EURASIP Journal on Applied Signal Processing 2002:8, 771–786 c  2002 Hindawi Publishing Corporation Reduced-Rank Chip-Level MMSE Equalization for the 3G CDMA Forward Link with Code-Multiplexed Pilot Samina Chowdhury School of Electrical Engineering, Purdue University, West Lafayette, IN 47907-1285, USA Email: samina@ecn.purdue.edu Michael D. Zoltowski School of Electrical Engineering, Purdue University, West Lafayette, IN 47907-1285, USA Email: mikedz@ecn.purdue.edu J. Scott Goldstein SAIC 4001 N. Fairfax Drive, Suite 400, Arlington, VA 22203, USA Email: sgoldstein@trg1.saic.com Received 31 July 2001 and in revised form 15 March 2002 This paper deals with synchronous direct-sequence code-division multiple access (CDMA) transmission using orthogonal channel codes in frequency selective multipath, motivated by the forward link in 3G CDMA systems. The chip-level minimum mean square error (MMSE) estimate of the (multiuser) synchronous sum signal transmitted by the base, followed by a correlate and sum, has been shown to perform very well in saturated systems compared to a Rake receiver. In this paper, we present the reduced-rank, chip-level MMSE estimation based on the multistage nested Wiener filter (MSNWF). We show that, for the case of a known channel, only a small number of stages of the MSNWF is needed to achieve near full-rank MSE performance over a practical single-to-noise ratio (SNR) range. This holds true even for an edge-of-cell scenario, where two base stations are contributing near equal-power signals, as well as for the single base station case. We then utilize the code-multiplexed pilot channel to train the MSNWF coefficients and show that adaptive MSNWF operating in a very low rank subspace performs slightly better than full-rank recursive least square (RLS) and significantly better than least mean square (LMS). An important advantage of the MSNWF is that it can be implemented in a lattice structure, which involves significantly less computation than RLS. We also present structured MMSE equalizers that exploit the estimate of the multipath arrival times and the underlying channel structure to project the data vector onto a much lower dimensional subspace. Specifically, due to the sparseness of high-speed CDMA multipath channels, the channel vector lies in the subspace spanned by a small number of columns of the pulse shaping filter convolution matrix. We demonstrate that the performance of these structured low-rank equalizers is much superior to unstructured equalizers in terms of convergence speed and error rates. Keywords and phrases: CDMA forward link, minimum mean square error equalization, pilot code. 1. INTRODUCTION Mobile units in current code-division multiple access (CDMA) cellular systems use a Rake receiver, which is a maximal-ratio combiner and can be interpreted as a bank of filters matched to the channel that combine the energy from multiple paths [1]. The Rake filter is the optimum (maximum likelihood) demodulator when there is no in- terference from other users [1]. In IS-95 and the proposed third-generation (3G) systems, orthogonal Walsh-Hadamard codes are used to spread the different users’ data symbols on the forward link. At the downlink receiver, after removing the coherent carrier, the signal is multiplied by the synchronized base station long code and then decorrelated with the desired user’s spreading code. In a flat fading environment, this will ensure that any interference due to other users in the same cell is eliminated. However, in urban wireless systems, the fading is of- ten not flat and the orthogonality of the underlying Walsh- Hadamard codes is destroyed at the receiver, resulting in multiple-access interference (MAI) at the receiver. Further- more, if the multipath delay spread is a significant portion of the symbol period, there will be considerable intersym- bol interference (ISI) in addition to the MAI. There are also major interference issues if the mobile unit is near the edge of a cell and is receiving significant out-of-cell transmission,