###### Abstract  
In this letter, we investigate the idea of interference spreading and its effect on bit error rate (BER) performance in a cognitive radio network (CRN). The interference spreading phenomenon is caused because of the random allocation of subcarriers in an orthogonal frequency division multiplexing (OFDM)-based CRN without any spectrum-sensing mechanism. The CRN assumed in this work is of underlay configuration, where the frequency bands are accessed concurrently by both primary users (PUs) and secondary users (SUs). With random allocation, subcarrier collisions occur among the carriers of primary users (PUs) and secondary users (SUs), leading to interference among subcarriers. This interference caused by subcarrier collisions spreads out across multiple subcarriers of PUs rather than on an individual PU, therefore avoiding high BER for an individual PU. Theoretical and simulated signal to interference and noise ratio (SINR) for collision and no-collision cases are validated for M-quadrature amplitude modulation (M-QAM) techniques. Similarly, theoretical BER performance expressions are found and compared for M-QAM modulation orders under Rayleigh fading channel conditions. The BER for different modulation orders of M-QAM are compared and the relationship of average BER with interference temperature is also explored further. bit error rate; interference spreading; random allocation; subcarrier collision; OFDM [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [  
Subcarrier collisions (i.e., high interference) can severely degrade the performance of both legacy and cognitive users. This work explores the concept of the random allocation of subcarriers in CRN that results in interference spreading among PUs. The basic intuition behind the idea of interference spreading is the random subcarrier allocation method, as illustrated in Figure 1, where the SUs randomly access the subcarriers of the primary network. From the figure, one can observe that because of this random subcarrier allocation, the SUs interference is uniformly distributed among the available subcarriers in the primary networks. As a consequence, there are subcarrier collisions and no-collisions for SU. The subcarrier set of each PU is assumed to be assigned by preserving the orthogonality among the sets of subcarriers for all PUs [7; 8; 9; 10]. Since SU does not have access to the information about the channel occupied by PUs (i.e., no spectrum sensing information is available), SU randomly accesses the subcarriers from the available subcarriers set in the primary network. Therefore, the subcarriers of a SU will collide with the subcarriers of the PUs with a certain probability. The main advantage of interference spreading is in the uniform distribution of the SUs interference among the subcarriers in the primary network. In other words, the SUs interference will not degrade a single PU but will be uniformly distributed among the all the different PUs subcarriers and free subcarriers. In addition, the interference spreading with random subcarrier allocation scheme is an energy-efficient method, as it does not require enabling a spectrum sensing mechanism. We also believe that after practical implementation and extensive field tests, the proposed interference spreading method could eventually be included in standards such as IEEE 802.22 wireless regional area network (WRAN) using white spaces in the television frequency spectrum [11]. The network configuration considered in this work is an underlay network configuration, where the subcarriers can be accessed concurrently for PUs and SUs. In this underlay network, the SUs adapt their transmit power to maintain the required interference temperature (IT) constraint. To maintain IT, SUs adapt their peak or average transmit power [7; 8; 12; 13; 14].