Channel estimation in the presence of transmitter and receiver I/Q mismatches for OFDM systems

In this paper, we study the problem of channel estimation in the presence of the transmitter and receiver inphase and quadrature-phase (I/Q) mismatches for orthogonality frequency division multiplexing (OFDM) systems. A new concept called channel residual energy (CRE) is introduced. We show that by minimizing CRE, we can jointly estimate the transmitter and receiver I/Q mismatches without knowing the channel information. The optimal solution is given in closed form. Once we have the I/Q parameters, an estimate of the channel response can be obtained by simple substitution. The proposed method needs only one OFDM block for training and the training data can be arbitrary. Simulation results show that the proposed method can achieve a good performance.     

Optimal ISI-free DMT transceivers for distorted channels withcolored noise

The design of optimal DMT transceivers for distorted channel with colored noise has been of great interest. Of particular interest is the class of block based DMT, where the transmitter and the receiver consist of constant matrices. Two types of block- based DMT transceivers are considered: the DMT system with zero padding (ZP-DMT) and the DMT system with general prefix (GP-DMT). We derive the bit allocation formula. For a given channel and channel noise spectrum, we design the ISI-free optimal transceiver that minimizes the transmission power for a given transmission rate and probability of error. For both ZP-DMT and GP-DMT systems, the optimal ISI-free transceiver can be given in closed from. We will see that for both classes, the optimal transceiver has an orthogonal transmitter. Simulation shows that the optimal DMT system can achieve the same transmission rate and the same probability of error with a much lower transmission power compared with other existing DMT systems     

Prediction-based lower triangular transform

A new nonunitary transform called the prediction-based lower triangular transform (PLT) is introduced for signal compression. The new transform has the same decorrelation property as the Kahurnen-Loeve transform (KLT), but its implementational cost is less than one half of KLT. Compared with the KLT, the design cost of an M×M PLT is much lower and is only of the order of O(M²). Moreover, the PLT can be factorized into simple building blocks. Using two different factorizations, we introduce two minimum noise structures that have roughly the same complexity as the direct implementation of PLT. These minimum noise structures have the following properties: (1) its noise gain is unity even though the transform is nonunitary; (2) perfect reconstruction is structurally guaranteed; (3) it can be used for both lossy/lossless compression. We show that the coding gain of PLT implemented using the minimum noise structure is the same as that of KLT. Furthermore, universal transform coders using PLT are derived. For AR(1) process, the M×M PLT has a closed form and needs only (M-1) multiplications and additions     

BER minimized OFDM systems with channel independent precoders

We consider the minimization of uncoded bit error rate (BER) for the orthogonal frequency division multiplexing (OFDM) system with an orthogonal precoder. We analyze the BER performance of precoded OFDM systems with zero forcing and minimum mean squared error (MMSE) receivers. In the case of MMSE receivers, we show that for quadrature phase shift keying (QPSK), there exists a class of optimal precoders that are channel independent. Examples of this class include the discrete Fourier transform (DFT) matrix and the Hadamard matrix. When the precoder is the DFT matrix, the resulting optimal transceiver becomes the single carrier system with cyclic prefix (SC-CP) system. We also show that the worst solution corresponds to the conventional OFDM system; the conventional OFDM system has the largest BER. In the case of zero forcing receivers, the design of optimal transceiver depends on the signal-to-noise ratio (SNR). For higher SNR, solutions of optimal precoders are the same as those of MMSE receivers.     

OFDM transmitters: analog representation and DFT-based implementation

The implementation of orthogonal frequency division multiplexing (OFDM) transmitters typically consists of a discrete DFT matrix and a digital-to-analog (DAC) converter. Many existing results on the analysis of OFDM systems, e.g., spectral roll-off, are based on a convenient analog representation. We show that the analog representation and the DFT-based OFDM transmitters are equivalent only in special cases. Using the analog system to analyze the DFT-based OFDM system may not be valid if there is no equivalent analog representation.     

Lapped unimodular transform and its factorization

Two types of lapped transforms have been studied in detail in the literature, namely, the lapped orthogonal transform (LOT) and its extension, the biorthogonal lapped transform (BOLT). In this paper, we will study the lapped unimodular transform (LUT). All three transforms are first-order matrices with finite impulse response (FIR) inverses. We will show that like LOT and BOLT, all LUTs can be factorized into degree-one unimodular matrices. The factorization is both minimal and complete. We will also show that all first-order systems with FIR inverses can be minimally factorized as a cascade of degree-one LOT, BOLT, and LUT building blocks. Two examples will be given to demonstrate that despite having a very small system delay, the LUTs have a satisfactory performance in comparison with LOT and BOLT.     

Factorability of lossless time-varying filters and filter banks

We study the factorability of linear time-varying (LTV) lossless filters and filter banks. We give a complete characterization of all, degree-one lossless LTV systems and show that all degree-one lossless systems can be decomposed into a time-dependent unitary matrix followed by a lossless dyadic-based LTV system. The lossless dyadic-based system has several properties that make it useful in the factorization of lossless LTV systems. The traditional lapped orthogonal transform (LOT) is also generalized to the LTV case. We identify two classes of TVLOTs, namely, the invertible inverse lossless (IIL) and noninvertible inverse lossless (NIL) TVLOTs. The minimum number of delays required to implement a TVLOT is shown to be a nondecreasing function of time, and it is a constant if and only if the TVLOT is IIL. We also show that all IIL TVLOTs can be factorized uniquely into the proposed degree-one lossless building block. The factorization is minimal in terms of the delay elements. For NIL TVLOTs, there are factorable and unfactorable examples. Both necessary and sufficient conditions for the factorability of lossless LTV systems are given. We also introduce the concept of strong eternal reachability (SER) and strong eternal observability (SEO) of LTV systems. The SER and SEO of an implementation of LTV systems imply the minimality of the structure. Using these concepts, we are able to show that the cascade structure for a factorable IIL LTV system is minimal. That implies that if a IIL LTV system is factorable in terms of the lossless dyadic-based building blocks, the factorization is minimal in terms of delays as well as the number of building blocks. We also prove the BIBO stability of the LTV normalized IIR lattice     

Paraunitary filter banks over finite fields

In real and complex fields, unitary and paraunitary (PU) matrices have found many applications in signal processing. There has been interest in extending these ideas to the case of finite fields. We study the theory of PU filter banks (FBs) in GF(q) with q prime. Various properties of unitary and PU matrices in finite fields are studied. In particular, a number of factorization theorems are given. We show that (i) all unitary matrices in GF(q) are factorizable in terms of Householder-like matrices and permutation matrices, and (ii) the class of first-order PU matrices (the lapped orthogonal transform in finite fields) can always be expressed as a product of degree-one or degree-two building blocks. If q>2, we do not need degree-two building blocks. While many properties of PU matrices in finite fields are similar to those of PU matrices in complex field, there are a number of differences. For example, unlike the conventional PU systems, in finite fields, there are PU systems that are unfactorizable in terms of smaller building blocks. In fact, in the special case of 2×2 systems, all PU matrices that are factorizable in terms of degree-one building blocks are diagonal matrices. We derive results for both the cases of GF(2) and GF(Q) with q>2. Even though they share some similarities, there are many differences between these two cases     

MINLAB: minimum noise structure for ladder-based biorthogonalfilter banks

We introduce a minimum noise structure for ladder-based biorthogonal (MINLAB) filter bank. The minimum noise structure ensures that the quantization error has a unity noise gain, even though the filter bank is biorthogonal. The coder has a very low design and implementation cost. The perfect reconstruction property is structurally preserved. Optimal bit allocation and coding gain formulas are derived. We show that the coding gain of the optimal MINLAB coder is always greater than or equal to unity. For both AR(1) process and MA(1) process, the MINLAB coder with two taps has a higher coding gain than the optimal orthonormal coder with an infinite number of taps. In addition to its superior decorrelation ability, it has many other desired features that make it a potentially valuable and attractive alternative to the orthonormal coder, especially for a high-fidelity compression     

Minimum redundancy for ISI free FIR filterbank transceivers

There has been great interest in the design of filterbank transceivers. Usually, with proper time domain equalization, the channel is modeled as an FIR filter. It is known that for FIR channels, the introduction of certain redundancy allows the receiver to cancel intersymbol interference (ISI) completely, and channel equalization is performed implicitly using FIR transceivers. This scheme allows us to trade bandwidth for ISI cancellation. In this paper, we derive the minimum redundancy required for the existence of FIR transceivers for a given channel. We see that the minimum redundancy is directly related to the zeros of the channel and to the Smith form of an appropriately defined channel matrix