Lms Filters for Cellular Cdma Overlay
نویسنده
چکیده
environment and which incorporates the use This paper extends and of a Wiener filter was described in [l]. By complements previous research we have performed on the performance of nonadaptive narrowband suppression filters when used in cellular CDMA overlay situations. In this paper, an adaptive LMS filter is applied to cellular CDMA overlay situations in order to reject narrowband duction: In our recent paper [I], the cts of using Wiener filters (or nonrs) for rejecting narrowband interference in cellular CDMA overlay are replacing the Wiener filter with an adaptive LMS filter, the adaptive CDMA receiver is constituted. As in [2], the adaptive LMS filter is modelled as consisting of a Wiener filter and a misadjustment filter operating in parallel (see Fig. 1). It is assumed that in the cellular system, there are C cells, each of which contains K active users and one base station. Therefore, there are CK active users, for the entire cellular system. The cellular mobile channel between a mobile user and a base station is assumed to be multipath Rician investigated. However, in practice, since cellular CDMA users are mobile, there are Doppler frequency-shifts. Also, since the cellular channel is fading, the signal and interference statistics are rarely constant. Thus, the Wiener filter must be made adaptive. The work concentrates on the uplink, steady-state, performance of CDMA overlay systems with adaptive LMS filters, assuming convergence has been achieved. Performance analysis: A receiver operating in a cellular CDMA overlay fading channel, where there are L paths associated with each user. As shown in Fig. 1, the receiver consists of the following parts: a bandpass (BP) filter, an adaptive LMS filter, a DS-despreader and a hard decision device. The input signal r ( t ) to the adaptive filter is the sum of all CDMA signals, a narrowband BPSK representing the signal which is overlaid by the CDMA network, and band-limited AWGN. That is, , where y is a propagation exponent, and ck denotes the cell in which the kth user is located; the users are numbered such that c, = int[l+ ( k + l),/K], where int(x) stands for integer part of x. The function E (y , ck , k ) represents the yth power of the ratio of the distance of the kth user to its own base station (ckth cell) to the distance of the kth user to the first cell base station (ck = 1). For the first cell (cell of interest), we 0-7803-29163 11. 08. 1 assume E (y , c k , k)l = because of perfect adaptive power control. The parameter fo denotes the CDMA carrier frequency, bk ( t ) is the kth binary information sequence with bit duration r, , ak ( t ) is a random spreading sequence with chip duration T, and processing gain N ( N = T, /T , ) , and AH (0 I AH I 1) and $ H are gain and phase of the specular component of the lth path fiom the kth user, respectively. It is assumed that Ak, = A for all k and E, and is uniformly distributed in [0,27c], respectively. The random gain Pkl and phase wkl of the fading component of the Zth path of the kth user have a Rayleigh distribution with B[PL]=2pkl = 2 p for all k and 2, and a uniform distribution in [0,2n 1, respectively. The path delay, -z kl , is uniformly distributed in [O,T ,] and, to simplify some of the analysis to follow, we assume 1 . --z 2 T, for 1 f f . The gains, delays and phases of different paths and/or of different users are assumed to be statistically independent. Furthermore, J and 0 denote the received non-fading BPSK narrowband interference power and phase, respectively, and d(t) is the binary data sequence of the narrowband interference, J(t), having bit duration . q = 1 367 The parameter p is (defined as the ratio of the interference bandwidth to the spread bandwidth (i.e., p'= TIT,). Finally, n(t) is band-liimited AWGN with two-sided power spectral1 density N 0 / 2 and bandwidth 2K-I. Note that, for simplicity, while we have bandlimited the noise, we have assumed that the BPF passes the signal undistorted. The adaptive filter output i s given by r f ( t )= C ( a m +um)*(t-wT,), where ct m , m = -M,-, M, denotes the mth tap weight of the Wiener filter, and um,m = -M,.-.,M, denotes the mth steadystate tap-weight of the misadjustment filter. :Most often, via a central limit theorem, it is argued that the steady-state tap weights of the misadjustment filter are jointly Gaussian [3] for small enough adaptation step size. Hence, with the joint Gaussian assumption, the tap-weight covariance matrix completely defines the statistics of the misad5ustment filter. When it is assumed that the sum of all active CDMA signals is Gaussian, the steady state covariance matrix of the tap weight vector can be obtained (approximately) by solving the following equations: M
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