Heidi Steendam and Marc Moeneclaey Uplink and Downlink Mc-ds-cdma Synchronization Sensitivity

In this paper, we consider the effect of synchronization errors on the performance of the multicarrier direct-sequence code-division multiple access (MC-DS-CDMA) system and compare the results for downlink and uplink transmission. To evaluate the effect of small synchronization errors on the BER performance of the MC-DS-CDMA system, we derive simple analytical expressions for the BER degradation that are based upon truncated Taylor series expansions. We point out that a constant carrier phase offset or a constant timing offset do not give rise to performance degradation, for neither uplink nor downlink MC-DS-CDMA. The MC-DS-CDMA system is strongly degraded in the presence of a carrier frequency offset or a clock frequency offset. This degradation is proportional to the squares of the frequency offset and the number of carriers. Further, the degradation in the uplink is a factor Ns (Ns is the spreading factor) larger than in the downlink, because the former suffers from a higher level of multi-user interference. The degradation caused by carrier phase jitter or timing jitter is the same in the uplink and the downlink, when the spectrum of the jitter is the same for all users. Further, the degradation is independent of the spectral contents of the jitter, the spreading factor and the number of carriers, but only depends on the jitter variance. 1. THE MC-DS-CDMA SYSTEM The MC-DS-CDMA system is a combination of the MC transmission technique and the CDMA multiple access (CDMA) technique. In MC-DS-CDMA, the serialto-parallel converted data stream is multiplied with the spreading sequence and then the chips belonging to the same symbol modulate the same carrier: the spreading is done in the time domain. MC-DS-CDMA has been proposed for mobile communications [1]-[3]. Without loss of generality, we use the terminology for the uplink. In MC-DSCDMA, the symbol sequence to be transmitted at rate Rs is split into Nc lower rate symbol sequences {ai,k, }, where ai,k, denotes the ith data symbol transmitted by user on the kth carrier of the multicarrier system; k belongs to a set Ic of Nc carrier indices. The symbol ai,k, is multiplied with a spreading sequence {ci,n, |n=0,...,Ns-1} with spreading factor Ns. Each user is assigned a unique orthogonal spreading sequence. The resulting Ns components of the spread data symbol ai,k, , i.e. {ai,k, ci,n, | n=0,...,Ns-1} are then serially transmitted on the kth carrier of the multicarrier system. Hence, the spreading is accomplished in the time domain. To modulate the spread data symbols on the orthogonal carriers, an NF-point inverse fast Fourier transform (inverse FFT) is used. To avoid that the multipath channel causes interference between the data symbols at the receiver, each FFT block is cyclically extended with a prefix of Np samples. The resulting sequence {si,n,m, } is fed to a square root raised cosine filter P(f ) with roll off and unit-energy impulse response HEIDI STEENDAM AND MARC MOENECLAEY p(t) at a nominal rate 1/T=(NF+Np)NsRs/Nc, resulting in the signal s (t). We assume the carriers inside the roll off area are not modulated. Hence, of the NF available carriers, only Nc NF carriers are actually used. Without loss of generality, we focus on the detection of the data symbols transmitted by the reference user ( =0). The transmitted signal s (t) reaches the receiver through a slowly multipath fading channel. Assuming the path gains are constant over the duration Nc/Rs of Ns FFT blocks, the corresponding channel transfer function experienced by the ith symbol from user can be denoted by Hch (f,i). Restricting our attention to widesense stationary uncorrelated scattering (WSSUS), the second-order moment E[|Hch (f,i)|] is independent of both f and i. The output of the channel is disturbed by additive white Gaussian noise (AWGN) w(t) with uncorrelated real and imaginary parts, each having a power spectral density of N0/2. Further, the signal of user is affected by a carrier phase error (t). The sum of the different user signals is applied to the receiver filter, which is matched to the transmit filter, and sampled at nominal rate 1/T. The contribution of user is disturbed by a timing offset i,n,m, T. In the uplink, where the contribution of each user is generated with a different transmit clock, upconverted by a different carrier oscillator and transmitted over a different multipath channel, the carrier phase error (t) and timing offset i,n,m, T generally depend on the user index . In the downlink, on the other hand, the base station synchronizes the different user signals, and upconverts the sum of the different user signals with the same carrier oscillator. Further, as the different user signals reach the receiver of the reference user through the same multipath channel, the carrier phase error (t) and timing offset i,n,mT are the same for all users. In the following, we assume that the transmitter (uplink) or receiver (downlink) of each user adapts its transmit clock phase such that NF samples can be found outside the cyclic prefix that are free from interference from neighbouring FFT blocks. The resulting NF samples are kept for further processing. As the removal of the cyclic prefix eliminates the interference between neighbouring blocks, the data symbols ai,k, transmitted during symbol interval i are not affected by intersymbol interference from other symbol intervals. Hence, we omit the symbol index i in the sequel. The NF selected samples are applied to an NF-point FFT, followed by one-tap equalizers gn,k that scale and rotate the FFT outputs. We denote by gn,k the coefficient of the equalizer, operating on the kth FFT output during the nth FFT block. We consider the case of the maximum ratio combiner (MRC). Each equalizer output is multiplied with the corresponding chip of the reference user's spreading sequence, and the Ns consecutive values are summed to yield the samples zk at the input of the decision device. Based on the sample zk, a decision is made about the data symbol ak,0. To measure the performance, we use the signal to interference and noise ratio (SINR), defined by SINRk( , )= PU,k/(PN,k+ PI,k)), where =NF/(NF+Np) and PU,k, PI,k and PN,k are the powers of the average useful component, the interference and the noise, respectively. Note that in general these powers depend on the carrier index k. In the absence of synchronization errors, the SINR reduces to UPLINK AND DOWNLINK MC-DS-CDMA SYNCHRONIZATION SENSITIVITY SINRk(0)= |Hk,0|Es,k,0/N0, where Es,k, is the symbol energy transmitted on carrier k by user , Hk, =H (mod(k;NF)/ (NFT))/T, mod(x;NF) is the modulo-NF reduction of x, yielding a result in the interval [-NF/2,NF/2], and H (f )=|P(f )| Hch, (f ). The quantity SINRk still depends on the particular realization of the transfer functions Hk, (k Ic, =0,...,Nu-1) and the spreading sequences during the considered sequence of Ns FFT blocks. Hence, a more convenient performance indicator is k SINR , which is obtained by replacing PX,k (X=U, I, N) by their averages k , X P over the fading characteristics and over all possible assignments of spreading sequences to the users. Because of the WSSUS assumption, E[|Hk, | ] does not depend on the carrier index. We assume perfect power control: Es=Es,k, E[|Hk, | ]. In this case, k SINR (0) reduces to Es/N0, which is independent of the carrier index k. The degradation (in dB) caused by the synchronization errors is defined by Degk=( SINR (0)/ k SINR ( , )). 2. CARRIER PHASE ERRORS In this section, we investigate the sensitivity of MC-DS-CDMA to carrier phase errors in the absence of timing errors ( n,m, =0). 2.1 Carrier Frequency Offset In the case of small carrier frequency offsets F ( =0,...,Nu-1), the carrier phase error linearly increases in time [4]: (t)= (0)+2 F t. For small carrier frequency offsets (|NF F T|<<1), the useful power and noise power can be approximated by k , U P =Es and k , N P , n c~ =N0. The contribution of user to the interference power is proportional to R , which is the correlation between the sequences { c~ } and