 2006. [3] B. Lu, X. Wang, and K. R. Narayanan, “LDPC-based space-time coded OFDM systems over correlated fading channels: Performance analysis and receiver design,” IEEE Transactions on Communications, vol. 50, no. 1, pp. 74–88, January 2002.
[4] B. Lu, G. Yue, and X. Wang, “Performance analysis and design optimization of LDPC-coded MIMO OFDM systems,” IEEE Transactions on Information Theory, vol. 52, no. 2, pp. 348–361, February 2004. [5] H. Suzuki, T. V. A. Tran, I. B. Collings, G. Daniels, and M. Hedley, “Transmitter noise effect on the performance of a MIMO-OFDM hardware implementation achieving improved coverage,” IEEE Journal on Selected Areas in Communications, vol. 26, no. 8, pp. 867–876, August 2008. [6] M. R. McKay and I. B. Collings, “Capacity and performance of MIMO-BICM with zero-forcing receivers,” IEEE Transactions on Communications, vol. 53, no. 1, pp. 74–83, January 2005. [7] B. M. Hochwald and S. ten Brink, “Achieving near-capacity on a multiple-antenna channel,” IEEE Transactions on Communications, vol. 51, no. 3, pp. 389–399, March 2003. [8] A. Matache, C. Jones, and R. Wesel, “Reduced complexity MIMO detectors for LDPC coded systems,” In Proceedings of the IEEE MILCOM, vol. 2, pp. 1073–1079, October 2004. [9] E. Costa and S. Pupolin, “M-QAM-OFDM system performance in the presence of a nonlinear amplifier and phase noise,” IEEE Transactions on Communications, vol. 50, no. 3, pp. 462–472, March 2002. [10] B. Murray, H. Suzuki, and S. Reisenfield, “Optimal quantization of OFDM at digital IF,” IEEE TENCON, November 2008. [11] S. A. Mujtaba, “TGn Sync proposal technical specification,” IEEE 802.11-04/0889r7, July 2005. [12] M. R. G. Butler and I. B. Collings, “A zero-forcing approximate loglikelihood receiver for MIMO bit-interleaved coded modulation,” IEEE Communications Letters, vol. 8, no. 2, pp. 105–107, February 2004. [13] G. Santella and F. Mazzenga, “A hybrid analytical-simulation procedure for performance evaluation in M-QAM-OFDM schemes in presence of nonlinear distortions,” IEEE Transactions on Vehicular Technology, vol. 47, no. 1, pp. 142–151, February 1998. [14] H. Suzuki, T. V. A. Tran, and I. B. Collings, “Characteristics of MIMO-OFDM channels in indoor environments,” EURASIP Journal on Wireless Communications and Networking, vol. 2007, no. Article ID 19728, January 2007.
Abstract—This paper considers MIMO-OFDM transmission with low density parity check (LDPC) codes. We employ a low complexity minimum mean-square-error (MMSE) softinterference-cancelation (SIC) based double iterative receiver (DIR). Results are presented for a real system implementation at 5.2 GHz. We achieve zero packet errors at 90% of the measured indoor locations, when transmitting at 600 Mbit/s, with 15 bit/s/Hz spectral efficiency and 26 dB signal-to-noise ratio. We show that the proposed receiver actually outperforms a list sphere detection (LSD) based single iterative receiver (SIR) at high coding rates, in practice. Investigations reveal that the LSDSIR is adversely affected by the non-Gaussian noise present at the receiver, while at the same time the MMSE-SIC-DIR is better able to handle transmitter noise present in the practical system.
I. I NTRODUCTION Multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) [1], [2] is the most popular transmission scheme adopted in next generation wireless standards. In many cases, MIMO-OFDM is combined with low density parity check (LDPC) codes [3], [4]. MIMO-OFDMLDPC packet error probability (PEP) results were previously presented in [5] for two receiver structures, zero-forcing (ZF) [6] and list sphere detection (LSD) [7], based on simulation as well as actual measurements, using four transmitters and four receivers (denoted as 4×4) in an indoor environment. In this paper we consider the use of a low-complexity minimum mean-square-error soft-interference-cancelation (MMSE-SIC) double iterative receiver (DIR) [4], [8]. The double iteration arises since there is an outer iteration between the MIMO detection and LDPC decoding, and an inner iteration within the LDPC decoder itself. In [4], LDPC codes with rate 1/2 were used, and it was shown that a soft maximum a posteriori (MAP) MIMO detection based DIR can perform within 1 dB from the ergodic capacity of a MIMO-OFDM system. It was also shown that the MMSE-SIC-DIR has only a small performance loss compared to the MAP-DIR. In [8], the performance of MMSE-SIC-DIR was examined using a rate 1/3 LDPC code. Almost no performance loss was observed compared to the MAP based DIR. In this paper we are interested in higher rate codes, which are needed to achieve the high end spectral efficiencies defined in next generation wireless standards. The contributions of this paper are as follows: • We present results from a 4×4 MIMO-OFDM-LDPC
transmission implementation at 5.2 GHz. With the MMSE-SIC double iterative receiver we achieve zero packet errors at 90% of the measured indoor locations, when transmitting at 600 Mbit/s, with 15 bit/s/Hz spectral efficiency and 26 dB signal-to-noise ratio (SNR). By comparison, the coverage for previous ZF and LSD based single iterative receiver (SIR) systems, as reported in [5], was 73% and 84%, respectively. Notably, the improved coverage was achieved with a lower computational complexity when compared to LSD-SIR. • We present an analysis of the practical system noise, that explains the superior performance of the MMSE-SICDIR, compared with the LSD-SIR, in practice. Similar to our observation for ZF-SIR in [5], the performance of MMSE-SIC is seriously underestimated if the transmitter noise is neglected in simulations. An important point to note, is that transmitter noise was found to be present in the practical MIMO-OFDM system, and it was not sufficient from a modeling point of view to consider it as simply adding extra effective uncorrelated noise at the receiver; particularly for the MMSE-SIC-DIR receiver. Transmitter noise can occur, for example, by nonlinearity of amplifier and phase noise in OFDM transmission [9] and/or quantization and clipping by digital to analog converters (DACs) [10]. In order to clarify our argument, we use the term apparent receiver noise to refer to the noise seen by the receiver, which is the combination of the noise generated both at the transmitter and the receiver. The noise inherent only to the receiver is referred as an inherent receiver noise. This paper is organized as follows. A brief overview of the system is given in Section II. Section III presents MMSE-SIC operation in the presence of transmitter noise. Measurement and simulation results are given in Section IV, followed by the conclusions in Section V. II. S YSTEM D ESCRIPTION Fig. 1 shows the block diagram of a MIMO-OFDM-LDPCDIR system. The LDPC encoder operates with a coding rate of 1/2, 2/3, 3/4, or 5/6, with an input block size of 864, 1152, 1296, or 1440 bits, respectively, as specified in [11]. The output (coded) block size is fixed to 1728 bits for all coding rates. Each of the spatial streams is mapped into M level quadrature amplitude modulation (M -QAM) symbols using
QAM Mapping S/P
...
LDPC Encoding
Source
F-to-T
QAM Mapping
F-to-T
(a) Transmitter.
...
T-to-F
T-to-F
MMSE-SIC and Bit Value Probability Estimation
LDPC Decoding
Sink
(b) Receiver.
Fig. 1: Block diagram of MIMO-OFDM-LDPC-DIR system.
Gray-labeling. While BPSK, QPSK, 16QAM and 64QAM are used in [11], only the later two are implemented in this paper for the interest of high data rate transmission. A set of QAM symbols together with pilot symbols are transformed into time domain symbols by the inverse fast Fourier transform (IFFT). 108 data and 6 pilot symbols as specified in [11] for 40 MHz bandwidth are used in this paper. Cyclic extension is added to provide a 400 ns guard interval which was found adequate to eliminate the effects of delayed multipath components in the indoor environment tested. The time domain signals are then transmitted to the air after appropriate frequency conversion. The IFFT, cyclic extension, and frequency conversion are grouped into a frequency to time domain conversion block, F-to-T, in Fig. 1. At the receiver, a MMSE-SIC detector produces streams of bit value probability estimates. The extrinsic bit value probabilities provided by the LDPC iterative decoder (the inner iteration), are used to form soft estimates of the transmitted symbols, which are then fed back in an outer (second) iterative loop to the MMSE-SIC detector. To arrive at the specific number of iterations we used, we ran simulations for 5, 10, 20, 40, and 80 inner iterations, and 1 to 6 outer iterations, and found that the best combination was 40 inner iterations, and 4 outer iterations. The process was terminated when the parity check operation detected no errors. III. MMSE-SIC WITH T RANSMITTER N OISE As noted in the introduction, our practical measurements indicate that transmitter noise can not be ignored in practice. In this section, we derive the MMSE-SIC detector in the presence of transmitter noise. In doing so, we make the simplifying assumption that the transmitter noise, when measured at the receiver, is uncorrelated. In this case, the MMSE-SIC has the same form as in [8], but with the noise variance term replaced by the apparent noise variance, as follows. Suppose Nt transmitters, Nr receivers, Nf OFDM data sub-carriers, and Ns OFDM data symbols are used in a MIMO-OFDM system, where Nr ≥ Nt . A consistent notation, (i, j, k, l), is used to denote the parameter at the ith transmitter,
jth receiver, kth OFDM data sub-carrier, and lth OFDM symbol, where i = 1, ..., Nt , j = 1, ..., Nr , k = 1, ..., Nf , and l = 1, ..., Ns . Here we assume a frequency domain flat fading channel model provided by an adequate cyclic extension [12]. The transmitted and received symbols are x(i, k, l) and r(j, k, l), respectively. The transmitted symbols are chosen from an M -QAM constellation set, s(m), m = 1, 2, ..., M , and var[x(i, k, l)]=1. AWGN at the transmitter is nt (i, k, l) with the mean of zero and the variance of ηt (i, k) while that at the receiver is nr (j, k, l) with the mean of zero and the variance of ηr (j, k). These noises are assumed to be uncorrelated. The noise generated by the non-linearity of the amplifier at an OFDM transmitter has been found to be approximated as a Gaussian noise in [13]. The channel transfer function is h(i, j, k), where the channel is assumed to be stationary for the duration of Ns OFDM symbols. The channel is normalized so that var[h(i, j, k)] = 1. The received signal vector is expressed as r(k, l) = H(k)x(k, l) + na (k, l),
(1)
where the channel transfer matrix H(k) is an Nr × Nt matrix whose jth row and ith column element is h(i, j, k). The apparent noise na (k, l) observed at the receiver is given by na (k, l) = H(k)nt (k, l) + nr (k, l).
(2)
The average apparent receiver SNR, S¯a , can be defined as Nt , (3) S¯a = ηa where Nt X ηa (j, k) = [|h(i, j, k)|2 · ηt (i, k)] + ηr (j, k). (4) i=1
Assuming that the estimate of the channel transfer matrix is correct, then the apparent noise can be estimated by transmitting known symbols as na (k, l) = r(k, l) − H(k)x(k, l).
(5)
For the packet transmission simulation and measurement described in the following section, (5) is used to estimate the variance of the apparent receiver noise. In the following derivation, we drop the index for k and l focusing on the MIMO detection at kth OFDM sub-carrier and lth OFDM symbol. The MMSE-SIC detector first forms soft estimates of the transmitted symbols by computing the symbol mean x ¯(i) based on the available a-priori information [8] M X x ¯(i) = s(m)PC (x(i) = s(m)). (6) m=1
The a-priori symbol value probabilities PC (x(i) = s(m)) are calculated from the extrinsic bit value probabilities PC (b(i, q) = c(m, q)) as PC (x(i) = s(m)) =
Q Y
(PC (b(i, q) = c(m, q))),
q=1
(7)
where b(i, q) is the value of the qth bit of the ith transmitted symbol x(i) and c(m, q) is the value of the qth bit of the mth chosen M -QAM constellation symbol s(m). For the initial MIMO detectioin, x ¯(i) = 0, ∀i, when using M -QAM constellation set. For the subsequent iterations, the extrinsic bit value probabilities are provided by the LDPC decoder. Interference-cancelled received symbol vector r0 (i), where the interference from the other antennas for the ith transmit antenna is canceled, is given by Nt X
r0 (i) = r −
x ¯(i0 )h(i0 ) Nt X
(x(i0 ) − x ¯(i0 ))h(i0 ) + na ,
(9)
where h(i0 ) is the i0 th column vector of H. A detection estimate x ˆ(i) of the transmitted symbol on the ith antenna is obtained by applying a linear filter w(i) to r0 (i) x ˆ(i) = wH (i)r(i) = (wH (i)h(i))x(i) +
H
1 16 1/2 240 6 27,648
0
0
(10) 0
H
(w (i)h(i ))(x(i ) − x ¯(i )) + w (i)na ,
i0 =1,i0 6=i
(11) where H represents the conjugate transpose operator. The filter w(i) is given by ¡ ¢−1 h(i), (12) w(i) = ηa INr + H∆(i)HH
2 16 3/4 360 9 41,472
3 64 2/3 480 12 55,296
4 64 3/4 540 13.5 66,208
5 64 5/6 600 15 69,120
is s(m), without using the extrinsic bit value probability for the qth bit of the ith transmitted symbol, is given as PC (x(i) = s(m), q) = 0.5
i0 =1,i0 6=i
Nt X
MCS mode index QAM number Coding rate Data rate (Mbit/s/Hz) Efficiency (bit/s/Hz) Bits per packet
(8)
i0 =1,i0 6=i
= x(i)h(i) +
TABLE I: MCS and associated parameters.
Q Y
PC (b(i, q 0 ) = c(m, q 0 )).
q 0 =1,q 0 6=q
(18) The updated symbol value probability PU combining the symbol value probabilities provided by the MMSE-SIC detection and the bit value probabilities from LDPC decoding is PU (x(i) = s(m), q) PD (x(i) = s(m))PC (x(i) = s(m), q) = PM . 0 0 m0 =1 PD (x(i) = s(m ))PC (x(i) = s(m ), q)
(19)
The updated bit value probability to be fed to the next iteration of LDPC decoding is M/2
PU (b(i, q) = 0) =
X
PCD (x(i) = s0 (m, q), q)
(20)
m=1
where s0 (m, q) is a set of symbols where the value of qth bit is 0, and PU (b(i, q) = 1) can be similarly derived. where the covariance matrix ∆(i) is ¢ ¡ 2 IV. M EASUREMENT AND S IMULATION R ESULTS ∆(i) = diag σx (1), . . . , σx2 (i − 1), 1, σx2 (i + 1), . . . , σx2 (Nt ) , (13) The actual packet transmission test was performed in the and σx2 (i) is the variance of the ith antenna symbol computed CSIRO ICT Centre in Marsfield, Sydney whose details are as given in [5]. Since the performance of MIMO-OFDM channels M can differ substantially with a small shift of antenna locations X σx2 (i) = |s(m) − x ¯(i)|2 PC (x(i) = s(m)). (14) (less than a half-wavelength in a typical multipath environm=1 ment) [14], it is important to test MIMO-OFDM transmission Following [8], we approximate x ˆ(i) by the output of an schemes at a large number of different locations within a equivalent AWGN channel with x ¯(i) = µ(i)x(i) + z(i), where small local area. For this reason, we use an antenna array positioner (AP) controlled by the PC to automatically position µ(i) = wH (i)h(i), (15) the receiving antenna array in different locations. The simuand z(i) is a zero-mean complex Gaussian variable with lation results given in Fig. 2 are based on the MIMO-OFDM channels measured on a grid of 80×80 = 6400 locations with variance η(i) given by 0.05 wavelength resolution. The actual packet transmission 2 η(i) = µ(i) − µ (i). (16) and simulation results given in Fig. 3 are based on a linearly aligned 80 locations with 0.05 wavelength resolution, due Given the detection estimates x ˆ(i), the symbol value proba- to time constraint on the actual packet transmission. Five bilities PD provided from the current MMSE-SIC detection is MIMO-OFDM-LDPC packets corresponding to the different approximated by modulation and coding schemes (MCS) shown in Table I are µ ¶ 2 sent to each of 80 receiving antenna array locations. To process 1 |ˆ x(i) − µ(i)s(m)| PD (x(i) = s(m)) ≈ exp − . 80×5=400 packets takes 5,762 seconds for LSD-SIR and πη(i) η(i) (17) 4,271 seconds for MMSE-SIC-DIR, respectively, on MATLAB For the qth bit of ith transmitted symbol, we derive the symbol running on an Intel Xeon PC at 3 GHz. value probabilities from the extrinsic bit value probabilities. Fig. 2 shows PEP simulation results for LSD-SIR and The symbol value probability that the ith transmitted symbol MMSE-SIC-DIR based on the 6400 measured MIMO-OFDM
0
PEP
10
16QAM 1/2 16QAM 3/4 64QAM 2/3 64QAM 3/4 64QAM 5/6 LSD-SIR MMSE-SIC-DIR
-1
10
-2
10
10
12
14
16
18
20
22 24 26 28 30 Average inherent receiver SNR (dB)
32
34
36
38
40
Fig. 2: Simulation results on LSD-SIR and MMSE-SIC-DIR packet error probability (PEP).
channels. As is commonly assumed, the simulations were performed assuming zero noise at the transmitter. The following observations can be made: • For coding rate 1/2, 16QAM, the MMSE-SIC-DIR performs better than LSD-SIR. • For higher coding rates the LSD-SIR shows the best performance. This is expected as the higher coding rate reduces the ability of LDPC decoding to improve bit value probabilities and thus reducing the ability of MMSE-SIC detection to cancel other-antenna-interference. Fig. 3 shows that the above observations do not always hold in practice. The figure shows PEP of MMSE-SIC-DIR and LSD-SIR as a function of average apparent receiver SNR, S¯a , based on actual packet transmission (denoted as ‘meas’) and simulation. The simulation curves are generated with varying ratios of transmitter noise variance in relation to receiver noise variance; from ηt =0 to ηt =ηr . The actual packet transmission results are indicated by the markers shown at 26 dB. Note that the irregularities seen in some of the PEP curves are attributed to the smaller number of MIMO-OFDM channels used in the simulation, i.e. 80 channels, as discussed above. Clearly, there is a discrepancy between the simulated curves which assume zero transmitter noise, and the measured values. For the MMSE-SIC-DIR we see that the measured PEP is significantly lower than that predicted under the assumption that all the apparent receiver noise is actually generated at the receiver (ηt =0). This can be explained by observing that curves for non-zero transmitter noise show significantly lower PEP, indicating that the MMSE-SIC-DIR is relatively unaffected by transmitter noise (compared with the effect of inherent receiver noise). Both Fig. 3(a) and 3(b) show that the MMSE-SICDIR curve corresponding to ηt =ηr /2 roughly matches with the measured point (shown as an open square, at 26 dB). In fact, this is similar to the case of a ZF-SIR, as reported in [5]. The measured results for LSD-SIR show higher PEP than predicted, irrespective of the amount of the transmitter noise. The deviation is considered to be due to the sensitivity of LSDSIR on the non-Gaussian characteristics of actual apparent
receiver noise affecting the accuracy of bit value probability estimates, as shown in [5]. Fig. 4 shows the variation of required SNR to achieve PEP=10−2 as a function of the transmitter noise and MCS. For comparison, we also show curves for the ZF-SIR. The following observations can be made. • The LSD-SIR results show little variation of required SNR as a function of transmitter noise for all MCS. Since the current method employed to calculate bit value probabilities from the LSD does not take into account the correlation of the noise, the performance of LSD-SIR is mainly determined by the variance of apparent noise. • The ZF-SIR results show an improvement of 4.3 dB in average from ηt =0 to ηt =ηr /2, and of 6.3 dB in average from ηt =0 to ηt =ηr independent of MCS. This can be understood by the fact that the performance of ZF-SIR mainly depends on the effective noise seen by the ZF detector, which is a combination of transmitter noise plus inherent receiver noise enhanced by the channel inverse. As the noise contribution is shifted from the inherent receiver noise to the transmitter noise, the performance of ZF detector improves irrespective of the MCS. • The MMSE-SIC-DIR results show a similar improvement as ZF-SIR at higher coding rates (2/3, 3/4, and 4/5), but a smaller improvement at a low coding rate (1/2). This is attributed to the fact that the performance of MMSE-SICDIR depends both on the amount of transmitter noise, in the same way as ZF-SIR, and on the FEC coding rate which affects the performance of other-antennainterference cancelation. V. C ONCLUSIONS A low complexity MIMO-OFDM-LDPC with a MMSESIC-DIR achieving 600 Mbit/s and 15 bit/s/Hz spectral efficiency has been successfully implemented on an actual radio hardware at 5.2 GHz. Zero error transmission was achieved at 90 % of indoor locations measured, with an average receiver SNR of 26 dB. The results set a benchmark for
0
0
10
10
PEP
PEP
LSD-SIR meas MMSE-SIC-DIR meas LSD-SIR sim MMSE-SIC-DIR sim ηt=0 -1
10
ηt=ηr/4
-1
10
ηt=ηr/2 ηt=ηr
-2
10
22
-2
24 26 28 30 Average apparent receiver SNR (dB)
32
10
22
(a) PEP (64QAM, rate 3/4 coding)
24 26 28 30 Average apparent receiver SNR (dB)
32
(b) PEP (64QAM, rate 5/6 coding)
Average apparent receiver SNR (dB) required at PEP=10 -2
Fig. 3: Packet error probability (PEP) based on actual packet transmission (meas) and simulation.
40
35
64QAM 4/5 64QAM 3/4 64QAM 2/3 16QAM 3/4 16QAM 1/2 ZF-SIR LSD-SIR MMSE-SIC-DIR
30
25
20
15
10 ηt=0
ηt= ηr/2
ηt= ηr
Fig. 4: Variation of required SNR to achieve PEP=10−2 as a function of transmitter noise.
the further improvement of a high spectral efficiency wireless communication with a reduced computational complexity. R EFERENCES [1] G. L. St¨uber, J. R. Barry, S. W. McLaughlin, Y. G. Li, M. A. Ingram, and T. G. Pratt, “Broadband MIMO-OFDM wireless communications,” Proceedings of the IEEE, vol. 92, no. 2, pp. 271–294, February 2004. [2] H. B¨olcskei, “MIMO-OFDM wireless systems: Basics, perspectives, and challenges,” IEEE Wireless Communications, vol. 13, no. 4, pp. 31–37, August 2006. [3] B. Lu, X. Wang, and K. R. Narayanan, “LDPC-based space-time coded OFDM systems over correlated fading channels: Performance analysis and receiver design,” IEEE Transactions on Communications, vol. 50, no. 1, pp. 74–88, January 2002.
[4] B. Lu, G. Yue, and X. Wang, “Performance analysis and design optimization of LDPC-coded MIMO OFDM systems,” IEEE Transactions on Information Theory, vol. 52, no. 2, pp. 348–361, February 2004. [5] H. Suzuki, T. V. A. Tran, I. B. Collings, G. Daniels, and M. Hedley, “Transmitter noise effect on the performance of a MIMO-OFDM hardware implementation achieving improved coverage,” IEEE Journal on Selected Areas in Communications, vol. 26, no. 8, pp. 867–876, August 2008. [6] M. R. McKay and I. B. Collings, “Capacity and performance of MIMO-BICM with zero-forcing receivers,” IEEE Transactions on Communications, vol. 53, no. 1, pp. 74–83, January 2005. [7] B. M. Hochwald and S. ten Brink, “Achieving near-capacity on a multiple-antenna channel,” IEEE Transactions on Communications, vol. 51, no. 3, pp. 389–399, March 2003. [8] A. Matache, C. Jones, and R. Wesel, “Reduced complexity MIMO detectors for LDPC coded systems,” In Proceedings of the IEEE MILCOM, vol. 2, pp. 1073–1079, October 2004. [9] E. Costa and S. Pupolin, “M-QAM-OFDM system performance in the presence of a nonlinear amplifier and phase noise,” IEEE Transactions on Communications, vol. 50, no. 3, pp. 462–472, March 2002. [10] B. Murray, H. Suzuki, and S. Reisenfield, “Optimal quantization of OFDM at digital IF,” IEEE TENCON, November 2008. [11] S. A. Mujtaba, “TGn Sync proposal technical specification,” IEEE 802.11-04/0889r7, July 2005. [12] M. R. G. Butler and I. B. Collings, “A zero-forcing approximate loglikelihood receiver for MIMO bit-interleaved coded modulation,” IEEE Communications Letters, vol. 8, no. 2, pp. 105–107, February 2004. [13] G. Santella and F. Mazzenga, “A hybrid analytical-simulation procedure for performance evaluation in M-QAM-OFDM schemes in presence of nonlinear distortions,” IEEE Transactions on Vehicular Technology, vol. 47, no. 1, pp. 142–151, February 1998. [14] H. Suzuki, T. V. A. Tran, and I. B. Collings, “Characteristics of MIMO-OFDM channels in indoor environments,” EURASIP Journal on Wireless Communications and Networking, vol. 2007, no. Article ID 19728, January 2007.
