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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.