BER Estimation of MIMO HSDPA : Chip Level Wiener Equalizer and Successive Interference Cancellation

Transcription

1 BER Estimation of MIMO HSDPA : Chip Level Wiener Equalizer and Successive Interference Cancellation Yongwoo Lee and Peter Voltz Department of Electrical and Computer Engineering Polytechnic Institute of New York University Melville, New York ylee09@students.poly.edu and voltz@rama.poly.edu Philip Pietraski and Rui Yang InterDigital Communications Melville, New York Philip.Pietraski@interdigital.com and Rui.Yang@interdigital.com Abstract In this paper we describe and simulate an accurate Bit Error Rate (BER) estimator for a chip level Wiener equalizer and combined equalizer/interference canceller for employment with the CDMA MIMO High Speed Downlink Packet Access (HSDPA) feature of the Third Generation Partnership Project (3GPP). In the MIMO system two data streams may be transmitted in the downlink to each user equipment (UE) using assigned multiple orthogonal CDMA codes of Spreading Factor 16. The two streams are mapped to the two transmit antennas via a weight matrix. Since the two streams use the same set of CDMA codes, it results in some direct interference between the two data streams at the receiver. The signal constellations from the two data streams interfere with each other and this complicates the BER estimation process. Treating this interference as AWGN is not sufficient for accurate BER estimation. The modulation type and order needs to be taken into account. Furthermore, the modulation order of the two data streams may also be different, e.g., QPSK may be used for one stream while 16QAM is used for the other. In this paper we describe the HSDPA transmitter and antenna weight matrix parameter calculations, as well as a chip level equalizer structure for which the BER is to be estimated. The transmit antenna weight matrix calculations are based on Channel State Information (CSI) and can be used, along with adaptive modulation and coding to optimize transmission. In the receiver a chip level matrix Wiener equalizer is first used to recover the two transmit antenna streams in a minimum mean square error sense. The equalizer is implemented using a generalized overlap-save filtering method using FFT processing. Following this, the transmitter processing is reversed to estimate the transmitted data. The BER estimator must take into account white noise at the receiver, the interference between codes from loss of orthogonality due to the multipath channel, self noise from different time shifts of the given user s code (also due to the multipath channel) and the crosstalk between the user s two data streams, which use the same CDMA codes. The BER estimator for both the basic Wiener filter receiver and the Wiener filter plus interference canceller will be analyzed and compared with simulated BER measurements. I. INTRODUCTION As a part of the Third Generation Partnership Project (3GPP), Release 5 contained the initial version of High Speed Downlink Packet Access (HSDPA) [1]. In order to keep up with increasing demands for higher data rate, Release 7 has been standardized as an evolution of HSDPA[]. Increased spectral efficiency can be explored as a benefit of Multiple Input Multiple Output (MIMO) and higher order modulation in the specification [3]. Closed loop Per Antenna Rate Control (PARC) [4] has been applied in the MIMO antenna structure. A Minimum Mean Square Error Chip Level Equalizer(MMSE CLE) approach has been discussed in order to recover orthogonality of user specific spreading codes [5]. An iterative algorithm has been suggested to simplify matrix inversion process of MMSE CLE [6]. In the present paper we use the Wiener filter [7], [8] for linear MMSE CLE and describe a Bit Error Rate (BER) estimator that can accurately incorporate noise and interferencects by utilizing system parameters, CSI and Wiener filter performance in various PARC scenarios. Successive Interference Cancellation (SIC) in MIMO HSDPA was proposed in [9], [10], [11] and interference management was introduced in [1]. In the following we extend the BER estimator to the interference cancellation case as well. The interfering transmit stream can be reconstructed based on hard decision from the Wiener filter and then its effect is cancelled from the other stream. This paper is organized as follows, Section II describes MIMO HSDPA system with Wiener filter at the receiver. In section III the BER estimation for the Wiener filter and Wiener filter with interference cancellation are discussed. In section IV simulation results are presented. Section V is a brief conclusion. II. SYSTEM DESCRIPTION Consider the transmitter diagram in Fig.(1) in which we assume two data streams are active. The data from each stream is represented by symbols from a QAM signal constellation (which may be different for the two streams, either QPSK or 16 QAM), and the symbols modulate N Walsh Hadamard spreading codes of spreading factor 16 (which are identical for the two streams). The resulting chip streams are then summed and multiplied by stream wights a 1 and a (assumed to be unity in this paper) to yield the chip-level sequences s 1 (n) and s (n), where n is the chip index, and then processed by a transit weighting matrix W, which chosed from among

2 Fig. 1. MIMO-HSDPA Transmitter TABLE I ITU VECHICULAR A CHANNEL Delay(nsec) Power(dB) the following four unitary matrix possibilities. { [ W e j 1 4 π e j 5 4 π, e j 5 4 π , e j 3 4 π e j 7 4 π e j 1 4 π ], [ 1 1 e j 7 4 π e j 3 4 π ] } The transmit antenna weight matrix choice is based on CSI and can be used, along with adaptive modulation and coding to optimize transmission. Finally the common pilot channel and other control/broadcast channels are added and the resulting streams are multiplied by the scrambling code to yield the transmitted chip-level sequences d 1 (n) and d (n). If we define the transmitted chip-level vector sequence by d(n) = [d 1 (n) d (n)] T, we can write d(n) = Ws(n) + z(n) (1) Where s(n) = [s 1 (n) s (n)] T and z(n) = [z 1 (n) z (n)] T. The receiver is shown in Fig.(). The channel frequency response matrix is H(e jω ), and the receiver noise vector is w(n) = [w 1 (n) w (n)] T. All block components shown are matrix LTI systems operating on chip-level timing. With r(n) = [r 1 (n) r (n)] T we have r(n) = H(n) d(n) + w(n) () The chip level equalizer G(e jω ) is a matrix Wiener filter designed to minimize the mean squared error E { ˆd(n) d(n) }, and is given by G(e jω ) = [ H (e jω )S 1 ww(e jω )H(e jω ) + S 1 dd (ejω ) ] 1 H (e jω )S 1 ww(e jω ) (3) Where S dd (e jω ) and S ww (e jω ) are the power spectral density matrices of d(n) and w(n). The equalizer is implemented using the overlap-save method with FFT computations. Next, the weight matrix from the transmitter is inverted and a diagonal scaling matrix R is applied to adjust the constellation of the desired signal to proper scale, as discussed below. Fig.. MIMO-HSDPA Wiener Filter Receiver Finally the data are recovered from s 1 (n) and s (n) by despreading with their individual codes. Note that thective spreading codes are actually the chip-by-chip products of the scrambling code with the original Walsh Hadamard codes c 1, c,..., c N. Since the scrambling code is common to all, the resulting spreading codes remain orthogonal. If we define Q(e jω ) = G(e jω )H(e jω ) and Q(e jω ) = W 1 Q(e jω )W we can express ŝ(n) in Fig.() as ŝ(n) = W 1 G(n) r(n) = Q(n) s(n) + W 1 Q(n) z(n) + W 1 G(n) w(n) (4) Consider the first term, which contains the desired signal components. We may expand the convolution as Q(n) s(n) = Q(0)s(n) + k 0 Q(k)s(n k) (5) Recall that s(n) contains the two chip streams, each of which consists of a number of the orthogonal spreading codes modulated by QPSK or 16 QAM symbols. The first term in equation(5) therefore contains codes which are mutually orthogonal. Note, however, that due to the Q(0) matrix, the two data streams become mixed together. The second term contains shifted versions of the codes and is considered a kind of self interference. Now let q11 q Q(0) = 1 (6) q 1 q And note that the first term in equation(5) may be written as q11 s Q(0)s(n) = 1 (n) + q 1 s (n) (7) q s (n) + q 1 s 1 (n) Which highlights two effects, namely that the signal streams s 1 (n) and s (n) are scaled, and that there is crosstalk between the two streams. The reason for the R matrix in the receiver is to re-scale the signal constellation of the data to be detected. A. Wiener filter receiver III. BER ESTIMATION The BER estimation consists of two steps. The first step is to separate out the noise and inter-cell interference terms which may bectively modeled as Gaussian random variables, vs. those that depend on the direct interference from the intra-cell

3 signal stream with the same spreading code as the desired signal. The second is to calculate average probability of symbol error based on interference-aware symbol constellation. After multiplying equation(4) by R we may write. where s(n) = A(n) s(n) + B(n) z(n) + C(n) w(n) (8) A(n) = R Q(n) (9) B(n) = RW 1 Q(n) (10) C(n) = RW 1 G(n) (11) We note that the first two terms in equation(8) contain spreading codes, and we separate out their unshifted versions as follows. where s(n) = A(0)s(n) + B(0)z(n) + (n) (1) (n) = A(n) s(n) + B(n) z(n) + C(n) w(n) A(0)s(n) B(0)z(n) (13) Note that since (n) contains only shifted versions of the spreading codes, it may be considered uncorrelated with the terms A(0)s(n) + B(0)z(n) in equation(1). From this point on we focus on the 1 st stream, the second stream being identical in development. The first stream s effective error, from equation(13) is 1 (n) = A 11 (n) s 1 (n) + A 1 (n) s (n) + B 11 (n) z 1 (n) + B 1 (n) z (n) Or, equivalently, + C 11 (n) w 1 (n) + C 1 (n) w (n) A 11 (0)s 1 (n) A 1 (0)s (n) B 11 (0)z 1 (n) B 1 (0)z (n) (14) 1 (n) = [A 11 (n) A 11 (0)δ(n)] s 1 (n) + [A 1 (n) A 1 (0)δ(n)] s (n) + [B 11 (n) B 11 (0)δ(n)] z 1 (n) + [B 1 (n) B 1 (0)δ(n)] z (n) + C 11 (n) w 1 (n) + C 1 (n) w (n) (15) Now, due to the assumed whiteness of s(n), z(n), w(n) and the well known expression for the output power spectrum of a linear system when given the input spectrum, we find the power spectrum of 1 (n) as S (1) ee (e jω ) = A11 (e jω ) A 11 (0) s + A1 (e jω ) A 1 (0) s + B11 (e jω ) B 11 (0) z + B1 (e jω ) B 1 (0) z + C11 (e jω ) w + C1 (e jω ) w (16) In which s is the power contained in each of the individual streams, s 1 (n) and s (n), and similarly defined are z and w for the components of z(n) and w(n). From equation(1) we have s 1 (n) = A 11 (0)s 1 (n) + A 1 (0)s (n) + B 11 (0)z 1 (n) + B 1 (0)z (n) + 1 (n) (17) At this point recall that s 1 (n) and s (n) contain the symbolmodulated spreading codes and that z 1 (n) and z (n) contain the pilot and other control/broadcast channels, which are orthogonal to the modulated spreading codes. Let δ (m1) i,1 denote the symbol from stream 1 on the i th spreading code. The superscript m 1 refers to the modulation order for this symbol. Similarly, δ (m) i, denotes the symbol from stream on the i th spreading code. To detect δ (m1) i,1 we de-spread s 1 (n) with spreading code c i (the product of the Walsh Hadamard code and the scrambling code), and since all codes together with the pilot channel are orthogonal, we may express the result as s 1 (k) c i (k) = A 11 (0) s N δm1 i,1 c i(k) c i (k) + A 1 (0) s N δm i, c i(k) c i (k) + 1 (k) c i (k) (18) Where N is the assumed number of codes used in each stream. This is easily re-written as s 1 (k) c i (k) = A 11 (0) SF + A 1 (0) SF s N δm1 i,1 s N δm i, + 1 (k) c i (k) (19) Where SF = 16. The constants A 11 (0) and A 1 (0) are known, given the CSI and the calculated Wiener filter G(e jω ), and we see from equation(19) that the third term may be well modeled as Gaussian noise, while the second term represents interference from the interfering stream s symbol, whose constellation is either QPSK or 16QAM. Since the power spectrum of 1 (k)is known from equation(16) we can readily calculate the variance of the third term in equation(19). The average symbol error rate can now be calculated as P sym avg (e) = δ (m ) i, P sym (e δ (m) i, )P (δ (m) i, ) (0) Fig.3 indicates the pattern of error that might arise if the

4 Fig. 4. Wiener filter IC receiver Fig. 3. Effective Symbol Energy Calculation 16 QAM constellation is used for both streams, The asterisks represent the 16 QAM points which form the desired stream and the circles represent the interfering stream s constellation. As the SNR increases the interfering stream s constellation shrinks with respect to that of the desired stream. In order to estimate BER from the Symbol Error Rate(SER) extensive simulations were run in order to provide a polynomial fit to the SER vs. BER curve. This polynomial is then used to convert the calculated SER to BER. B. Wiener Filter with Interference Cancellation at the receiver In this section we consider the use of the transmit weight matrix together with interference cancellation at the receiver to improve performance, and extend the BER estimator to that case. The idea is to choose the matrix W to maximize the total received power from the first stream, for example, and then to demodulate the first stream accurately and subsequently subtract its effect form the second stream in order to improve the performance of stream. This process is illustrated in Fig.4. In step 1 the transmitter chooses W so that the total received power from stream 1 at both receive antennas is maximized. Then the Wiener filter receiver described above is used to demodulate the data from both streams. These hard decisions are then used to re-generate the transmitter streams s 1 (n) and s (n), which are now denoted by s H 1 (n) and s H (n) to indicate that they contain the hard decisions rather than the original data symbols. In step thect of the stream 1 data is estimated by passing stream 1 only ( using s H 1 (n) and with stream zero d out ) through the same transmit processing and channel as before, up to the point just prior to the equalizer. Then, in step 3, the estimated effect of stream 1 is subtracted out of both streams and the resulting signals are passed through a modified receiver. The modified receiver takes into account that in this second pass processing there is effectively only one transmitted stream, namely stream, since thect of stream 1 has been subtracted out. Therefore, in calculating the new Wiener filter G IC1 (e jω ), the power spectral matrix of d(n) is changed. The BER estimation process for stream in the interference cancellation case now follows along the same lines as for the stand-alone Wiener filter, as described above. In the simulation results shown below, interference cancellation of stream from stream 1 is also carried out, although in all cases it is the stream 1 power that is maximized. It should be noted that, in the case of interference cancellation, there can be better weight matrix strategies than to maximize the power of one or the other stream. For the purposes of illustrating the BER estimator in this paper, however, we use that strategy. IV. SIMULATION RESULTS In this section we present simulated vs. calculated (estimated) BER results for several scenarios. In all the figures the parameter I or /I oc is a SNR parameter that represents the ratio of the transmit power spectral density at the transmit antenna to the power spectral density of an effective band limited white noise signal as measured at the receiver antenna. The four cases illustrated are: Case I - both streams are QPSK, Fig.(5), Case II - the first stream is QPSK and the second stream is 16 QAM, Fig.(6), Case III - the first stream is 16 QAM and the second stream is QPSK, Fig.(7), and case IV - both streams are 16 QAM, Fig.(8). All the simulations incorporate the ITU Vehicular-A (VA) channel, whose power delay profile is shown in Table I. For each graph fifty randomly picked snapshots of the fading channel model were used and resulting BER s averaged. For each snapshot, the W matrix was chosen to maximize the first stream power. In each figure the simulated and calculated (estimated) BER curves are shown for the Wiener filter alone, and for the Wiener filter/interference canceller. In case III it is interesting to note that even though the stream 1 power is maximized, stream has better performance because of the QPSK constellation on stream vs. the 16 QAM on stream 1. V. CONCLUSION An accurate BER estimator for a MIMO HSDPA system with antenna weight selction(transmit beamforming) and Wiener filter equalizer at the receiver, has been presented along with it s extension to the case with interference cancellation in the receiver. The BER estimator computes the BER based

5 Fig. 5. Simulated BER and Estimated BER in Case I Fig. 7. Simulated BER and Estimated BER in Case III Fig. 6. Simulated BER and Estimated BER in Case II Fig. 8. Simulated BER and Estimated BER in Case IV upon current channel state information. This estimator can be employed in aiding the choice of adaptive modulation and coding parameters in order to improve system throughput. REFERENCES [1] Technical specification group radio access network;physical layergeneral description(release5), 00. [] Technical specification group radio access network;physical layergeneral description(release7), 007. [3] H. Holma, A. Toskala, K. Ranta-aho, and J. Pirskanen, High-speed packet access evolution in 3gpp release 7 [topics in radio communications], Communications Magazine, IEEE, vol. 45, no. 1, pp. 9 35, dec [4] E. Tuomaala and M. Kuusela, Performance of spatial multiplexing in high speed downlink packet access system, 005, pp [5] L. Mailaender, Linear mimo equalization for cdma downlink signals with code reuse, IEEE Trans. Wireless Commun., vol. 4, no. 5, pp , Sep 005. [6] C. Mehlfuhrer and M. Rupp, A robust mmse equalizer for mimo enhanced hsdpa, oct. 006, pp [7] Norbert Wiener, Extrapolation, Interpolation, and Smoothing of Stationary Time Series, An MIT Press Classic, Cambridge, MA, [8] Athanasios Papoulis, Signal Analysis, McGRAW-HILL BOOK COM- PANY, New York, NY, [9] G.D. Golden, C.J. Foschini, R.A. Valenzuela, and P.W. Wolniansky, Detection algorithm and initial laboratory results using v-blast spacetime communication architecture, Electronics Letters, vol. 35, no. 1, pp , jan [10] A. Adjoudani, E.C. Beck, A.P. Burg, G.M. Djuknic, T.G. Gvoth, D. Haessig, S. Manji, M.A. Milbrodt, M. Rupp, D. Samardzija, A.B. Siegel, II Sizer, T., C. Tran, S. Walker, S.A. Wilkus, and P.W. Wolniansky, Prototype experience for mimo blast over third-generation wireless system, IEEE J. Sel. Areas Commun., vol. 1, no. 3, pp , apr [11] M. Melvasalo, P. Janis, and V. Koivunen, Mmse equalizer and chip level inter-antenna interference canceler for hsdpa mimo systems, May 006, vol. 4, pp [1] M. Wrulich, C. Mehlfuhrer, and M. Rupp, Interference aware mmse equalization for mimo txaa, Mar 008, pp