This work proposes a fully distributed improved weighted average consensus (IWAC and WAC-AE) technique applied to cooperative spectrum sensing problem in cognitive radio systems. This method allows the secondary users cooperate based on only local information exchange without a fusion centre (FC). We have compared four rules of average consensus (AC) algorithms. The first rule is the simple AC without weights. The AC rule presents {performance comparable to the traditional cooperative spectrum sensing} (CSS) techniques, such as the equal gain combining (EGC) rule, which is a soft combining centralised method. Another technique is the weighted average consensus (WAC) rule using the weights based on the SUs channel condition. This technique results in a performance similar to the maximum ratio combining (MRC) with soft combining (centralised CSS). Two new AC rules are analysed, namely weighted average consensus accuracy exchange (WAC-AE), and improved weighted average consensus (IWAC); the former relates the weights to the channel conditions of the SUs neighbours, while the latter combines the conditions of WAC and WAC-AE in the same rule. All methods are compared each other and with the hard combining centralised CSS. The WAC-AE results in a similar performance of WAC technique but with fast convergence, while the IWAC can deliver suitable performance with small complexity increment{. Moreover, IWAC method results in a similar convergence rate than the WAC-AE method but slightly higher than the AC and WAC methods}. Hence, the computational complexity of IWAC, WAC-AE, and WAC are proven to be very similar. The analyses are based on the numerical Monte-Carlo simulations (MCS), while algorithm's convergence is evaluated for both fixed and dynamic-mobile communication scenarios, and under AWGN and Rayleigh channels.