Design and analysis of the UW-OFDM signal

Abstract

Unique word (UW-) OFDM is a novel multicarrier system that is shown to be suitable for cognitive radio systems. To construct the UW-OFDM signal, a code generation matrix is required to introduce redundancy in the frequency domain, implying that the code generation matrix must satisfy a number of conditions. In this paper, we use an algebraic construction method to separate the conditions imposed by the signal shape from the code design. The degrees of freedom resulting from this construction method are used to optimize different performance measures (i.e., the minimum Euclidean distance and the power) at the transmitter or at the receiver side. Based on the algebraic decomposition, a composite channel can be defined. Irrespective of whether the optimization is done at the transmitter or the receiver, we shown in the paper that always the strongest modes of this composite channel must be excited.Index Terms-multicarrier communication, error rate, Euclidean distance, tight frame UW-OFDMIn multicarrier communication systems, typically a guard interval is used to combat the effect of intersymbol interference. In traditional multicarrier systems, this guard interval is added on top of the signal containing the data, resulting in a signal with extended symbol duration. Unlike these standard multicarrier systems, unique word (UW-) OFDM counteracts intersymbol interference without the necessity to extend the DFT block with a guard interval. In UW-OFDM, this guard interval is part of the DFT interval, i.e., the last N u samples of the DFT interval are reserved for the unique word, which is a sequence of known samples. In [1], it is shown that UW-OFDM outperforms cyclic prefix (CP-) OFDM with respect to the bit error rate in fading channels. This is confirmed in [2] where a theoretical analysis of the error rate performance shows that UW-OFDM is always able to achieve full diversity, whereas in CP-OFDM only a diversity one is obtained unless precoding is used. Further, it is shown in [3] that UW-OFDM hasThe author gratefully acknowledges the financial support from the Flemish Fund for Scientific Research (FWO). This research has been funded by the Interuniversity Attraction Poles Programme initiated by the Belgian Science Policy Office. much lower out-of-band radiation compared to CP-OFDM. Hence, UW-OFDM is an excellent candidate for cognitive radio systems.To construct the UW-OFDM signal, we use the two-step approach. First, we generate the time-domain sequence corresponding to the data symbols, resulting in a block of N u zeroes at the end of the DFT interval. In this block of zeroes, we add the unique word symbols during the second step. The construction of the data contribution containing a block of zeroes in the time domain requires the presence of redundancy in the frequency domain. Consequently, assuming the DFT size equals N , a maximum of N − N u data symbols can be transmitted per DFT block.The UW-OFDM signal is generated as follows. First, the N d ≤ N − N u data symbols a d are fed to the N m × N d code...

Theoretical Performance Evaluation and Optimization of UW-OFDM

“…When the number of non-zero eigenvalues exceeds the number N d of data symbols, many combinations to select the eigenvalues exist. Similarly as for the case of the optimization of the minimum Euclidean distance at the transmitter, the degree of freedom can be used to optimize other performance measures, e.g., in [22], this freedom is used to minimize the transmitted energy.…”

“…In this construction, we still have some degree of freedom, as we can select in Case 1 any matrix W that forms a tight frame and in Case 2 out of the set of non-zero eigenvalues of the matrix U H B HHHH BU, a subset of N d eigenvalues. In the following, we select in Case 2 W so that the transmit energy is minimized [22]. Note that Case 1 and Case 2 correspond to the normalization of the transmitted energy E T = N d E s and received energy E R = N d E s , respectively (see (13)).…”